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A PRACTICAL ARITHMETIC STEVENS
M BUTLER
RUI C
No
At
(flarneU IniaerBttH 3tliata,
N. g.
DATE DUE MAY 20
A PRACTICAL ARITHMETIC
The tine
original of
tliis
book
is in
Cornell University Library.
There are no known copyright
restrictions in
the United States on the use of the
text.
http://www.archive.org/details/cu31924000431621
PEACTICAL ARITHMETIC BY F. L.
STEVENS
PROFESSOR IN THE NORTH CAROLINA COLLEGE OF AGRICULTURE AND MECHANIC ARTS, AUTHOR OP " AGRICULTURE FOR beginners"
TAIT BUTLER president AMERICAN ASSOCIATION OF FARMERS' INSTITUTE
MRS.
F. L.
WORKERS
STEVENS
FORMERLY TRAINING TEACHER, COLUMBUS, OHIO NORMAL SCHOOL , \
r}
f
NEW YORK CHARLES SCRIBNER'S SONS 1910
meTH
COPYRIGHT, 1909, BY
CHARLES SCRIBNER's SONS
c
/'
:
-v.*
^^I^\\\\\^,/
li'
V
PEEFACE The
primary object of arithmetic
is
student to acquire skill in computation.
to
enable
tlie
In addition to
the attainment of this essential end, great benefit
is
de-
rived from the exercise of the reasoning powers and
While the first of these must ever remain the fundamental reason for the study of arithmetic, and the second will always be held in high esteem, there is a third major object which the teaching of arithmetic may accomplish, one which is usutheir consequent development.
entirely ignored in the preparation of an namely, the incidental teaching of valuable facts by basing the problems of the book upon the problems of real life. In the preparation of this book, it has been the aim ally almost
arithmetic
;
of the authors to secure the
maximum
results in these
three functions of arithmetic teaching. It is chiefly in the careful consideration which has been given to the subject-matter of the problems, and to the inferences that will unconsciously and unavoidably remain
in the
mind
of the pupil, that this
book
differs
from other
arithmetics.
computation comes from learning a few methods, Methods have followed by extensive drill or practice. been carefully and clearly presented in this book, and an abundance of drill problems provided. The development of the reasoning powers comes from Skill in
work with problems requiring careful analysis before proceeding to the more mechanical solution. A large number
PREFACE
VI
of carefully graded thought problems, necessitating accurate analysis, serves this end.
The
special value of this book, however,
depends upon
the fact that a large proportion of its problems bring out clearly in their statement or in their solution important
upon the practical activities of life. Since the one fundamental industry of America, especial attention has been given to this subject, and a large proportion of the thought problems are based upon agriculture, without, however, in any way leading to facts bearing
agriculture
is
neglect of other industries.
The problems relating to agriculture are based upon wholly reliable information, uf)on the most recent findings of the State Experiment Stations and of the National
Department of Agriculture. The facts used in these problems and the legitimate inferences which may be djiawn from them are trustworthy. In solving these problems, the pupil will unconsciously absorb and retain
many
valuable facts and principles relating to agricul-
tural practice, such, for example, as selection, purity
and
the value of seed
vitality, judicious use of fertilizers,
balancing of animal rations, crop rotation, prevention or treatment for plant diseases, conservation of soil moisture, preservation of
soil fertility,
prevention of insect injury,
economy in methods of harvesting, proper dairy methods, the improvement of the herd by selection, poultry culture, value of good roads, etc.
A
feature of value
is
the outline problems to be com-
by the pupils with data from their homes. Teachers, parents and pupils are invited to write to the authors of this book for information upon any agricultural pleted
points involved.
THE AUTHORS. Raleigh, N.C, November, 1908.
CONTENTS FAQS
Notation and Numeration The Arabic System The Roman System United States Money
1 1
9 11
Addition
13
Addition of United States
Money
19
Subtraction
.
Subtraction of United States
Money
Multiplication Multiplication of United States
Division
.
.
Money
36
....
52
61
64
Money
68 72
Cancellation
Review Problems
74
Divisors and Multiples
86
Tests of Divisibility, Greatest
mon
41
^ 57
r
Short Division Long Division Division of United States
29
Common
Divisor, Least
Com-
Multiple.
Decimal Fractions
92
Notation and Numeration
92
Addition
95
Subtraction
97
Multiplication
99 103
Division
Review Problems
106
Common Fractions
113 120
Addition vii
CONTENTS
viii
PAGE
Subtraction
122
Multiplication
125 129
Division
Review Problems
138
Accounts and Bills
147
Denominate Numbers
150
Units
of
Length, Reduction, Metric Units of Measure,
Representation of Magnitudes, Surface Measure (English
and Metric), Surveyor's Measures, Measures of Volume (English and Metric), Measures of Weight (English and Metric), Measures of Time, Angle Measure, Counting, Addition and Subtraction, Multiplication, Division.
Review Problems
179
Measurements
186
Practical Measurements
198
Plastering, Painting, Paving, Carpeting, Papering,
and Brickwork,
Wood
Masonry
Measure, Board Measure,
Round
Logs, Temperature, Longitude and Time, Standard Time.
Review Problems
216
Percentage
227
and Loss Commission Commercial Discount Profit
256
Insurance
260 263 265
Taxes
Interest
.......... .........
Stocks and Bonds
Bank Discount Partial
275 285 293 296
Payments
Ratio
The
268
302 Nutritive Ratio, Specific Gravity.
Proportion Levers,
Compound
308 Proportion.
CONTENTS
ix PAGE
Powers
318
Roots
321
Miscellaneous Review Problems
326
Appendix
367
Surfaces of Solids,
Root, Proof of
Volumes of Solids, Extraction of Cube Fundamental Processes by casting out
Nines, Arithmetical Progression, Geometrical Progression,
Tables of Measures, Weights of Produce, Interest Tables, Cattlemen's Notation, Lumbermen's Notation.
:
:
PKACTICAL ARITHMETIC oiOic^
NOTATION AND NUMERATION EXERCISE 1. 2.
3. 4. 5.
How many How many How many How many How many
ones in
378 6.
one hundreds,
How many What name
10.
50207 35842 26459
tens,
and ones
in
743
437
982
456 874
847
225 629
953
one hundreds in this number, 1000?
How many
tens,
?
one hundreds in 200, 400, 600, 900?
7.
9.
9?
tens and ones in 18, 36, 45, 47, 98
8.
6387 7080 8824
2, 8,
— ORAL
tens in 20, 30, 50?
425 896 549
876 123
1.
is
given to this number?
thousands, hundreds, tens, and ones in
4702 1400 1814
6512 8150 3096
5068 6740 2263
6728 4963 9184
How many thousands in this number, 10000? How many ten-thousands, thousands, hundreds, and ones
in
:
34291 78354 52796
23845 91846 87964 1
10205 35841 88249
23814 87961 18462
PRACTICAL ARITHMETIC 11.
How many
12.
How many hundred-thousands, ten-thousands, thou-
thousands in this number, 100000?
sands, hundreds, tens,
259132
and ones
in:
:
NOTATION AND NUMERATION
Numbers
5.
more than four
of
written with a
comma between
To read a number.
6.
left
7.
usually
are
78,121
Begin at the right and point
periods of three figures each
and read each period as
name
figures
the periods, thus:
63,105,005
1,642,001
off into
3
if it
;
then begin at the
stood alone, adding the
of the period.
The
place value of a figure.
What
have upon the value of a figure to move the left in
its
period?
jNIoving a figure
value tenfold. decreases
its
To move
it
effect does it it
one place to
one place to the right?
one place to the
left
increases its
iNIoving a figure one place to the right
value tenfold.
exercise
2.
— oral
The Meaning of Numbers There are 5 people
in
my
mother, daughter, and 2 sons.
would be 100 people.
neighbor's
home
:
father,
In 20 such homes there
In a small village of 100 homes
Ten times as many peocommunity would be 5000, and in 100 such towns together there would be 500,000 people. The following numbers show the population of some Read the numbers and try to capital cities in 1900. there are about 500 inhabitants.
ple as this in one
realize their 1.
Albany,
meaning
PRACTICAL ARITHMETIC 5.
NOTATION AND NUMERATION 11.
Figures
or
Digits
are
5
symbols used to express
numbers. 12.
The process of reading numbers is called Numeration.
13.
Numbers may be expressed by
Figures, Letters, or
Words.
EXERCISE Write these numbers in separate periods
3.
— WRITTEN
figures,
using the
comma
:
1.
Six hundred seventy-five.
2.
Two hundred
3.
Four hundred
ninety-six.
4.
Two hundred
twenty-nine.
5.
Fouj hundred
6.
One thousand,
thirteen.
eight.
three hundred fifty-two.
7.
Six thousand, forty.
8.
Eighty thousand, eighty.
9.
Seven thousand, three hundred.
10.
Thirteen thousand, four hundred
11.
Ninety-nine thousand, nine.
12.
Forty-four thousand, sixteen.
13.
Four hundred
14.
Three thousand, fourteen.
15.
Nine thousand, seventy-seven.
16.
Fifty thousand, sixty-eight.
17.
Eleven thousand, nine hundred seventy -three.
18.
Seven hundred eighty-five thousand, two,
six thousand, one
fifty.
hundred
fifty.
to
PRACTICAL ARITHMETIC
6 19.
Ninety-two thousand, one hundred
20.
One
21.
Eight thousand, four hundred eighty-two.
22.
Nineteen million, one hundred fifty-six thousand.
23.
Eight million,
24.
Five thousand, one hundred thirty-one.
25.
Sixty-three million, sixty-eight thousand, seven.
14.
The
million, three
six.
hundred ninety-seven thousand.
six.
art of writing
numbers
is
called Notation.
BXBECISE 4.— WRITTEN Write in figures the following numbers, which express the wool production and the states,
number
of
arranging in columns and using the
the periods, as in Exercise
hogs in several
comma between
2.
POUNDS OF WOOL, PRODUCED IN
1906
North Carolina, eight hundred seventy-one thousand, two hundred fifty. 1.
2. Alabama, hundred fifty. 3.
Montana,
five
hundred sixty-eight thousand, seven
thirty-five million, eight
hundred
fifteen
thousand. 4.
Florida, three
hundred sixteen thousand,
six hun-
dred two. 5.
Wyoming,
thirty-two million, eight hundred forty-
nine thousand, seven hundred
fifty.
6.
Texas, nine million, three hundred sixty thousand.
7.
Missouri, four million, six hundred seven thousand,
three.
NOTATION AND NUMERATION
NUMBER OF HOGS
New
8.
hundred
7
IN 1907
York, six hundred seventy-five thousand,
five
forty-five.
Iowa, eight million, five hundred eighty-four thou-
9.
sand, five hundred.
Pennsylvania, nine hundred eighty-nine thousand,
10.
six
hundred
sand, three 12.
,
hundred eighty.
Illinois,
sand, seven
four million, four hundred forty-nine thou-
hundred
five.
Texas, two million, eight hundred sixty thousand,
13.
eight
eighty-five.
Kentucky, one million, two hundred thirteen thou-
11.
hundred seventy-nine. Ohio, two million, four hundred thirty-six thousand,
14.
seven hundred ninety-seven.
Alabama, one million, two hundred
15.
sand,
two hundred
16.
Nebraska, four million, eighty thousand.
The following tant cities. ize
fifty-one thou-
fifty-one.
are the distances between several impor-
Write the numbers
in figures
and try to
real-
what they mean.
By
rail from Albany, N.Y., to Troy, N.Y., six from Utica, N.Y., to Rome, N.Y., fifteen miles from Syracuse, N.Y., to Rochester, N.Y., eighty-one
17.
miles;
;
miles. 18.
From
St.
Paul,
Minn., to
thousand fifty-three miles; cinnati, O.,
Portland, Ore., two
from Cleveland, O., to Cin-
two hundred sixty-three
miles.
PRACTICAL ARITHMETIC
8 19.
From Chattanooga,
Teiin., to
xour hundred ninety-two miles
New
Orleans, La.,
from Nashville, Tenn.,
;
New
Orleans,
to
La.,
hundred twenty-
six
from
four
miles
New
Orleans, La.,
;
to Atlanta, Ga., four
hundred ninety-six miles. 20.
Street Scene From a Copyright,
1907,
Atlanta, Ga.
in
By water from
New York
to Liver-
pool, three
thousand
fifty-eight
miles
;
from San Francisco
photog:raph.
by Underwood & Dnderwood.
to
Yokohama, four
thousand, seven hundred ninety-one miles. 21.
From New York
to Manila, sixteen thousand, five
New York
hundred miles; from
to
Havana, one thou-
sand, four hundred twenty miles. 22.
From New York
to Strait of Magellan, six thousand
eight hundred ninety miles
San Francisco, 23.
By
rail
six
;
from Strait
from
New York
to
three hundred eighty-five miles
thousand two hundred 24.
The
of
Magellan to
thousand one hundred ninety -nine miles.
;
Omaha, one thousand San Francisco, three
to
fifty miles.
railroads of the
United States aggregate one
hundred ninety-three thousand
miles, bearing thirty-eight
thousand locomotives, fourteen thousand coaches, carrying yearly six hundred million passengers, and one ion tons of freight.
They
bill-
cost about five billion dollars.
ROMAN NOTATION The system of notation and numeration alreadyis commonly called the Arabic System. There still another system known as the Roman System. 15.
explained is
16.
Roman system
In the
of
seven capital
notation
and combinations of these letters are used to express numbers. The letters and their letters of the alphabet
values are as
17.
A
:,
I
V X
L
C
D
M
1
5
10
50
100
500
1000
bar placed over a letter increases
thousand 18.
follovsrs
fold, e.g.,
When
V
denotes 5000;
X
these symbols are used in combination their
values are governed by the following laws
Each repetition
I.
XX denotes
value a
its
denotes 10,000.
of a letter repeats its value, e.g.,
XXX denotes
20,
:
30,
CC
denotes 200,
MMM
denotes 3000.
When
II. its
value
XI
is
a letter
to be
placed after one of greater value,
is
added
to that of the preceding letter,
VII represents 5 and XVI represents 10 and 5 and 1, or 16 CXXI 2, or 7 represents 100 and 10 and 10 and 1, or 121. e.g.,
represents 10 and
1,
or 11
;
;
III.
;
When
a letter
value, its value
value, e.g.,
IX
is
When
placed before another of greater
represents 10 less
50 less 10, or 40
IV.
is
taken from that of the letter of greater
;
XC
a letter
1,
or 9;
XL
represents
represents 100 less 10, or 90. is
placed between two letters of 9
::
PRACTICAL. ARITHMETIC
10 greater value,
which follows
CXC
its
value
it, e.^.,
is
XIX
taken from that of the letter represents 10 and
9,
or 19;
represents 100 and 90, or 190.
BXEECISE
5.
— WRITTEN
Express in Arabic notation 1.
XI
11.
XXVII
21.
2.
XX
12.
XCV
22.
3.
XIV
13.
XLIV
23.
4.
XXX
14.
LXXIV
24.
5. 6. 7.
8. 9.
10.
XL XVI LV
15.
XLIX
MDXLVI MDCCXLIV MMDCCXCIII VCCCLXXVI
25.
27.
XDCCXCIX DXLIV
28.
MDCCLXXXIII
19.
MCXL MCXLV
29.
MMCCCCLXIV
20.
MDLIV
30.
MMMDCCXIX
16. 17.
LIX LXXVIII
CCLIV CDLVI DCIX
MDLX
18.
26.
EXERCISE 6.— WRITTEN Express in 1.
Roman
notation
UNITED STATES MONEY 19.
Dollar. !?
25
is
20.
In the money of the United States the unit is the In writing it is expressed by the sign |, e.g., read twenty -five dollars.
Our monej' system
is
based upon the same system of
tens and groups of tens which tion.
That
we
studied in Arabic nota-
ten units of one order
is,
make
a unit of the
next higher order. 21.
Ten ten-cent
pieces equal one
A
cent pieces equal a ten-cent piece.
Ten
dollar.
one-
smaller divi-
still
money which we do not commonly use is called Mills. Ten mills equal one cent. Ten cents is one-tenth of a dollar. One cent is one one-hundredth of a dollar. One mill is one one-thousion of our
sandth of a dollar. 22.
The period used
to separate
dollars
and cents
is
called the Decimal Point. 23.
ment
The
following diagrams serve to show the arrange-
of dollars, cents,
and
iiaills
as they are written:
CO
F3
a m —
.
a>
-7.
.a
1245 245
•t
.
11
+->
3
2 4 5
T3 +3 J5 +J .
2 4 5
:
;
:
:
PRACTICAL ARITHMETIC
12
EXERCISE
Read
7.
— ORAL
and cents
as dollars
1.
I 8.24
5.
I 25.06
9.
1349.99
13.
$ 542.89
2.
$ 8.72
6.
I 91.07
10.
^698.42
14.
I 560.90
3.
I 9.87
7.
f 92.09
11.
1100.10
15.
$1845.24
4.
$10.25
8.
$900.09
12.
I 99.99
16.
$6291.98
Read
as dollars, cents,
and
mills 23.
$981,701
26.
$699,764
17.
$5,842
20.
$ 17.001
18.
$3,205
21.
$ 70.070
24.
$909,701
27.
$263,809
19.
$4,998
22.
$191,672
25.
$340,034
28.
$ 89.617
EXERCISE
8.
— WRITTEN
Express the following in figures, using the dollar sign
and decimal point
Twenty
1.
and
dollars
and
fifty cents;
thirty-four dollars
five cents.
Eighteen dollars and thirty-five cents; ninety -five
2.
dollars
and twenty cents; thirty-one dollars and sixty
cents
one hundred twenty dollars and four cents.
3.
lars
;
One hundred
and nineteen cents
cents; 4.
fifty
dollars ;
and ten cents
fifty-four dol-
;
fifty-three dollars
and
fifty-five
nineteen dollars and ninety cents.
Eighty dollars and one cent, five mills cents
;
;
fifty dollars and
three hundred dollars and six cents, one mill
four hundred thirty-three dollars and thirty-three cents. 5.
Five hundred dollars and three-tenths
dollars
and thirty-three hundredths
;
;
two hundred
one hundred dollars
and three hundred thirty-three thousandths.
:
ADDITION 24. The growth of an apple twig in 1905 was 4 inches and in 1906 it was 6 inches. How many inches did it grow in the two years?
Addition is
is
the
process of finding the
number
that
equal to two or more numbers taken together. 25.
The
result obtained
by adding numbers
is
called
+, is called Plus. means that they are
When
the Sum. 26.
The sign
of addition,
placed between numbers
it
to be
added. 27.
The
sign of equality,
numbers shows that they are
=, when placed between equal. Thus 7 + 3 = 10 is
read seven plus three equals ten. 28.
Find the sums
of the following,
which include
the combinations of two numbers from one to nine 2
+7=
all
PRACTICAL ARITHMETIC
14 6
+3=
;
ADDITION
15
If a fruit cake requires 3 lbs. of currants, 2 lbs. of
8.
and
raisins,
1 lb. of citron,
used in the cake
If the increase in
9.
how many pounds
temperature at Raleigh, N.
1907 was 26 degrees from February to
May
from
August, what was the
to
of fruit are
?
perature during the six months
May and
C,
in
14 degrees
total increase in tem-
?
If the temperature decreases 8 degrees from July September and 33 degrees from September to March,
10.
to
what
the total decrease in temperature
is
11.
The number
New England
States,
these sections
12;
the
How many
Pacific States, 10.
12.
from each of several
of senators
our country in 1890 was as follows
tions of
all
?
Middle
:
sec-
from the
States,
the
8;
senators were there from
?
The number
of senators from the
tions of our country in 1890
was
as follows
How many
the Northwest, 24.
two largest :
sec-
the South, 28
senators were there from
these sections? 13.
A 4
silage,
and 3
ration for a
of
entire ration
15 lbs. of hay, 30
is
of cotton-seed meal, 3 lbs. of
lbs.
lbs.
cow
What
corn meal.
Count from 3
to 99
15.
Count from 4
to 100
16.
Count from 6
to 96
17.
Count from 9 to 99 by nines.
18.
At
the
of
the weight of the
?
14.
for
is
lbs.
wheat bran,
by
threes.
by
by
fours.
sixes.
Raleigh, N.C., in 1907 the lowest temperature
month
of
October was 36 degrees, the highest
PRACTICAL ARITHMETIC
16
What was
temperature was 45 degrees higher. est
temperature
Two
19.
skilled laborers earned
How much
a day.
Two
20.
The
tilizers
$
did the two earn together
How much
A ration for
lbs. of
A
23.
1000
What
ration
clover seed, acre
is
the weight of the ration?
for
a
and
fattening beef animal weighing
corn silage, 12
man
vs^ishes to
and 4
lbs. of
corn stover,
of cotton seed.
lbs.
seed an acre for a
11 lbs. of timothj', 6
iises
when doing
6 lbs. of corn,- 8 lbs. of oats,
lbs. of
is
the weight of the ration?
If a
24.
30
What
is
of cotton-seed meal, is
?
?
a horse vreighing 1000 lbs.
What
hay.
lbs. is
5 lbs.
did the two earn
harvesting and other expenses f 3.
3,
moderately hard work 15
?
cultivation of an acre of corn costs $6, the fer-
the cost of the crop per acre 22.
13 and $5 respectively
unskilled laborers earned respectively il.25
and f 1.50 a day. 21.
the high-
?
lbs. of
how many pounds
meadow and
red top, and 5
of seed does he
lbs. of
sow on the
?
If
25.
contain 5
1000
lbs.
lbs. of
phosphoric acid, does
it
contain
of
how many pounds
ton of dry clover hay used 39
nitrogen, 37 lbs. of potash,
phoric acid in growth,
27.
of these plant foods
?
If the plants in a
26. lbs. of
rials
an average mixed stable manure
nitrogen, 6 lbs. of potash, and 3 lbs. of
how many pounds
were used by the plants If a ton of
and 11
lbs. of
phos-
of these mate-
?
wheat straw
iased
in
growing 11
lbs.
ADDITION of nitrogen, 23 lbs. of potash, acid,
how many pounds
from the 28.
17
and 4
of these
lbs.
of phosphoric
materials were taken
soil ?
If a
ton of oat grain used in growing 35
lbs.
of
nitrogen, 9 lbs. of potash, and 13 lbs. of phosphoric acid,
how many pounds
of these materials
were used
?
PRACTICAL ARITHMETIC
18 column.
column
The sum of the hiiudreds' column + 1 from the tens' The last sum is placed under the column 17.
is
added. 30.
Write the immbers to be added
Rule for Addition.
so that the figures representing units stand
under
tens under tens, hundreds under hundreds, etc. at the riglit
units,
Begin
and add each column separately, placing the
sum underneath
if it is
column exceeds
nine, set
less
than ten.
down
If the
sum
of
any
the right-hand figure and
add the other figure or figures to the next column at the left.
EXERCISE
Add:
11.
— WRITTEN
ADDITION OF UNITED STATES MONEY 31.
Add
14.25, $16.50, f .45, 1150, 13.455.
'"'5
S4 ^':;3 '^
16.50 .45
150.00 3.455
1174.655
Write the numbers
to be
added so ihat units
of the same order shall stand in the same col-
umn, with the decimal points
Add
as in integral numbers.
in the
sum should stand
in a vertical line.
The decimal point
directly in line with
the decimal points of the numbers added.
EXERCISE
12.
— "WRITTEN
Add: 1.
12.50 3.05 .90 .06
7.25
1340.006
11.006 21.05 3.425
2. 3. 4. 5.
6.
Add Add Add Add Add Add
300.10
62.62
106.001
324.05
75.141
231.005
$3.05,
13.
$20,006,
$30,006
10.01
42.14
EXERCISE 1.
4.
3.
2.
10.50 3.75
— WRITTEN $45.2.5,
$6.25,
$3,755.
$63.43, $25,002, $23,025, $300.45, $62,725. $90.,93, $84,005, $2,005, $16.85, $4.35, $1.98.
$63.05, $400.62, $50.50, $200.20, $3.75, $4.25.
$50,005, $560.35, $428.72, $34.91, $863,100. $678.78,
$67249.16,
$6798.98. 19
$9381.62,
$862.98,
:
PRACTICAL ARITHMETIC
20
EXBHCISB
Find the sum 1.
of
14.
— WBITTEN
ADDITION EXERCISE
The exports Country
15.
of cheese for
— WRITTEN
1901-1905 were
21
PEACTICAL ARITHMETIC
22 17-21.
Find the sum
of
22-33.
Find the sum
of each line of
columns
a, h,
d, e.
c,
numbers from 1
to
12 without copying.
Find the sums of the numbers in diagonal rows, a 2, also c 1, J 2, a 3, and all other possible rows
34-47.
thus
b 1,
:
having the same direction, as d 1 to a 48-61.
onal rows dl, sible
e 2, also c 1,
rows having the same direction.
EXERCISE 1.
4, etc.
sums of the numbers in diagd 2, e S, and by all other pos-
Similarly, find the
A dairyman
16.
— WRITTEN
has 6 cows.
The
gives 18 lbs. of
first
milk, the second 11 lbs., the third 23 lbs., the fourth
26
lbs.,
they 2.
the fifth 32
all
If
lbs.,
the sixth 40 lbs.
200-lb.
a
sack of fertilizer contains 8
nitrogen, 10 lbs. of potash, and acid,
how many pounds
a sack 3.
How much
do
give?
16
lbs.
lbs.
of
of phosphoric
of these plant foods are there in
?
If a reader costs
metic 49
cts.,
pencils 7 cts.,
43
a history 86
cts.,
an
a geography $1.08, a tablet 8
cts.,
pens and
what
is
cts.,
arith-
the cost of the equipment?
4. In the stomach and crop of a bob-white there were found 400 pigweed seeds, in another 500 ragweed seeds,
in another 550 sheep-sorrel seeds, in another 640 seeds of
pigeon grass.
sumed by 5.
How many
of these
these four bob-whites
When
thoroughly dry, the weight of the different
parts of the cotton plants as follows:
weed seeds were con-
?
lint
300
lbs.,
grown on an seed 507
acre of land was
lbs., bolls
363
lbs..
ADDITION
23
leaves 566 lbs., roots 130 lbs., stems 604 lbs.
What was
the total weight of plants produced to yield 300 lbs. of lint cotton ?
If the material
6.
follows
2379
1190
and shucks 397
lbs.,
how
lbs.,
How
did the ears and stover together weigh? did the stover weigh
A
7.
acre in corn weighs as
ears 4325 lbs., stover, which consists of stalks,
:
lbs., leaves
much much
grown on an
?
farmer sold the following products during the
year: 1 horse |145, 9 beef animals |468, 18 hogs $234,
13 lambs 152, 309 bus. potatoes $12Q, 10 bales cotton 1528, 150 bus. seed oats |75, 100 bus. seed corn |100, 50 chickens $22, 200 doz. eggs $38, 12 turkeys $21, 220 bus.
wheat $191.
The
8.
:
neck 40
alive,
lbs.,
36
lbs.,
round steak 183 138
lbs.
weighed 1550
chuck 237
porter-house steak 103
ribs plate
did his total sales amount?
different parts of the dressed carcass of a beef
animal that, when lows
To what
lbs.,
lbs., sirloin lbs.,
What
weigh
as fol-
prime ribs 117 steak 87
shank 30
is
lbs.
lbs.,
lbs., flank,
lbs.,
rump
52
lbs.,
the weight of the dressed
carcass ?
A New
England cottage was built at a cost as follows: masonry $250, lumber and mill work $700, carpentering $400, plumbing $170, painting $90, hardware 9.
$20, heater, $200. pleted 10.
What
did the house cost
when com-
?
A
cottage planned to cost $1000 was built for the
following cost: foundation and brickwork $428.80, lumber $370.15, carpentering $264.87, painting and plaster-
PRACTICAL ARITHMETIC
24
What
ing 8253.25, hardware 138.90, tin work, |13.78. did the house actually cost
A
11.
?
farm costing $5250
equipped as
is
follows:
house 11579.42, farm mules 1850.00, 1 horse 1175.00,
hogs
$275.00,
cattle
1672.00.
What
equipment
?
implements
1112.00,
and
tools
the total value of the farm and
is
its
COST OF FURNISHING A HOUSE
Two young articles.
people equip their
Find the cost
of each
home with
room
the following
separately.
Kitchen: Linoleum, 120.00; range, 145.00;
12.
11.50; chair, $1.00;
utensils,
$13.00; laundry
$8.25; refrigerator, $21.00; lamp, 45
table, outfit,
clock, $1.00;
cts.;
cutlery, 75 cts.
Dining Room
13.
:
Table, $20.00
;
six chairs, $24.00;
sideboard, $30.00; rug,$12.00; clock,$4.98; silence cloth,
$1.25 kins,
$4.50
;
lamp, $2.97
;
3 dozen napkins, $9.48
;
2 dozen nap-
$4.30; six table-cloths, $15.00; six plated knives, ;
six solid silver forks,
$12.00
12 solid silver spoons,
;
$10.00; three tablespoons, $6.00;
dishes,
$15;
glass-
ware, $7.45. 14. ris
Living Room: Lamp, $3.50;
chair,
$14.60;
arm-chair, $7.50 rug, 15.
;
chair,
$5.45;
table,
$15.00; Mor-
rattan chair,
$9.25;
bookcase, $9.45; magazine stand, $6.25;
$34.50.
Hall: Lamp, $3.25;
hall
rack,
$16.35;
chair,
$3.45; rug, $6.00. 16.
Bedroom: Bureau, $22.35;
washstand, $4.00;
toilet set,
chiffonier,
$11.25;
$6.25; chair, $2.75; lamp.
ADDITION
25
11.50; bed, $13.00; springs, 15.00 sheets,
19.60;
;
mattress, 115.00; 12
12 pillow cases, 15.00; 2 pairs blankets,
f 10.00; 1 comfortable, 11.00; 2 counterpanes, 13.45; 2 dozen towels, 16.00; 1 dozen yards toweling, $1.80; rug or matting, $5.80. 17.
Find the
18.
If a family of
total
amount spent
in furnishing the house.
two persons spends
for rent $130,
food $210, clothing $80, fuel $30, light $6, insurance $24, replenishing $ 10, carfare $5, literature $5, charity $10, and saves $20, what
A
19.
second family of
is
the income?
five
persons spends for house
rent $240, table expense $364,
clothing $175, fuel $52,
light $3, hired help $50, renewals $50, dentist $25, boys
spending money $13, spending money of other children $5. 20.
What is the income? What is the cost of raising
an acre of corn, estimat-
ing rent at $3.03, fertilizer $1.86, preparation of the soil
$1.62, planting $.42, cultivating $1.80, harvesting
$3.00, and other expenses $1.76? 21.
cotton,
What
is
the total cost of raising an acre of upland
allowing for the rent of land $3.25,
fertilizer
$2.46, preparing the soil $3.00, seed $.21, planting $.28, cultivating $2.31, picking $3.37,
$1.65,
wear
of
tools $.62,
ginning and pressing
marketing $.64, and other
expenses $1.42? 22.
A
man owns
5 horses.
The
first is
worth $90, the
second $125, the third $175, the fourth as
much
as the
and second, the fifth .as much as the second and fourth. What was the value of the 5 horses? first
PRACTICAL ARITHMETIC
26 23.
The number
1900 was
world in
of miles of railroad in the
North America 216,000, Europe 173,000, Asia
:
South America and West Indies 28,000, Aus-
36,000, tralasia
What was
Africa 12,000.
15,000,
the
total
mileage ? Alabama, S Arkansas, S
P
California,
Colorado
.
.
.
Connecticut, N.E.
.
.
.
M
Delaware, Florida, S Georgia, S
Idaho Illinois,
Indiana,
E.C E.C
Iowa,W.C Kansas, W.C Kentucky, E.C Louisiana, S
Maine, N. Maryland,
E
M
Massachusetts, N.E.
Michigan, E.C Minnesota, W.C. Mississippi, S Missouri,
.
.
.
.
.
W.C
Montana Nebraska, W.C.
.
.
.
Nevada
New New New
Hampshire, N.E. Jersey,
York,
M..
.
M
North Carolina, S. North Dakota, W.C.
.
Ohio, E.
. .
.
.
.
.
.
C
Oklahoma, S Oregon, P Pennsylvania,
Rhode
M.
Island, N.E. South Carolina, S. South Dakota, W.C. Tennessee, S Texas, S
Utah
.
.
.
.
.
.
.
.
.
.
.
1,828,697 1,311,564 1,485,053 539,700 908,420 184,735 528,542 2,216,331 161,772 4,82i;550 2,516,462 2,231,853 1,470,495 2,147,174 1,381,625 694,466 1,188;044 2,805,346 2,420,982 1,751,394 1,551,270 3;i06,665 243,329 1,066,300 42,335 411,588 1,883,669 7,268,894 1,893,810 319,146 4,157,545 790^391 413,536 6,302,115 428,556 1,340,316
401,570 2,020,616 3,048,710 276,749
The
adioininsT
,
the
the States
of
table
^ population
"^
^,
.
gives
United Q^n -^^""•
of
.
the
States
in
-.
Fmdj
„, ^4.
tion
-^
^ the popula-
New
the
of ^.
-,
land
bv
^i.
tji-
.
j
indicated
NF rf-j ^^"^^
,-
^^-
lation
^Iio *^^
the
of j-
oj. ^ j States, indicated 4.
„_
t^-
tion
i
by ht M. i,
.i
the ^
of
^ , Central ,
patpri ^^^^'^
Western ,.
States,
indi-
"W P ^^•
Vnr '^^
Find the popuianonula-^ ^^^ ^^^
,? tion
T^r.T.^^
P^P^" Middle
^ Find the popula-
^6.
q.
Eng-
^-
.
States,
of •
,
the Southern jj u by 4.
indicated
States, S. 28. .
tion
States ^^^^^s,
P.
Find the popula^ ^ of
the
Pacifio
indioatfld inaicacea
bv Dy
:
ADDITION Vermont N.E
343,641 1,854,184 518,103 958,800 2,069,042 92,531
M
Virgima, Washington,
West
P M.
Virginia,
.
.
.
Wisconsin, E.C
Wyoming
The remaining
30.
the population
27
Find the popula-
29.
.
.
,
Eastern
the
of
tioii
Central ^^nrrai
Statp^i States,
cated by
inrli indi-
E.C.
States are Plateau States.
What
is
?
Except in leap year the days in the months number January
31
,
J,
How many
31.
„^
in
year?
year that
a
April
30
M*y
31
j^,
gj
February
31
after
August September October
November December 34.
after
.... .... ....
The
30 31 30
'^ow
31
first?
not a leap
twenty-second
first ?
^he fourth
many days
December
of
how many days
is
January
33^
twenty-fifth of
January
The
32.
days are there is
is
of
after
July •'
is
January
how many
days
first?
SOME IMPORTANT DATES 33.
From
the discovery of America by Columbus in
1492 to the founding of
From
Augustine 73 years elapsed.
the founding of St. Augustine to the settlement
Jamestown 42 years these two settlements ? of
36.
St.
From
founding of
elapsed.
What were
the dates of
the discovery of America in 1492 to the
New Amsterdam 122 New Amsterdam
the founding of
Pilgrims 6 years elapsed.
two settlements
?
years elapsed.
From
to the landing of the
What were
the dates of these
PRACTICAL ARITHMETIC
28 37. first
From
the
first
General Assembly in 1681 to the
Colonial Congress 84 years elapsed.
From
the
first
Colouial Congress to the second Colonial Congress 9 years elapsed.
What were
the dates of these two Congresses?
Signing the Declaration of Independence
38.
From
the
first
General Assembly in 1681 to the
Declaration of Independence 95 years elapsed.
From
the Declaration of Independence to the adoption of the
Articles of Confederation 5 years elapsed.
What were
the dates of these two events? 39.
From
the
first
General Assembly in 1681 to the
adoption of the Constitution 106 years elapsed. From the adoption of the Constitution to the election of the first President of the United States 2 years elapsed.
What were
the dates of these events?
SUBTRACTION One
32.
dairy
cow produces
How much
week, another 5 pounds.
duce than the other
The is
9 pounds of butter in a
more does one pro-
?
process of finding
how
mucli greater one number
than another, or finding the difference between two
numbers,
is
The
33.
another
is
number from which
larger number, or the
subtracted,
The
34.
called Subtraction.
is
called the Minuend.
smaller number, or the
number
subtracted,
is
called the Subtrahend.
The
35.
result obtained in subtracting is called the
Remainder or
The
36. it is
sign of subtraction,
—
,
placed between two numbers,
number is
Difference.
read,
is
it
called Minus.
means
to be subtracted from the
eight minus
1-1= 2-1= 3-1= 4-1= 5-1= 6-1=
17.
first, e.g.,
8
— ORAL
2-2= 3-2= 4-2= 5-2= 6-2= 7-2= 29
When
that the second
(less) five equals three.
EXERCISE
•
is
3-3= 4-3= 5-3= 6-3= 7-3= 8-3=
— 5=3
PRACTICAL ARITHMETIC
30
7-1 =
SUBTRACTION EXERCISE
18.
31
— ORAL
Practice subtracting these numbers until the differ-
ences can be told instantly.
PRACTICAL ARITHMETIC
32
BXBBCISB
19.
— ORAL
1. If a twig grew 6 ins. in 1906, and 4 which year produced the greater growth?
greater
3. 4.
If
a strawberry plant
injured by insects, the plant
?
How much
ber were 17,
tember
are
leaves are there on
limb on the north side of a tree measures 9
If the
6.
?
has 12 leaves and 4
how many sound
and one on the south longer
2
?
If a
5.
1907,
How much
?
What number taken from 10 leaves What number with 6 makes 10 ?
2.
ins. in
number
side measures 11
longer
which
is
the
?
of rainy
how many
ft.,
ft.,
and cloudy days in Septemwere there in Sep-
clear days
?
7.
Subtract by threes from 99 to
8.
Subtract by fours from 100 to 0.
9.
Subtract by sixes from 96 to
10.
Subtract
11.
If the
bj'
0.
0.
sevens from 98 to
0.
highest temperature for July in the Middle
Atlantic States was 99 degrees, and the lowest temperature 57 degrees, what was the range in temperature? 12.
grow
The highest is
degrees.
soil
104 degrees
;
temperature at which wheat
will
squash and corn grow at 115
At how much higher temperature
and corn grow than wheat
will squash
?
Melons grow best at a soil temperature of 99 degrees, and clover at 70 degrees. How much higher temperature is required for melons than clover ? 13.
SUBTRACTION 14.
The
boiling point of water
ing point 32 degrees.
What
33
212 degrees, the freez-
is
the difference in degrees
is
between the boiling and freezing points? 15.
A
man
wishes to start a small fruit garden.
The
has 115. to invest.
How much 16.
strawberry plants cost 25
If 6 doz.
sum
original
A
18.
A
?
ins. in
25
cts.,
how much
is
cts., still
and 4 raspleft
of the
?
normal child 6 height,
yrs. old
and has
normal child of 9
in height, is
trees
He
cost 1 10.
for smaller plants?
is left
berry plants cost *.25,
44
and
for the plants
lattice
If 2 pear trees cost 35 cts., 2 apple trees
how much 17.
is left
and
trellis
yrs.
weighs 45
a chest
lbs.,
measurement
weighs 60
lbs.,
and has a chest measurement
measures
of 23 ins.
measures 50
of 25 ins.
ins.
What
the increase in weight in 3 yrs.? 19. 20.
3 yrs. 37.
875 446 429
What
is
What
the increase in height in 3 yrs. the
is
in
increase
chest
?
measurement
in
?
From 875 Since
take 446.
we cannot take 6
add one of the 7 tens units.
We
now have
iinits
from 5 units we
to the 5 units,
making 15
6 units to be subtracted from
15 units, which leaves 9 units to be written under the Since we have already taken 1 ten from the 7 4 tens from 6 tens we have 6 tens remaining in tens' column. tens leaves 2 tens, which is written under tens' column; 4 hundreds from 8 hundreds leaves 4 hundreds. The remainder, units' column.
therefore, is 4 hundreds, 2 tens, 9 units, or 429.
:
PRACTICAL ARITHMETIC
34
From 584
38.
584 296 288
Since
take 296.
we cannot take
6 units from 4 units
we must
take one of the 8 tens, which added to 4 units makes
14
6 units from 14 units leaves 8 units.
units.
we have
Since
already taken 1 ten from the 8 tens,
we
We
cannot take 9 tens from 7 tens, so we must take 1 hundred from 6 hundreds, which added to 7 tens
have 7 tens
makes 17
we have
left.
tens.
9 tens from 17 tens leaves 8 tens.
Since
already taken 1 hundred from the 5 hundreds
have 4 hundreds 2 hundreds.
we
2 hundreds from 4 hundreds leaves The remainder, therefore, is 2 hundreds, 8 tens, left.
8 units, or 288.
Add
39.
the remainder to the subtrahend in each of
the last two examples.
The sum
of the
to the minuend.
What do you
is
add the
work
test the subtraction
If the
sum
equal
equals
is correct.
Rule for Subtraction.
40.
?
Hence, to
remainder and subtrahend together. the minuend, the
observe
remainder and the subtrahend
Write the subtrahend under
the minuend, placing units under units and tens under
Begin at the right and subtract each figure of the subtrahend from the corresponding figure of the minuend, and write the remainder underneath. tens, etc.
If
any
figure of the subtrahend
is greater than the corresponding figure of the minuend, increase the figure of the minuend by taking one of the next higher order,
which
will be an increase of ten.
Then diminish by 1 the order of the minuend from which the 1 was taken, and subtract.
EXERCISE
20.
— WRITTEN
Subtract and prove 1.
52-26.
2.
37-28.
SUBTRACTION
35
94-58.
11.
786-235.
4.
93-25.
12.
598-213.
5.
92-68.
13.
647-238.
6.
81-18.
14.
321-216.
7.
70-36.
15.
976-247.
8.
90-27.
16.
876-381.
9.
50-13.
17.
358-149.
10.
95-47.
18.
467-248.
3.
SUBTEACTION OF UNITED STATES
MONEY exercise
21.
— oral
Makixg Change buy
I
1.
a
book
receive from 50 cts.
A
2.
5
cts.,
how mucb change Make change in two ways.
for 42 cts. ?
;
yard of ribbon costs 12
spool of thread
cts., a
How much
a paper of pins 5 cts.
receive from a fifty-cent piece
?
shall I
change do
Make change
I
in three
ways.
A
3.
yard of silk costs 63
A
4.
copy
cts., 1 doz.
Make change
a bolt of tape 5 cts.
"Arabian Nights"
of
for
buttons 10
$1
in
cts.,
two ways.
costs $1.10.
Make
change for 12.00.
8.
Make Make Make Make
9.
A
5. 6.
7.
change for $2.00 when you owe $1.75; $.15. change for $5.00 when you owe $1.49; $2.58. change for $5.00 when you owe $3.18; $2.16. change for $2.00 when you owe $1.23; $1.87.
pair of shoes costs $2.25, hat $1.00, tie 50
4 handkerchiefs 72
cts.
How much
cts.,
change does the
merchant return for $5.00? 10.
Make change
41.
Subtract $45,755 from $90.20.
.rrjrr i
when you owe $ .81
;
$ 7. 84.
Since the subtrahend has mills and there are no
*Q0 200
—4u. ———DO^
for $ 10.00
mills lu the minuend, a cipher ,
„
is
added to
fill
the
..-
place 01 mills.
The subtrahend
is
written under
the minuend so that units of the same order shall 36
SUBTRACTION
37
stand in the same column, and the decimal points be in a vertical line.
The decimal
Subtract as integers.
point in the
remainder should stand directly under the decimal points of the
minuend and subtrahend.
EXERCISE 22.— WRITTEN Subtract and prove: 1.
$4.24-111.10.
11.
11.00-1.75.
2.
13.86 -#1.25.
12.
111.00 -$3.25.
3.
14.50-.¥3.20.
13.
$90.99-180.25.
4.
110.75- $8.41.
14.
$77.42 -$65.94.
5.
$6.54 -$4.37.
15.
$93.20 -$84.25.
6.
$9.27 -$8.16.
16.
$525 -$177.02.
7.
$12.50 -$8.25.
17.
$197 -$184.09.
8.
$17.28-18.25.
18.
$3.333 -$2,999.
9.
$18.24 -$9.16.
19.
$16.725 -$.50.
$20.50 -$10.25.
20.
$28.07 -$.125.
10.
EXERCISE 23.— WRITTEN 1.
of
Ill
a day's milking of 769 lbs. of milk from a herd
Jersey cows there are 661
many pounds 2.
lbs.
and the remainder
solids-not-fat,
69
butter-fat.
cows there are 675
solids-not-fat,
lbs.
of
How
from a herd of Hol-
lbs. of
and the remainder
is
water, 69 lbs. of butter-fat.
many pounds of butter-fat in the day's milking? many pounds less of butter-fat than in problem 1 ? 3.
lbs.
of butter-fat in the day's milking?
In a day's milking of 769
stein-Fresian
of water, is
The 3d
of
February 1907
is
How How
the 34th day of the
;
PRACTICAL ARITHMETIC
38 year
;
many
the 5th of June
How
the 156th day of the year.
days between these dates ?
The 10th
4.
is
September
of
the 10th of June
is
the 283d day of the year
What
the 191st day of the year.
is
is
the difference in dates?
The 22d
5.
142d day of the year
of April is the
31st of October
is
What
the 303d day of the year.
;
the
is
the
difference in dates? 6. Jamestown, Va., was settled in 1607; the Jamestown Exposition, near Norfolk, Va., occurred in 1907.
How many The
7. is
years elapsed between the dates boiling point of water
is
?
212 degrees.
simmering temperature at 180 degrees.
at
Water
What is
the
difPerence in temperature? 8.
alive,
82
If a
lbs. less 9.
farmer
how much
A
kills a
than the live weight
?
butcher killed a beef animal of good quality
that weighed 1148
1179
hog that weighs 369 lbs. when weigh if it weighs
will the dressed carcass
What
lbs.
lbs. is
and an
inferior one that
the difference in the weight of the
dressed carcasses of these beeves the
first
529
lbs.?
10.
If
animal was 397
4000
lbs. of
:
potash 80
lbs.,
How much 11.
mainder
is
of the
second animal
ordinary fertilizer contains plant food lbs.,
nitrogen 80
lbs.,
and
of plant food are there?
not plant food ?
lbs. of
and 2152 is
the loss in weight of
if
and
how many pounds
that
In 4000
of water
lbs.
phosphoric acid 320
as follows
weighed
cotton-seed hulls there are 444 lbs.
lbs. of indigestible
digestible.
How much
is
The
matter.
digestible
?
re-
SUBTRACTION 12.
408
In 4000
lbs. of
corn there are 436
lbs. of indigestible
ible.
13.
How many
A man
39
took 1500
lbs. of
pounds of seed should he also
14.
digest-
seed cotton to the gin and
How many
receive, all of the seed cot-
not lint being seed?
is
If
is
pounds of digestible matter are there?
received a bale of lint weighing 493 lbs.
ton that
water and
lbs. of
The remainder
matter.
to
cultivate an acre
fertilizers for it $3,
of
corn costs f 4.50, the
harvesting $3.50, and other expenses
f 1.00, and 35 bus. of corn worth §17.50, and a ton and a quarter of stover worth i 5, are produced, what is the farmer's profit? 15.
If
1083
lbs. of
cotton are harvested from a
ized field
planted with selected seed, and 670
harvested
from an unfertilized
seed was used, what zation 16.
and seed
To grow
is
a ton of oats requires
tons.
464 tons of water.
tons, potatoes require
How much
by potatoes than by corn
?
By
385 tons,
more water is required by oats ? By
clover than
by corn ? By clover than by potatoes by corn ? By oats than by potatoes ?
clover than oats than 17.
If pat
straw uses 163
lbs. of potash,
trogen, and 28 lbs. of phosphoric
48
lbs.
of potash, 176
lbs.
of
phosphoric acid in every 10,000
acid,
56
18.
?
By
lbs. of ni-
and oat grain uses
nitrogen, and 68 lbs. of lbs. of
yield,
which uses
the most of each plant food, the straw or the grain?
much more
fertili-
?
A ton of corn requires 271 and clover 577
are
where unselected
field
the increase in yield due to
selection
fertil-
lbs.
How
of each ?
In Michigan, soy beans with tubercles on their
PRACTICAL ARITHMETIC
40 roots
113
yield
nitrogen to the acre
of
lbs.
tubercles 76 lbs. of
pounds' increase in nitrogen was there
were present 19.
139
the tubercles
?
Cow-peas with tubercles on their roots yielded nitrogen and without tubercles 118
lbs. of
acre.
when
without
;
How many
nitrogen to the acre.
What
lbs. to
the
was the gain when tubercles were present
?
A
good clay soil contains 12,760 lbs. of potash, a good sandy soil 4840 lbs. of potash, to the acre, in a How much more potash is there in layer one foot deep. 20.
clay soil than in sandy soil per acre one foot deep
?
HEIGHTS OF MOUNTAINS
The heights of some of the highest mountains are Mt. Aconcagua 28,082 ft., Mt. Blanc 15,744 ft., Mt. Everest 29,002 ft., Mt. McKinley 20,464 ft., Mt. Mitchell 6711 ft. :
21.
Mt. Mitchell
United States.
Mt. Mitchell 22.
the highest mountain in the eastern
How much
How much
Aconcagua
higher
is
Mt. McKinley than
?
Mt. Aconcagua
Americas.
23.
is
is
the
higher
highest mountain in the is
Mt. Everest than Mt.
?
Mt. Blanc
is
the highest mountain in the Alps.
How much higher is Mt. Everest than Mt. Blanc ? 24. How much higher is Mt. Aconcagua than McKinley 25.
Mt.
?
The
greatest
How many feet
known depth
less is this
of the ocean
is
27,930
ft.
than the height of Mt. Everest ?
.
MULTIPLICATION 42.
at tlie
If a
blackbird destroys 3 cabbage
same
rate
worms
how many cabbage worms
will
in 1 hr.,
it
destroy
333333
in 2 hrs.?
3
In 5 hrs.?
In 6 hrs.?
numbers are
to be added, it is
3
3
3
3
3
3
3
3
3
3
3
3
3
8
3
3
3
3
3
In 3 hrs.?
In 4 hrs.?
In 7 hrs.
?
3
9 12 15 18 21
6
When
several equal
shorter to obtain the result by the process
To
tiplication.
sums
we must
multiply, however,
as
much Mul-
learn the
most common numbers added to themselves numbers of times. Thus in the problem above
of the
definite
we
known
see that 3 taken 2 times gives 6, taken 3 times gives
9, etc.
43.
The number
to be repeated
is
called the Multipli-
cand. 44.
The number which
multiplicand 45.
The
another 46.
When
is
is
indicates
to be repeated
result obtained
is
how many
times the
called the Multiplier.
by multiplying one number
b}?-
called the Product.
The sign
of multiplication is an inclined cross
placed between two numbers 41
it is
X
read " times," or
42
PRACTICAL ARITHMETIC
"multiplied by."
When
the multiplier precedes the mul-
x between them,
tiplicand with the multiplication sign
the sign
is
read " times "
cedes, the sign
is
A
47. is
is
the multiplicand pre-
read "multiplied by,"
read 3 times 8 equals 24, the expression
when
;
or,
number that
is
3
x
8
= 24,
is
regarding 8 as the multiplier,
read, 3 multiplied
called a Concrete
e.g.,
by
8 equals 24.
applied to any particular object
number,
e.g.,
1 bird, 3 caterpillars,
48 hrs. 48. is
A
number
that
an Abstract number, 49.
stract
is iiot
applied to a particular object
e.g., 1, 3, 48.
In multiplication the multiplier
is
always an ab-
number.
The most useful products are shown in the following tables. They should be committed to memory. 50.
1x1=
1
MULTIPLICATION
5x4 = 20
43
PRACTICAL ARITHMETIC
44 If it costs
2.
f 3 to harvest an acre of corn,
how much
will it cost to harvest 7 acres ?
many
tons will 6 acres produce If it costs
4.
5.
will
cost to treat the seed for 8
it
?
If
an acre of unfertilized land with unselected seed
produce 1 bale of cotton,
produce 6.
?
4 cents an acre to treat seed oats to pre-
vent oat smut, what will acres
how many
bales will 9 acres
?
If 1 acre of fertilized
land with very carefully
lected seed will produce 2 bales of cotton, will 9 acres produce 7.
in
in
At §50
problem 5 8.
A
?
what
will be the value of the cotton
a bale,
what
will be the value of the cotton
?
square field
12 rods on a side.
is
field,
If the school
day
is
it
take to plant 8 A.
the
If a child sleeps
hours does
it
sleep in 1
5 hours long,
10 hours each night,
week
school
how many
?
and 5 hours in school
day of 24 hours, how many hours
are left for play?
how many
?
?
If 10 hours are spent in sleep
in each
?
tons of coal at i 8 a ton
hours are there in a school week
14.
is
If it takes 7 lbs. of ordinary seed corn to plant an
how many pounds will 11. What is the cost of 6
13.
What
or the perimeter?
acre,
12.
se-
bales
a bale,
distance around the 10.
how many
?
At $50
problem 6 9.
how
If 1 acre of corn produces 9 tons of silage,
3.
in a school
week
MULTIPLICATION 15.
There are 12 inches
are there in 3 feet
in 1 foot.
What name
?
45
is
How many
inches
given to a measure 3
feet long ? 16.
in 9 hours 17.
man walks
If a
it
If a horse travels 6 miles
20.
21.
will
it
22.
will it 23.
how
far will
go in 9 hours
how
15 miles an hour,
how
?
an ocean liner goes 17 miles an hour, how far
If
go in 9 hours
?
an automobile travels 20 miles an hour,
how
far
go in 9 hours ? If
far will 24.
far will he
?
If a freight train averages
If
how
a bicycle rides 12 miles an hour,
he go in 9 hours
far will it
go
?
man on
If a
an hour,
steamboat goes 9 miles an hour,
If a
far will
far will he
?
go in 9 hours 19.
how
?
go in 9 hours 18.
3 miles an hour,
an express train averages 35 miles an hour,
it
go in 9 hours
To properly cook
how
?
a
ham
it
should be kept at sim-
mering heat 30 minutes for every pound of weight after first
being plunged into boiling water and kept boiling for
10 minutes. 25.
dozfen,
will it take to
cook a
9-lb.
ham
?
With spool cotton at 6 cents a spool or 50 cents a how many cents are gained by buying by the dozen
rather than 51.
How long
by the spool on a purchase
Find the product of 856 x
of 5 dozen spools
?
4.
Write the multiplier 4 under the multiplicand 856, placing the units of the multiplier under units of the multiplicand, and
begin at the right to multiply.
:
PRACTICAL ARITHMETIC
46 r^i-n
4 X 6 = 24. The 4 is written in units' column. The 2 tens are to be added to the product of tens. tens = 20 tens. 20 tens plus the 2 tens, carried from the multiplication of units, gives 22 tens, or 2
4x5
*'*-^*
hundreds and 2 tens. 2 tens is written under tens' column and 2 hundreds are to be added to hundreds' product. 4x8 hundreds = 32 hundreds, which with 2 hundreds makes .34 hundreds. 34 hundreds is written under hundreds' column. The product is 3424.
EXERCISE Find the product
X
25.
— WRITTEN
of
1.
2
365.
18.
3
X 1845.
35.
T
x
37,863.
2.
4 X 197.
19.
5
X 7543.
36.
6
x
31,245.
3.
3
X
754.
20.
6
X 1896.
37.
8
x
43,036.
4.
5
X 863.
21.
4 X 9806.
38.
5
x
68,734.
5.
7
X
189.
22.
3
X 5431.
39.
2
x
81,896.
6.
6
X
275.
23.
2
X
9864.
40.
8
x
52,783.
7.
4x986.
24.
4x1896.
41.
9x28,357.
8.
5
X
184.
25.
5
X 8652.
42.
7
x
48,021.
9.
7
X
689.
26.
8
X 6541.
43.
8
x
52,163.
10.
8
X
173.
27.
9 X 1864.
44.
4 x 59,136.
11.
9
X 602.
28.
8
x 8250.
45.
2 x 24,386.
12.
3
X 456.
29.
9
X 3475.
46.
9 x 12,854.
13.
6x629.
30.
4x8364.
47.
7x47,829.
14.
8
371.
31.
6
X 7928.
48.
9 x 79,836.
15.
7x864.
32.
3x6471.
49.
8x64,281.
16.
9
X 298.
33.
7
X 5498.
so.
3 x 97,645.
17.
3x672.
34.
9x3762.
51.
6x58,792.
X
MULTIPLICATION 52.
What
effect does it
47
have upon a number to move
it
one place to the left in the period?
Moving
a figure one place to the left has the same effect
by 10, e.g., 84 x 10 = 840. To multiply by 10, place a cipher at the right of the multiplicand, thus moving each figure one place to the To multiply by left and increasing its value 10 times. 100, place two ciphers at the right of the multiplicand. To multiply by 1000, place three ciphers at the right of the as multiplying it
multiplicand.
EXERCISE 26.— WRITTEN 1.
Multiply 42 by 10, by 100, by 1000.
2.
Multiply 24 by 10, by 100, by 1000.
3.
Multiply 93 by 10, by 100, by 1000.
4.
Multiply 930 by 10, by 100, by 1000, by 10,000.
5.
Multiply 860 by 10, by 100, by 1000, by 10,000.
Find the product
53.
QJo .f.
33680
of 842
x
40.
The product is found by multiplying the multiplicand by 4 of the multiplier as if it stood alone and increasing the product ten times by placing a cipher at the right.
EXERCISE
27.
— WRITTEN
1.
Multiply 35 by 40, by 400, by 4000, by 400,000.
2.
Multiply 350 by 40, by 400, by 4000, by 400,000.
3.
Multiply 3500 by
3,
by
30,
by
300,
by 3000, by
6,
by
60,
by
600,
by 6000, by
30,000. 4.
Multiply 3500 by
60,000.
:
PRACTICAL ARITHMETIC
48 54.
Rule for multiplying when either multiplier or
Multiply the multiplicand
multiplicand ends in ciphers.
by the multiplier without regard to the ciphers, and annex as
many
ciphers at the right of the product as are found
at the right of the multiplier 55.
and multiplicand.
Multiply 4280 by 200. Multiply as
4280 n/^^
856000
if
the problem read 428
ciphers the
X
2, secur-
In thus omitting
ing the product 856.
multiplicand
is
decreased
the
tenfold
and the multiplier one hundred fold, and the product is therefore decreased 10 X 100 or 1000 fold. The product then is 1000 x 856 or 856,000.
EXERCISE
28.
— "WRITTEN
Multiply 1.
876,420 by 3600.
7.
690,000 by 36,420.
2.
960 by 4600.
8.
86,290 by 720.
3.
87,640 by 300.
9.
370 by 6700.
4.
79,842 by 34,000.
lo.
296,380 by 3000.
5.
88,967 by 360.
li.
28,460 by 7200.
6.
37,900 by 67,000.
12.
67,981 by 37,100.
56.
Find the product of 627 x 5864.
To find the product of 5864 multiplied by 627 we must think of 627 as 6 hundreds plus 2 tens plus 7 units, or 600 20 7. Multiplying 5864 by each of these numbers
+
+
and c, we obtain the three partial products and 3,618,400. The sum of these products is This method of securing the partial products by
separately as in
a, h,
41,048, 117,280, 3,676,728.
separate multiplications
is
that in multiplying by a
number having ciphers
needlessly long.
Since
we know
at the right
:
PRACTICAL ARITHMETIC
60 5.
2473 by 906.
6.
2482 by 7002.
lO.
8345 by 9008.
7.
2954 by 906.
ii.
5878 by 809.
8.
4375 by 603.
12.
7854 by 508.
58.
9.
Rule for Multiplication.
7876 by 903.
— Write
under the multiplicand, units under tens, etc;
multiplier
units, tens
under
Multiply the multiplicand by each figure of
the multiplier. tial
the
Place the right-hand figure of each par-
product under the figure of the multiplier used to
obtain
it.
Add
the partial products.
Since regarding either
number
as multiplier or multi-
plicand does not affect the product, in practice the smaller
used as the multiplier.
is
EXERCISE
31.
—WRITTEN
Multiply 1.
7564 by 73.
14.
8957 by 79.
27.
2.
8715 by 86.
is.
6428 by 64.
28.
8163 by 799.
3.
4781 by 86.
16.
6753 by 97.
29.
2345 by 986.
4.
3692 by 90.
17.
8429 by 68.
30.
9543 by 576.
5.
5878 by 46.
18.
8867 by 29.
31.
7432 by 438.
6.
4689 by
19.
8456 by
32.
6473 by 823.
7.
5873 by 256.
20.
6397 by 86.
33.
9761 by 82.
8.
6381 by 634.
21.
9876 by 38.
34.
8472 by
9.
9537 by 752.
22.
2785 by 89.
35.
9781 by 73.
10.
2175 by 396.
23.
5432 by
92.
36.
9999 by
99.
11.
7009 by 438.
24.
7654 by 47.
37.
8756 by
65.
12.
8254 by 576.
25.
8765 by 59.
38.
9522 by
76.
13.
7826 by 86.
26.
3528 by 463.
39.
7543 by
57.
76.
25.
3264 by 287.
S4.
MULTIPLICATION
The
pupil
may
51
use the following problems sufficiently
to gain skill in multiplying.
Multiply the number at small a in the diagram
40-55.
by each number •
56—295.
in the larger circle.
Multiply each of the other numbers
smaller circle by each
number
in
the
in the larger circle.
similar circles, pasting
may assign these problems by chance by making them upon pasteboard, and mounting the smaller
one upon a pin so that
it
Note.
The
teacher
may
revolve freely.
:
MULTIPLICATION OF UNITED STATES
MONEY 59.
Multiply 195.35 by 25.
195.35 25
Multiply as in integral numbers, and point
47675
in the product as
many
^re places for cents in the multiplicand.
19070
12383.75
EXERCISE Find the product
of
32.
— WRITTEN
:
1.
2.
165.83
189.57
148.75
$46.98
9
8
28
35
3.
4.
5.
6.
7.
8.
1640.25
$542.40
$864.19
$506.69
.89
127
.95
1588
Multiply 9.
$43.95 by 875.
14.
$675.30 by 981.
$640.50 by 846.
is.
$1250.25 by 806.
$981.23 by 852.
is.
$3540.-30 by 905.
17.
$2859.65 by
is.
$875.90 by 350.
10. 11. 12.
$300.20 by 945.
13.
$756.25 by 372.
•
52
off
places for cents as there
79.
MULTIPLICATION
EXBBOISE Since each State
1.
senators,
A
2.
how many
A man
3.
week ?
senators are there in Congress
For a month
costs
will be the cost at
What
6.
7.
for a 9.
will
will be his
?
be his wages
cost as
him 16.50 each his coat, what is
?
23 yards of carpet for a
11.25 a yard
floor,
what
?
will be the cost of 18 cords of
wood
at f 3.25
?
What
ing 284 8.
and shoes
4 times as much
If it requires
a cord
What
26 days
What
earns $3.50 a day.
the cost of his outfit 5.
of
?
For 26 days ?
gun
his
represented in Congress by 2
is
If a hunter's coat
4.
and
— WRITTEN
mechanic earns $2.75 a day.
wages for a week ?
for a
33.
53
lbs.
will be the cost of 3 barrels of sugar weigh-
each at 6
cts.
How many feet of room 12
What
ft.
will
sizes are used,
a
pound
?
picture moulding will be required
long, 15
ft.
wide
?
moulding cost for the above room
one at ceiling at 2
cts.
if
two
a foot and a plate
rail at 7 cts. a foot ?
10.
A
storm moving eastward across the United States,
travelling at the rate of 36 miles an hour,
moves how
far
in 3 days ? 11.
If 1
cow drinks 73
pounds of water 12.
If it costs
will 16
lbs. of
water daily,
cows drink
?
28 cows
how many ?
69 cows
?
18.13 for labor and $7.39 for material
for each acre, to spray a vineyard 6 times, cost to spray 7 acres 6 times ?
what
will
it
PRACTICAL ARITHMETIC
54 13.
a
If
melon
100 gallons of Bordeaux mixture are sprayed upon field to
prevent blight, and to make this mixture
6 lbs. of blue stone, at 7 cts. a pound, at 1 ct. a pound, are used,
what
and the
What
will 1 spraying cost ? If
14.
unsprayed melons
and 12
lbs. of lime,
cost of labor
is
33
cts.,
will 6 sprayings cost ?
all die,
and sprayed melons
yield 150 baskets to the acre, at 76 cts. a basket, what is
the gain 15.
arid
If
by sprajdng
8 acres of melons?
unsprayed grape-vines yield 1
sprayed vines yield 4
lbs. each,
spraying an acre which yields 376 If
16.
spraying potatoes
lb. for
what
lbs.
is
each vine,
the gain by
when not sprayed?
5 times increases the yield
68 bushels per acre, and spraying 3 times increases the yield 32
what
bushels,
sprayings?
With
is
the increase from the last 2
potatoes at 65
cts.
a bushel, what are
the 2 extra sprayings worth to the farmer?
an average and poor seed yields 8034 lbs. per
If the best selected potato seed yields
17.
of 11,100 lbs. per acre
how much more
acre,
will 9 acres yield
when
planted
with good seed than with poor seed? If a dairy
18.
many pounds
cow
eats 40 lbs. of silage each day,
of silage will it take to feed 17
how
cows 180
days?
One
19.
acre,
field of
and another
tion, yields
wheat of 9 acres yields 22 bushels per
of the
same
31 bushels an acre.
size,
due to better prepara-
What
is
the difference in
the value of the wheat produced on the two fields
wheat 20. lint
is
worth 87
One
cts.
when
per bushel?
seven-acre field of cotton produces 215 lbs. of
cotton and 430 lbs.
of
seed on each acre, while
MULTIPLICATION another
1000
field of the
lbs. of
same
size
produces 500
What
seed per acre.
a
cts.
If
21.
pound and seed
1 ct. a
when
is
worth
in each pound,
how many weed
seeds are
?
sample of unclean clover seed was found to con-
tain 27,600
sowed
cotton
pound?
there in each bushel weighing 60 lbs.
A
and
an unclean sample of clover seed contains 990
weed seeds
22.
lbs. of lint
the difference in the
is
value of the crop from the two fields
11
55
weed seeds
to an acre,
in each
pound.
how many weed
15
If
lbs.
were
seeds were planted on
each acre? 23.
A
sample of clover seed offered for
338,300 weed seeds in each pound.
contained
sale
How many weed
seeds were there in each bushel of 60 lbs.? 24.
What
is
the value of an acre of celery yielding
1500 dozen stalks at 26 ing expense 25.
of
is
259,
cts. a
what
is
dozen?
soil.
how much
feet in the
If this soil
will the
If the
annual grow-
the profit per acre ?
There are 21,780 cubic
an acre of
foot,
$*
weighs 79
upper 6 inches of
upper 6 inches lbs. soil
per cubic
on an acre
weigh ? 26.
A
man bought
a car-load of cattle, 25 in number,
each animal weighing 961
lb., at
4
cts. a
pound.
After
each had gained 889 lbs. in weight, they were sold for 6
cts.
a pound.
What was
his profit or loss
consumed was worth $977, and the
if
the feed
cost of labor to
do the
feeding 1125?
A man
bought 1728 acres of land at 167 an acre. He spent $3600 on improvements and then sold 79 acres at 27.
PRACTICAL ARITHMETIC
56
$170 an
160 acres at $165 an
acre,
acre',
215 acres
$148 an acre, 450 acres at $132.18 an acre, and the How much did he gain or lose ? at $45 an acre. 28.
A
common
house-fly lays her eggs in broods of
At
about 120 each.
this rate,
how many
expected from 29 overwintering
warm days 29.
of spring
be
first
?
Mosquitoes lay eggs in masses of about 350 each.
the hatching period from 9 such masses
The white ant
often lays as
in a day.
How many
ing ants at
tlie
31.
may
flies
during the
flies
How many mosquitoes may be expected 30.
at
rest
end
A man in month
may
?
many
as 80,000 eggs
be expected from 30 lay-
of 4 days' laying
?
each of his working months earns $67.50
and spends $28.37. ing one
eggs
the end of
at
What
are his savings yearly, allow-
of vacation during
which he spends $56.97
more than usual ? 32.
A
man bought
long, at 86 cts. a yard. 33.
A
39 strips of carpet, each 17 yards
What
did they cost
?
teamster hauling 4 loads of sand a day, of 27
cubic feet to the load, hauls
how many
cubic feet in 12
days? 34.
Five boys purchase a camp outfit at the following
prices: a 9-ft. tent for $5.80,
two hammocks
at 55 cts.
each, five bathing suits at 55 cts. each, 1 clothes
60
cts.,
2 pairs of oars each.
bag
at
camp stove at $1.74, one boat at $19, at $1 a pair, 4 fishing outfits at $1.89
1 junior
What was
Two
boys paid
left for
the other
the cost of the outfit?
toward the
outfit $12.22.
three to pay
?
What was
DIVISION 60.
If 3 gallons of
milk yield 18 ounces of butter,
many ounces will 1 gallon yield? To solve this problem we must separated into 3 equal parts.
how
think of 18 ounces as
Separating 18 ounces into
3 equal parts will give 6 ounces in each part.
The
61. is
process of separating a
number
into equal parts
called Division. 62.
The number
to be divided, or the
separated into equal parts, 63.
The number
is
number
that indicates into
how many
parts the dividend
is
to be separated, or the
which the dividend
is
to be divided,
64.
The
to be
called the Dividend.
is
equal
number by
called the Divisor.
by Division
called
the
number of ounces of butter contained milk we divided 18 ounces by 3 (not by 3
in 1
result
obtained
is
Quotient.
To
find the
gallon of lons)
which gave
gal-
Three, the divisor in this
6 ounces.
an abstract number, and the term 3 gallons serves only to indicate the number of groups into which
problem,
is
18 ounces 65.
is
When
to be separated.
the dividend
is
concrete and the divisor
abstract, the quotient is like the dividend,
=6
oz. 57
e.g.,
18
oz.
-f-
is
3
:
PRACTICAL ARITHMETIC
58
When
66.
must be 18 oz.
-=-
the dividend and divisor are concrete, they
alike
6 oz.
will
be abstract,
e.g.^
= 3.
Division
67.
and the quotient
is
indicated by the sign, -^, or
by writing
the dividend above the divisor with a line between, thus
18
3
-=-
68.
= 6,
or
When
JgS.
= 6, is
by 3 equals
6.
not exact, the part of the
is
called the Remainder, e.g., 15
-r-
2
=
with 1 as a remainder.
When
two or more numbers are multiplied together produce a product, e.g., 3 x 6 = 18, the numbers so
69.
to
read, 18 divided
the division
dividend remaining 7,
is
multiplied are called the Factors of the product. 70.
In the problem 18
product 18 and one factor
may
-h 3, 3,
observe that
we have
to find the other factor.
the
We
therefore think of division as the process of finding
one factor when the product and the other factor are given.
EXERCISE Find the quotients sion correct 1.
34.
— ORAL
of tlie following
by multiplying the
and prove the
factors together
divi-
PRACTICAL ARITHMETIC
60 12.
A
French franc equals about 20
How many 13.
cts. in
our money.
francs in $3.00?
A German mark equals about
24
in our money.
cts.
How many marks in |2.88? 14. An Italian lira equals about 20 cts. in our How many lire in $5.60? 15. A Dutch florin equals about 40 cts. in our How many florins in $3.60? 16. An Austrian florin equals about 36 cts. money. How many florins in $1.80? 17.
what 18.
At is
19.
21.
7
days in 1 week;
in 42 days
?
If a
man
in 98 days
?
how many
week's in
?
earns $ 8 while a boy earns $
3,
how much
boy earn while the man earns $48?
If
an adult
120 grams
much
in our
the cost of each suit?
will the 20.
money.
$ 72 a dozen for suits for sixteen-year-old boys,
There are
28 days
money.
man
of protein,
eats 360
does he average per meal If a laboring
grams
and 60 grams of
man
of carbohydrates,
fats each day,
how
?
eats 150
grams
of
protein, 99
grams of fats, and 516 grams of carbohydrates each day, what is the average per meal ? 22.
If a
man
can do as
much work
require 8 23.
men
If a
to build
man
how
it it
it ?
can hoe twice as
boys and 3 men hoe a
amount does each hoe
and
long will
as 3 boys,
requires 48 boys 3 days to build a fence,
much
field of 5 acres ?
as a l)oy, in
and 4
a day, what
SHORT DIVISION When
71.
the divisor
is
so small that the
performed mentally, the process 72.
Divide 9672 by
The
4)9672 2418
is
work can be
called Short Division.
4.
divisor
is
written at the left of the dividend
with a curved line between them and a line underneath the dividend. To divide 9672 by 4, begin at the left and find how many times the divisor, 4, is contained in the first figure of the dividend. 4 is contained in 9 two times, with a remainder 1. Reduce the 1 to the next lower order, making 10, which with 6 makes 16 4 is contained in 16 four times. 4 is contained in 7 one time, with a remainder 3. This remainder reduced to the next lower order makes 30, which with 2, the next figure of the dividend, makes 32 4 is contained in 32 eight times. The quotient, therefore, is 2418. ;
;
73.
Divide 3651 by
7.
7)3651 521 with 4 remainder,
commonly written with 6 makes 36.
7
is
7
is
not contained in the
first
figure of the dividend, 3, so the
3 must be reduced to the next lower order, making 30, which contained in 36 five times, with 1 re-
4.
Reduce 1 to next lower order, making 10, which with 5 makes 15. 7 is contained in 15 two times and 1 remain1 is reduced to next lower order, making 10, which with der. mainder.
1
makes
der.
The
11.
This
7 is contained in 11 one time, with 4 as remainfinal
remainder
quotient, therefore,
is
is
indicated with the quotient.
621, with 4 remainder. 61
:
PRACTICAL ARITHMETIC
62
EXERCISE Find the quotient
36.
— WRITTEN
of
1.
376- h2.
15.
8736
7.
29.
56,216^-12.
2.
695- 4-5.
16.
7086^6.
30.
83,542
31.
64,902-11.
-T-
-f-
15.
3.
459- 4-9.
17.
8232-4.
4.
376
4-5.
18.
8361^9.
32.
85,563
-=-14.
5.
714 4-4.
19.
5643
-^ 8.
33.
37,642
-^ 12.
6.
628 4-7.
20.
3716-^7.
34.
48,527-^-15.
7.
984--4-8.
21.
5472^6.
35.
87,585-9.
8.
594-4-7.
22.
7483
-f-
5.
36.
96,464
-=-22.
9.
4895
23.
8721
-f-
7.
37.
83,691
-r-
77,585^11.
-=-6
12.
10.
9656
24.
9212^9.
38.
11.
7985 ^9
25.
73,236-4-11.
39.
23,075-14.
12.
7983
26.
24,631-4-12.
40.
89,576
13.
8457
27.
75,477^12.
41.
98,254-15.
14.
2708
28.
36,286^21.
42.
61,082-4-21.
6
200?
How many tens in 20? How many How many thousands in 2000?
To
divide by 10, 100, 1000, etc., set off as
74.
-V-
11.
hundreds
many
in
figures
at the right of the dividend as there are ciphers in the divisor.
The
The
figures
thus set
off
other figures are the quotient,
as remainder.
468
-4-
100
= 4,
EXERCISE
are
e.g.,
45
the remainder. -^
10
= 4, with 5
with 68 as a remainder.
37. -.ORAL
1.
57,683
100.
3.
38,425^100.
2.
76,493-4-100.
4.
54,580-100.
-=-
:
DIVISION
63
5.
42,676^-1000.
8.
57,826
6.
26,257^1000.
9.
32,814-10,000.
7.
14,637^1000.
10.
82,740^-10,000.
75.
-- 10,000.
Divide 4560 by 200.
Cut off ciphers at the right of the 200, also two figures at the right of the dividend. Dividing 45 by 2 gives 22, with 1 remainder. The whicli represents 100, added to the 6, wliich represents 60,
200 )4560
221-^
1,
gives 160 remainder.
When off,
and
the divisor ends in one or more ciphers, cut these
number of figures from the Then divide by the figures re-
also cut off an equal
right of the dividend.
maining.
Place the figures cut
at the right of the remainder,
if
off
from the dividend
there
is
form the true remainder.
EXERCISE Find the quotient 1.
of
38.
— WRITTEN
a remainder, to
LONG DIVISION 76.
Long division
exception that quotient
is
all
the same as short division, with the
is
the processes are written in
written over the dividend, the
The
full.
first figure of
the quotient being written over the right-hand figure of the dividend used in obtaining 77.
it.
Divide 32,962 by 49. tabi.e ^p Peoditots
found helpful in the beginning of the study of long division to form a table of products of the divisor with numbers from 1 to 9. The problem is arranged as in short division, with the exception that the quotient is written either above (or at the right of) the dividend. Since 49 is not contained in It will be
32,
we must
use the
dividend, 329, for the
first
is
4.
three figures of the
first partial dividend.
consulting the table of products,
294
= 49 2 x 49= 98 3 x 49 = 147 v 49 = 196 . aq^qa^ ~ o X "iJ = -94 7 X 49 = 343 8 x 49 = 392 1 Xt;9
we
By
find that
the largest of the products that does
9
x
49=
441
not exceed the partial dividend, 329.
294 49
49)32962 ^^^
is
is the product of 6 x 49 hence, contained in 329 six times. 6 is ;
written over the 9 of the dividend.
The product
of the 6
x
49, 294, is sub-
'^^^
tracted from 329, v/hich leaves as a
343
remainder 35.
132
dividend,
The next
figure of the
annexed to form the secdividend. 343 is the largest
6, is
98
ond
34 remainder,
of the products that does not exceed
partial
this partial dividend, 366. 0,4
343
is
the
DIVISION
65
product of 7 X 49 hence, 49 is contained in 356 seven times. 7 is written over the 6 of the dividend and 343, the product of ;
X 49, is subtracted from 356, which leaves 13 remainder. The next figure of the quotient, 2, is annexed to form the third 7
partial dividend, 132.
98 is the largest of the products that does not exceed this partial dividend, 132. 98 is the product of 2 X 49 hence, 49 is contained in 132 two times. 2 is writ;
ten over 2 of the dividend and 98 ing 34 the final remainder. 78.
subtracted from 132, leav-
Divide 1,270,563 by 396. -'^fter
32081^-5-
^^^
some
practice the quotient figures
can be estimated without making the table of products. The first partial dividend is 1270. 396 is contained in 1270 three times. 3x396 = 1188. 1188 subtracted from 1270 leaves 82 remainder. Annexing 6 gives the second partial dividend, 825. 396 is
-^
il££_ '^-•^
'^^
3363 3168
2 x 396 = 792. from 825 leaves 33 reAnnexing 6 gives the third par-
contained in 825 two times.
792 subtracted
195
mainder. tial
is
dividend, 336.
396
is
not contained in 336, so a cipher
is
written over the 6 of the dividend and the next figure of the
annexed to 336 to form the next partial diviis contained in 3363 eight times. 8 x 396 = 3168. 3168 subtracted from 3363 gives 195, the final remainder. dividend, 3,
is
79. I.
.
396
dend, 3363.
Rule
for
Long
Division.
Write the divisor
at the left of the dividend with a
curved line between them. take the fewest
dend that
number
For the
first partial
dividend
of figures at the left of the divi-
will contain the divisor,
and write the
partial
quotient over the right-hand figure of the partial dividend. II.
Multiply the divisor, by this quotient, and write the
product under the partial dividend used.
PRACTICAL ARITHMETIC
66
Subtract this product, and to the remainder annex
III.
the next figure of the dividend for the second partial dividend.
Divide as before, and continue the process until
IV.
the figures of the dividend have been used to
make
all
partial
dividends.
V. If there be a remainder, write Proof.
and
Find the product
to this product
work
is
it
with the quotient.
of the divisor
add the remainder,
if
and quotient, any.
correct, the result will equal the dividend.
If the
DIVISION
67
:
DIVISION OF UNITED STATES
MONET
Divide $741.32 by 86.
80.
$8.62 oo^ijj
l^l.oz
688
Divide as in integral numbers, writing the of the quotient over the right-hand
first figure
533
figure of the first partial dividend.
516 JJ2
decimal point in the quotient directly over the decipoint in the dividend.
Place the
™^
172 81.
Divide $46.75 by $.25.
187 25)4675
Change the dividend and divisor to cents which by 25 cents. The
25 2^7 onA
gives 4675 cents to be divided
answer
is 187.
~175 175
BXEECISB Find the quotient
40.
—WRITTEN
of
1.
$17.28^12.
6.
$52.56^16.
2.
$17.28 ^$12.
7.
$52.54 -$16.
3.
17.28^.12.
8.
$52.54 -.16.
4.
856.90^41.
9.
$438.90-21.
5.
856.90
^$41.
10. 68
$438.90- $21.
DIVISION
EXERCISE 1.
If
If 27 bushels of
for
the
lbs.,
what
is
the
If
what
lbs.,
is
the
?
weigh 1792
lbs.,
what
is
the
37 bushels of peas Aveigh 2220
lbs.,
what
is
the
If 32 bushels of corn
weight of 1 bushel of peas 6.
is
wheat weigh 1620
weight of a bushel of corn 5.
what
1 bushel of oats ?
weight of a bushel of wheat 4.
lbs.,
?
19 bushels of oats weigh 608
If
weight of 3.
— WRITTEN
bushels of rye weigh 448
8
weight of 1 bushel 2.
41.
69
How many
?
?
boys' sweaters at 95 cts. can be bought
16.65? 7.
A
double
plow
harness
$11.48 and a
costing
double carriage harness costing $45.92,
how many plow
harnesses can be had at the cost of 1 carriage harness 8.
If a beef animal
weighs 1284 9.
weighs 960
lbs. at
the beginning
feeding period, and after being fed
of the
40
If
how many
lbs.,
how much
lbs.
of silage
did
gain a day
162 days
?
the ration for a dairy cow,
is
acres of corn will
it
?
it
take to produce silage for
15 cows for 150 days, 1 acre of corn producing 18,000
lbs.
of silage ? 10.
A
base-ball outfit for the Asheboro
Nine consists of the following Association ball 70
cts.,
articles
:
High School an American
9 Junior League bats at 25 cts.
each, 1 catcher's mit fl.OO, 3 fielder's gloves at 55 cts., 1
30
first-baseman's cts.,
1
mit 90
cts.,
amateur mask 50
4 cts.,
infielder's
9
pairs
gloves
at
shoe plates
PRACTICAL ARITHMETIC
70
10
per pair, catcher's breast protector fl.lO, 9 uni-
cts.
What
forms at $1.25 each, 9 sweaters at $1.25 each. part of the entire cost should each member pay ?
The
11.
eleven of Shelby ville
foot-ball
equipped with the following articles ball
60
with bladder $1.50, each, 11
cts.
pairs of
15
inflater
boy's
:
cts.,
Academy is Rugby foot-
11 jackets at
pants at $1.00 eash, 9 pairs
shin guards at 45 cts. per pair, 6 pairs shoulder pads at
30
per pair, 1 head harness at 75
cts.
the cost of the outfit' does each
The Asheboro High School
12.
ordered a tennis outfit as follows 75
What each
will
part of
Tennis Club
Girls'
2
hardwood cts.
per
poles at
set,
court
net $2.00, 2 back-stop nets $2.15 each.
cost to equip three courts
member pay
if
the club
is
The Croquet Club has
13. set.
cts., it
:
guy ropes and pins 23
a pair,
cts.
marker 95
What
cts.
member pay ?
?
What
part will
composed of 40 members ? 2 croquet sets at $2.50 a
What
There are 16 members.
part of cost does
each pay? 14.
If a
and puts it
on 5
man buys
1 ton of commercial fertilizer for $24
on 4 acres, and another ton for $ 20 and puts
it
acres,
how many
additional pounds of cotton to
the acre must he produce on the
pound
to
thereon 15.
first field at
pay for the greater cost of the
10
fertilizer
cts. a
used
?
The following
results
for
a period
of
5
years'
spraying Irish potatoes to prevent disease are recorded
New York
:
in
gain per acre due to spraying every 2 weeks,
123, 118, 233, 119, 63 bushels;
gain per acre due to 3
sprayings, 98, 88, 191, 107, 32 bushels.
What was
the
DIVISION
71
average gain for the 5 years with 3 sprayings ? the average gain from spraying every 2 weeiis ?
What was If potatoes
average 57
cts. a bushel and spraying cost on an average an acre each time, what was the average gain from spraying 3 times?
77
cts.
16.
If 5 gallons of spraying
an apple orchard of 1000
tree in
mixture be used to each trees and Paris green at
cts. a pound be used, 1 lb. to 150 gals, of water, what would be the cost of the Paris green for 2 sprayings? What would it cost per tree?
20
A pig weighing
50
lbs. cost
of corn at 50 cts. a bushel
and 400
17.
After eating 8 bus.
14.
lbs. of
11 a hundred pounds, it weighs 250 pound must it be sold to make a net
wheat middlings
At how much
at
lbs.
a
profit of
18.
What
19.
At
is
f3?
the average of 79, 83, 160, 74, and 62?
three places in the Florida peninsula the
num-
ber of partly cloudy days in the year was 233, 145, 113, the
number
of cloudy days
was
What was
59, 74, 81.
the
average number of cloudy, partly cloud}', and clear days as
shown by these observations?
A
man bought 782
acres of land for $98,762 and $18 an acre. Wliat was the average price paid? What was the average gain or loss per acre ? 20.
sold
it
21.
at
The deaths from consumption
in 1900
were 111,059.
in the
W^hat was the average number of
deaths for each day in the year (365 days) 22.
The deaths from typhoid
for 1900
daily ?
were 35,379.
United States
?
fever in the United States
What was
the average
number
:
CANCELLATION 82.
How many
83.
Divide 24 x 12 by 6 x 12.
x 6 contained in 12x6? How many times is 3 x 10 contained in 6 x 10? How many times is 6 x 7 contained in 12 x 7 ? times
6x12 = 72
24x12 = 288 What
factor
If the factor
dend and
common
is
12
3
is
is
3
5x^7x^
^1-
78x2 ~
= 4.
struck out, or cancelled, from both
divi-
'^'
24^6 = 4.
2.
Cancelling the common factor 2 from the 4 of the dividend and the 2 of the divisor gives 2 in the dividend.
common gives
dividend.
72
divisor, does it affect the quotient?
Divide 5 x 27 x 4 by 18 x
2
h-
to both dividend and divisor?
2iiil| = 24 or 6 X ;i;2 6
3
288
Cancelling the
from 18 gives 2; from 27 Cancel 2 from both divisor and
factor 9
3.
Multiplying the remaining factors of the dividend
gives the quotient, 15.
84.
is the process of shortening work in by removing or cancelling equal or common from the dividend and divisor.
Cancellation
division factors
EXERCISE
42.
— WRITTEN
Solve by cancellation 1.
Divide 7 x 6 x 16 by 6 x 8 x 72
7.
CANCELLATION
73
2.
Divide 11 x 27 x 30 by 9 x 15 x
3.
Divide 15 x 48 x 70 x 11 x 40 by 30 x 16 x 7 x 22 x 50. Divide 84 x 18 x 5 by 91 x 4 x 15.
4.
3.
5.
Divide 27 x 12 x 35 x 14 by 9 x 3 x
6.
Divide 48 x 35 x 42 x 54 by 12 x 7 x 6 x
7.
Divide 63 x 36 x 48 x 96 x 27 by 81 x 9 x 12 x 48.
8.
Divide 420 x 68 x 88 x 22 by 210 x 11 x 44.
9.
Divide 42 x 35 x 56 x 4 x 12 by 28 x 49 x 14 x 10.
10.
Divide 17 x 9 x 12 x 11 x 28 by 34 x 6 x 72 x 6 x 22.
11.
Divide 24 x 15 x 8 x 4 x 7 by 14 x 8 x 6 x
12.
Divide
13.
18 cows, each eating 4
9.
4.
20xl6x5x3x6by5x8x3xl0x6.
day, can be fed
how
how many pounds
cotton-seed meal a
lbs. of
long on 360
72 quarts of berries at 9
14.
5.
lbs. of
cts.
meal?
a quart equal in value
of sugar at 6 cts. a
pound?
15. How long will it take a horse travelling 8 miles an hour to go as far as an express train goes in 3 hours at 32 miles an hour ?
If
16.
many
42 bushels of wheat make 9 barrels of
bushels will
How many
17.
must be given 35
cts.
18.
in
it
take to
make 27
how
barrels?
bushels of corn worth 49
cts.
a bushel
exchange for 63 bushels of oats worth
a bushel?
How many
bushels of oats worth 28
must be grown on an acre to equal in value bushels of corn worth 42 cts. a bushel? 19.
flour,
A lumber mill
How many
cuts 60,000
ft.
of
cts.
a bushel
a crop of 56
lumber in 6 hours.
feet will it cut in 3 days of 8 hours each
?
PRACTICAL ARITHMETIC
74
exercise 43. — "written
Review Problems
The population
1.
Chicago in 1840 was 4470,
of
in
was 1,698,675. What was 1870 it was the yearly increase in population from 1840 to 1870? What was the yearly increase from 1870 to 1900 ? What 300,000, in 1900
was the daily increase
The value
2.
?
the hay crop
of
States for five years
1902
it
was
raised in
as follows
:
What was
.
the United
the total value
for five years ?
average value
What was the ?
How
much
below the average was the value of the smallest crop
The value
3.
of the corn exported
States for five years
was
as follows
?
from the United
:
1902
116,185,673.
1903
140,540,673.
1904
$30,071,334.
What was its total value? What was its average value? What was the difference be-
1905
147,446,921.
tween the largest and
1906
162,061,856.
smallest
4.
A
the
amount exported?
farmer has a small herd of 5 dairy cows which
produce as follows: No. No. No. No. No.
= 396 lbs. butter a year, at 26 cts. a pound, = 323 lbs. butter a year, at 26 cts. a pound, 3 = 257 lbs. butter a year, at 26 cts. a pound, 4 = 176 lbs. butter a year, at 26 cts. a pound, 5 = 147 lbs. butter a year, at 26 cts. a pound, 1
cost of feed $59.00
2
cost of feed $57.50
cost of feed $55.67 cost of feed $52.38 cost of feed $49.84
:
REVIEW PROBLEMS
What
is
the yearly profit on the herd
or loss ou each
75
What
?
is
the profit
cow?
If he sells Nos. 4 and 5 and buys instead 2 other cows which produce as follows:
Xo. 6 Xo. 7
= =
298
lbs.
276
lbs.
what will be
butter a year at a cost for feed of $57.23 butter a year at a cost for feed of $54.50
his yearly profit
The value
5.
ou the herd? on each cow?
of the cotton exported
from the United
States for 5 years was as follows
1902
....
1903
.
1904
.
1291,598,350. xA/ n«!>+
t^of.-)
1905
.
1906
.
.
.
A
6.
TUT"
n
CI
-fhci ^-*-»fril
iT-olna
,-..,_._.
OAQ
Of?
the exported cotton?
r\-t
What
I
!iS381,398,939.
1401,005,921.
farmer delivered
'^^'
^^^'^
^""''""^^
^"^"^^
^^^"^^ to
a
creamery during
May
3674 lbs. of milk, during June 4876 lbs.', July 3929 lbs., August 3167 lbs., September 3067 lbs., October 2913 lbs. What was the total number of pounds during the half year?
During November a farmer delivered to the creamery 2974 lbs. of milk, during December 2984 lbs., January 2798 lbs., February 2890 lbs., March 3043 lbs., April 3364 lbs. What was the total number of pounds deliv7.
ered during the latter half of the year?
was
this than in the
8.
What number
warmer
How much
less
half of the year?
multiplied by 256 with 23 added to
the product will give 5399? 9.
will
Light travels 186,680 miles a second. it
travel in 29 seconds?
How
far
PRACTICAL ARITHMETIC
76 10.
will
it
11.
Sound
How
1130 feet in a second.
travels
far
travel in 29 seconds ? It
How
earth.
round numbers, 25,000 miles around the many times will a light wave go round the
in
is,
earth in a second? 12.
visible 13.
What
the
is
number nearest
by 234 without
is di-
This being used on 4,970,129 farms
spent for fertilizers. of
how many
dollars'
worth on each farm ?
In 1880 the expenditure of the United States for
fertilizers
in 1900 for
which
In the United States in 1899, $49,099,936 was
was an average 14.
to 3980
a remainder?
it
in 1890
was $28,500,000, was $54,750,000.
fertilizers
it
was $38,500,000, more was spent
How much
1900 than in 1880? in 1900 than
in
How much
1890? in 1890 than in 1880?
less in
in
1900
than in 1880 and 1890 together? 15.
The shrinkage
in weight of corn
tween December and
May
about 9
is
dred pounds.
What would
bushels (1 bu.
= 56 lbs.)? The
an average 4
cts. a
Will this advance
lbs.
16.
price of corn advances on
bushel between December and May.
in price
The expenses
may
be-
for every hun-
be the loss in weight of 900
compensate for the
shrinkage with corn in December at 57
the seed
due to drying
of raising
loss
due
to
per bushel?
an acre of white pine from
be stated as follows
Cost of seedlings, $2.00.
cts.
:
Cost of land, $6.00.
Trans-
planting to nursery, $1.21.
Transplanting to
Taxes,
Taxes, second decade, $3.04.
first
decade, $1.69.
Taxes, third decade, $4.39.
What is the total
cost ?
field,
$5.45.
Taxes, fourth decade, $5.74.
REVIEW PROBLEMS
77
CUTS OE BEEF
The above tive weights,
animal 1550
illustration shows butchers' and Western retail prices
;
lbs.,
1.
Neck, 40
weight of
live
dressed weight of carcass 1046
Cheap Cuts
No.
cuts, their rela-
VALirABLE Cuts
@ 4 cts.
lbs.
lbs.
No.
Prime
3.
of Rib, 117 lbs.
@
16
cts.
No.
2.
Chuck, 237
lbs.
@ 7 cts.
No.
No.
8.
Shank, 30
lbs.
@
2 cts.
No.
Porterhouse Steak, 103
4.
@
22 .5.
lbs.
cts.
Sirloin Steak, 87 lbs.
@
18
cts.
No.
9.
No.
10.
Plate, 138 lbs.
No.
11.
Shin, 23 lbs.
17.
Flank, 52
The
it
@ 5 cts. @ 5 cts. @ 4 cts.
difference
dressed weight
was
lbs.
is
No.
6.
No.
7.
10
Rump, 36 lbs. @ 10 Round Steak, 183
between the
?
lbs.
@
cts.
live
weight and the
the waste in slaughtering.
in the animal illustrated
cts.
How much
PRACTICAL ARITPIMETIC
78 18.
The
and 11 are and are all
parts of the carcass in the
numbered
1, 2, 8,
9,
10,
forward and lower parts of the animal,
How many
less valuable.
these cheaper parts
What
?
is
pounds are there
their total value
in
?
19. The parts numbered 3, 4, 5, 6, and 7 are in the hind quarters and upper portion of the body, and are more How many pounds are there in all these parts? valuable.
What 20.
is
their total value
What
is
?
the difference in the total weights of the
cheaper and the more expensive cuts ference in their values
?
What
the dif-
is
?
pound of the entire What is carcass? What is the average value per pound of the cheaper outs? What of the more expensive cuts? the average value per
21.
22.
One animal weighing 1550
lbs.
produces a dressed
carcass of 1046 lbs. that sells for 9 cts. a
pound
;
an
ferior animal of the same live weight produces a carcass
990 is
lbs. that sells for 8 cts.
a pound.
the value of the better animal
How much
in-
of
greater
?
POULTRY 23.
If 1 gallon of
water glass mixed with 16 gallons
makes a solution which will preserve 50 dozen what is the gain in putting up 25 dozen fresh eggs summer when they are worth 15 cts. a dozen and keep-
of water
eggs, in
ing them until winter 24.
27
cts.
If a lot of 8
a dozen,
when they
are
worth 25
dozen eggs that weighs 9
how much do they bring
a
cts. a
dozen?
lbs. sells for
pound?
What
will be the gain in selling another lot of 8 dozen eggs
that weighs 14 lbs. for the same price per pound instead of the usual
way of
selling
them
at the
same price per dozen ?
EEVIEW PROBLEMS
A flock of hens averages 12
25.
yearly.
If
dozen eggs for each hen
they each consume $1.45 worth of feed, what
pay
for their care, losses
from death, and
is
left to
if
the eggs bring an average price of 26.
If to raise
feed $3.87, what
"22 cts.
If a flock of
hens fed dry mash and grain produces cts.
a dozen, and a second
same number fed wet mash and grain pro-
flock of the
duces 163 dozen eggs at a cost of 10
much 28.
109
greater
29.
is
the profit from the
dozen
If the total
lbs.,
what
If
for
:
and brooders fl.OO,
the average cost per chick?
is
216 dozen eggs at a cost of 11
for 22 cts. a
profit,
a dozen?
73 chicks to 8 weeks of age costs
eggs set $2.50, heat for incubators
27.
79
is
cts.
a dozen,
first flock if
eggs
how sell
?
weight of the chicks in problem 26 be
the average cost per
they are sold at 23
cts.
pound
each,
?
what remains
to
pay for the labor and profit? 30.
By
inquiry find the local prices and costs in your
neighborhood, and substitute them in problems 25 and 26.
PRACTICAL ARITHMETIC
80
PREVENTION OF PLANT DISEASES
Total Yield of Marketable Potatoes from Two Rows Sprayed
Total Yield of Marketable Potatoes from Two Rows not Sprayed 31.
In treating seed oats to prevent oat smut, 1 ounce
of formalin is
used to every 3 gallons of water, and 1
lon of this mixture suffices for 1 bushel of oats.
many ounces
of formalin will be
gal-
How
needed to treat 24 bushels
of oats? 32.
Using 3 bushels
of seed oats to the acre,
what
will
be the cost of sufficient formalin to treat seed for 80 acres at 35 cts. for each 16 ounces 33.
?
The Bordeaux mixture
consists of blue stone 5
lbs.,
and water 60 gallons. With blue stone costing 7 cts. a pound and lime at 1 ct. a pound, what will the materials for 150 gallons of Bordeaux mixture cost ? lime 5
34.
lbs.,
It requires
about 150 gallons of Bordeaux mixture
to spray an acre of Irish potatoes once.
materials for 3 sprayings cost?
What
will the
REVIEW PROBLEMS
81
Spraying apple trees twice with Bordeaux-Parisgreen mixture to prevent worminess costs 13 cts. for each 35.
If this increases the value of the yield f 1.37 for
tree.
each tree, what will be the gain by spraying an orchard of 87 trees ?
The
36.
and materials
cost of labor
spraying an
for
acre of grapes to prevent the black rot being as follows,
what
is
labor
and materials
the cost of each spraying and the total cost of for the six sprayings?
Cost op Material
1st
spraying
2cl
3d
....
Cost of Labor
$0.45
$1.13
spraying
0.68
1.13
spraying
0:68
1.10
4th spraying
1.86
1.47
5th spraying
2.06
1.65
6th spraying
2.06
1.65
I^
Total 37.
The average
Total Cost
IZI
cost of spraying Irish potatoes to pre-
vent blight being $5.18 an acre, and the average increase in value being
$19.07 an
from spraying
?
38.
acre,
what
is
the average profit
Six unsprayed apple trees yielded 188 sound apples
and 4244 rotten apples.
Six similar trees spra3'ed yielded
What was the gain What was ?
8674 sound apples and 989 rotten ones. for each tree in
sound apples from spraying
the decrease in rotten apples for each tree 39.
What would
it
cost
to
?
spray the potatoes and
apples and to treat all the oat seed planted within a mile of
your school? 40.
What would
the profit be
if
it
equalled per acre
the increase indicated in the above problems
?
PRACTICAL ARITHMETIC
82
A Bountiful Harvest
FARM CROPS The average
41.
cts.
for the
United States
1906 was about 15 bus., the price was
for each acre in
67
wheat
yield of
What was
a bushel.
the value of the yield per
acre? 42.
The average
duced in the 43.
37
If it
for
cts.
yield in some States
How much
others 32 bus.
latter
costs
is
about 10 bus.,
greater value per acre
is
in
pro-
than in the former?
$2.16 for
housing, $1.20
fertilizer,
96
cts.
threshing,
for
for seed,
76
cts.
for
marketing, and 12.81 for rent per acre in the United
what
States,
is
the average
left
to
pay for labor and
profit ? 44.
What
is left
for labor
and
profit in the low-yielding
States? 45.
What
is
left
for
labor and profit in the higher-
yielding States? 46.
If
one farm yields 40 bus. an acre and another farm
16 bus. an acre, each at a cost of $9.67,
how much
greater
KEVIEW TROBLEMS
80
the value of the yield on the former farm, supposing the farms to consist of 79 acres each? How much greater is
is
the profit? If a 3000-lb.
47.
on these
fields,
crop of cow-pea hay per acre
grown
is
the stubble and roots will add 28 lbs. of
nitrogen, worth 19 cts. a pound.
What
is
the value of
the nitrogen added? 48. Find by inquiry the average yield of each of the above crops in your locality, and substitute your local
value in the problems, and solve.
SHIPPING
Goods are shipped by express or freight, the former commonly being used for lighter articles or when speed is
necessary.
The
freight rate varies with the articles
shipped, there being some twelve or more classes.
following table the class the
name
of the article.
ally equal to that
Empty
on 100
is
The
is
usu-
the class of goods shipped.
(6) a
Vegetables
:
potatoes,
onions, cabbage, etc. (6)
up (1) not set up (2)
Bicycles, set
up (1) up
furniture, not set
(2) Furniture, old, value limited to
made
Furniture, old, car-load lots
Clothing (1) furniture, set
smallest charge
lbs. of
barrels (6)
Trunks of baggage (1) Trunks limited to 1 5 hundred (D 1)
New New
In the
indicated in parenthesis after
$ 5 per 100 (4)
Bicycles,
Vegetables,
canned,
less
than car-load (2) Vegetables, canned, in earload lots (4)
PRACTICAL ARITHMETIC
84
Flour (6)
Grapes (1)
Apples and pears in
Baled hay (D)
bas-
Plows, set up (2) Plows, not set up (4)
kets (2)
Apples and pears in sacks
Power Power
or barrels (6)
Grain in bulk (D)
The
freight rate between
1st class 11.03, 2d 92
5th 54
E
54
6th 43
cts.,
cts.,
H
66
cts.,
two
A
33
49.
What
B
39
lbs.
being
:
4th 65
cts.,
D
cts.,
cts.,
33
:
will be the freight on a shipment of bicycles,
lbs., set
they be not set up
up
?
How much
Not set up ? In a shipment of what is the saving in freight if
?
cheaper
is
it
furniture not set up than to ship 51.
cts.,
cts.
bicycles weighing 500 lbs.,
50.
per 100
cities
cts.,
Solve the following problems
weight 200
cutter,
3d 79
cts.,
up (1) not set up (3)
cutter, set
How much
cheaper
is it
to ship 1500 lbs. of it
set
up
new
?
to ship 1500 lbs. of old
household furniture, value limited to 15 per hundred
pounds
in case of loss, than to ship the
new furniture set up ? Than of new furniture not set up ? 52.
What
to
ship
How many
goods shipped by the hundred will
same for freight 53.
What
is
empty
of
the same weight
the cost of shipping one car-load (20,000
is
lbs.) of old furniture?
lbs. of
same weight
pounds it
of the same
take to cost the
?
the difference in freight cost between 200
barrels
and the same weight
of trunks of
KEVIEW PROBLEMS
What
54.
85
the difference in cost of freight on a ton
is
(2000 lbs.} of canned vegetables and the same weight not
canned ?
What
55.
the difference in cost between a car-load
is
(24,000 lbs.) of
two separate shipments,
sent in
What
56.
1900
canned vegetables and the same weight
lbs.
barrels
is
the
difference
in freight
on 1700
lbs. of
wheat
The express charge between were given above from 1 to 2 lbs.,, 45
3 to 4 lbs., 60 cts.
from
cts.
from 15
is
25
cts.
cts.
lbs.,
for less than 1 lb., 35
70
lbs.,
55
25
to
f 2.30 from 50 to 100 hundred for weights greater than 100
lbs.,
lbs.,
lbs.,
Which
fl.OO
11.15 from
and
i|2.30 per
will be the difference of cost for a 200-lb.
will be
?
the difference between freight and
express charges on 300 lbs. of apples in baskets 60.
from 7 lbs.,
lbs.
trunk shipped by express and by freight
clothes
cts.
from 5 to
cts.
from 10 to 15
fl.lO from 20
lbs.,
What
of
the points for which freight
7 +n 10 lbs., 85 cts.
What
lbs.
?
from 2 to 3
from 4 to 5
to 20 Ib^.,
25 to 50
59.
between
on 1700
costs the most, the freight
rates
58.
cost
apples in baskets and the same weigiit in
of
Which
flour or
75
by the hundredweight?
?
57.
cts.
i.e.,
way when boxed, 11 lbs.?
will be the cheaper
weighing,
?
to ship a suit of
How much
cheaper ? 61.
Pupils
may add problems
concerning
produce
shipped to or from their nearest freight and express offices.
AND MULTIPLES
DIVISOKS
Name two factors of 18, 25, 32, 81, 120. Name three factors of 18, 30, 45, 50, 66. Name a factor common to 12 and 36. 85.
taken as one of the factors of 18, what
If 3 is
How
other factor ?
The
is
the second factor found
process of separating a
number
the
is
?
into its factors
is
called Factoring. 86.
An
exact Divisor of a
number
is
a factor of that
number. 87.
A
factor or a divisor that
more numbers
is
called a
Common
EXERCISE Find a common divisor
common
to
two
:
32, 48, 64.
35, 45, 60.
5.
63, 72, 81.
9.
2.
21,35,70.
6.
45,24,54.
lO.
27,36,75.-
3.
12, 24, 36.
7.
15, 30, 36.
ii.
12, 18, 22.
4.
36, 28, 72.
8.
18, 24, 54.
12.
72, 81, 96.
Name
all
the factors or exact divisors of
A number that has is
called
or
— ORAL
1.
88.
1
44.
is
Divisor.
no factors or divisors except
a Prime Number,
e.^.,
7,
3, 7, 19.
itself
and
11, 19, are prime
numbers. 89.
Factors that are prime numbers are called Prime
Factors.
DIVISORS 90.
posite 91.
A
number not a prime number
is
87
Com-
called a
Number.
Which
of the following
by 2 or have 2
ble
AND MULTIPLES
numbers
as a factor
are exactly divisi-
2, 4, 6, 9, 11, 13, 14, 15,
:
16, 17, 21, 22, 27, 30 ? 92.
Every number which contains the
factor 2
is
called
an Even Number. 93.
Numbers
that are not divisible by 2 are called Odd
Numbers. 94.
Numbers
that have no
common
factors are said to
be prime to each other.
EXERCISE
45.
— WRITTEN
Write a
list of all
prime numbers below 100,
2.
Write a
list of all
odd numbers below 100.
3.
Write
1.
all
the exact divisors of
all
the
numbers from
1 to 50. 4. 8,
Separate the following into prime factors
5.
4, 5, 7,
Separate the prime, composite, even, and odd numbers
in the following, 7,
:
10, 12, 13, 14, 16, 18, 21, 24, 25, 30, 34, 36.
and give reasons
for
your answers
:
1, 6,
10, 11, 12, 14, 19, 21, 24, 26, 27, 32, 33. 6.
Write a
list
of the
tain 2 as a factor.
figure of each 7.
Write a
What
numbers from 2 to 50 that condo you note regarding the units'
number? list of
tain 5 as a factor.
figure in each case?
the numbers from 5 to 100 that con-
What do you
note regarding the units'
;;
:
PKACTICAL ARITHMETIC
88
numbers from 3 to 60 which What do you note regarding the contain 3 as a factor. sum of the figures or digits of each number? 8.
Write a
9.
Write a
list
list
tain 9 as a factor, in the
sum
A
95.
of the
of the
and
numbers from
9 to 90 that con-
whether 9
exactly contained
find
is
of the digits of each of these
number
is
divisible
numbers.
:
by 2 if the units' figure is 2, 4, 6, 8, or by 3 if the sum of its digits is divisible by 3; by 4 if the number represented by the two right-hand ;
figures
by 5 by 8
is
so divisible
the units' figure
if
if
the
is
5 or
;
number represented by the three right-hand
figures is so divisible
by 9
if
the
sum
of its digits
is
so divisible.
Find the prime factors of 720.
96.
5 )720
2)144 According to divisibility test 5 factor. 2, 2, 3,
is
a factor.
2
and fifth factor, ,3 is the Hence, the prime factors of 720 are 5, and 3.
second, third, fourth,
EXEECISB 46.— Find the prime factors
of
1.
670..
5.
420.
9.
2.
981.
6.
462.
10.
3.
310.
7.
741.
11.
4.
2650.
8.
1575.
12.
is
a
last 2, 3,
AND MULTIPLES
DIVISORS
The
97.
common to Greatest Common
greatest factor or divisor that
two or more numbers (G.C. DO-
is
called
the
89 is
Divisor
Find the G. C. D.
SS.
04
_
^®
y ^ V 4
9
of 24
and
30.
and 30 are 2 and
common
'
fore, 2
X3
=6
is
common
factors of 24 Multiplying these factors gives the Gr. C. D. There-
^'^^ ^^^^ *^®
3.
the G. C. D.
two or more numbers, separate the numbers into their prime factors and find the product of the prime factors that are common 99.
Rule.
to all the
To
find the G. C.
numbers.
EXERCISE
D.
of
90
PRACTICAL ARITHMETIC
Divide the greater number by the smaller 101. Rule. and the divisor by the remainder; continue the process The last divisor will be the until there is no remainder.
G. C. D.
DIVISORS AND MULTIPLES 105.
_ 70—0 on
Find the L. C. M. y g „ r.
The prime
r
7
70. of 30
factors
'^^® prime factors of 70 are
obtain a
and
and
of 30
91
number which
are 2x3x5. 2x5x7. To
will contain
both 30
which multiplied
to-
of finding the L. C.
M.
of
Find the L. C.
J\I.
of
70, the factors 2, 3, 5, 7, are selected,
gether give 210, the L. C. M. 106.
The following method
two or more numbers
is
also used.
30, 70, 18.
2)30
107.
By
Rule.
bers, separate
multiplying together the
and the
divisors,
630, L. C.
M.
To
find the L. C.
each number into
ing each factor the greatest in
final quotients
2x5x3x7x3,
its
of
of times that
it
any one of the given numbers, find the product
factors.
get
two or more numprime factors, and tak-
M.
number
we
appears of these
:
DECIMAL FRACTIONS EXERCISE 1.
Name
name 2.
the smallest
51.
— OEAL
common
silver coin in
our money;
the largest silver coin.
The
smallest silver coin
is
equal to what part of the
largest ? 3.
coin
Name is
Of the 4.
the smallest coin in our money.
The
smallest
equal to what part of the smallest silver coin? largest silver coin
Read the following
?
as dollars, dimes,
and cents:
13.33, 14.44, $5.55, 16.66, f 7.77, 19.99. 5.
Read the following
as
dollars,
tenths,
and hun-
dredths of a dollar: $8.33, $4.44, $5.55, $6.66, $7.77. $9.99.
EXERCISE Write the following
52.
— WRITTEN
as cents, using the dollar sign
1.
55 hundredths of a dollar.
2.
90 hundredths of a dollar.
3.
36 hundredths of a dollar.
4.
34 hundredths of a dollar.
5.
25 hundredths of a dollar.
6.
10 hundredths of a dollar.
7.
1 dollar
8.
5 dollars and 15 hundredths.
and 10 hundredths.
92
:
:
:
DECIMAL FRACTIONS 108.
As
dollars
may
be divided into tenths and hun-
may
dredths, so units of anything
How many To 10 109.
The
thousandths 110. is
The
called
commonly 111.
a
be divided.
tenths of a thing are
To 100
units?
93
equal
to
1 unit?
units?
division of units into tenths, hundredths, or is
called Decimal Division.
part of a unit obtained by decimal division
Decimal
Decimal fractions are
Fraction.
called Decimals.
The
period placed at the left of tenths,
e.g., .2, is
called the Decimal Point. 112.
Decimal fractions may also be expressed thus
.2 or two-tenths.
It
may
be also written
written, the decimal fraction
a
Common Fraction. 113. The following
is
table gives the
names
mal places •a
°
no
•OS
a .9 = 2
*
5 " ""Ho ^ o
J S
j= il "O
cs cS
S 3
Sj,
oj
si
4672.198462 EXERCISE
Read the following
53.
^-^.
When
so
expressed in the form of
— OBAIj
of the deci-
:
PKACTICAL ARITHMETIC
94
EXERCISE
Name
54.
— ORAL
the place at the right of tenths, at the right of
hundredths, at the right of thousandths, the fourth place, the
fifth,
the sixth, the seventh.
Read the following 1.
15.004.
4.
0.0001.
7.
50.504.
lo.
98.7256.
2.
25.102.
5.
1.4111.
8.
75.6281.
ii.
100.2376.
3.
30.675.
6.
10.1063.
9.
86.5467.
12.
105.20068.
EXERCISE Write
form
— "WRITTEN
:
Five-tenths, three-tenths, four-tenths, one and one-
1.
tenth
in decimal
55.
.
Six
2.
and eight thousandths, eight and forty-two
thousandths, two ten-thousandths, ten millionths.
One hundred
3.
forty-five thousandths, three
hundred
eighty-one thousandths, four ten-thousandths, two hun-
dred and two hu.ndredths. Five and six-tenths, nine and one-tenth, seventy-five hundredths, four hundred and four thousandths. 4.
5.
Write these common fractions _1_ _e^ _i 6 s
as decimal fractions
common
0.25, 0.250, 0.2500.
:
_9_
_3_.
10' 10' 6.
iTT' 10T5' 100' lOOO'T'OOOODistinguish between 0.300 and 0.00003.
7.
Express as
8.
Annexing a cipher
value 9.
how many
times
fractions to a
:
whole number increases
its
?
Does annexing a cipher to a decimal
affect its value?
:
ADDITION OF DECIMALS Add: 25.725,62.8,909.003,4.23681.
114.
25.725
^^^
g2.8
decimals as in the addition of United Place the decimal points in a
States money.
909.003
vertical line,
and add as
numbers.
in integral
4.23681
EXERCISE Find the sum 1.
of
5.47
56.
— WRITTEN
:
2.
16.62
7.87
112.63
3.
0.125
4.
6.87
5.097
19.00
152.00
25.608
5.03
7.75
7.537 5.03
0.107
5.
19.083, 0.96, 5.03, 27.107, 5.1464, 0.905.
6.
489, 0.16, 0.49, 7.07, 5.0909, 0.0008.
7.
37.204, 3.1459, 143.59, 3415.18.
8.
6.2525, 62.525, 625.25, 6252.5.
9.
Express as decimals and add
h% 30^,
:
41.039
-^% ^\%, -^%\, j;^\^o'
300^^0^.
EXERCISE 57.— WRITTEN 1.
The amount
of protein in
pounds contained
worth of each of the following kinds
of beef
is
in 10 cts.
as follows
tenderloin steak .064, sirloin steak .081, loin roast .090, rib roast .088,
round
steak, first cut., .130, 95
round steak
:
PRACTICAL ARITHMETIC
96 .135,
chuck
cut, .205,
shank
.129, rumiJ .114, shoulder .155, round, second
neck
.256.
total
amount
do
spend?
I
I
.207, brisket .20, plate .230, flank .284,
buy 10
The amount
2.
worth
cts.
of protein
purchased
how much
found in 10
of protein
each of the following kinds of pork
is
Find the
each.
of ;
money-
worth
cts.
smoked ham
:
bacon .065, smoked shoulder .108, fresh
ham
of
.071,
.112, fresh
shoulder .120, ribs and loin .134, fat salt pork .019.
buy 10 At what I
cts.
worth of each, how much protein do
If
buy?
cost?
The amounts
3.
I
of protein in
pounds found
in 10 cts.
cutlet .089, loin and rib worth of veal are as follows .093, leg .098, shoulder and breast .18, chuck and neck :
.133,
knuckle or shank
amount
of protein purchased
of these cuts of veal.
The monthly
4.
.346, flank .424.
moderate
rainfall,
2.7, 4.4, 4.1,
if I
What
buy 10
Find the
cts.
worth
total
of each
does such a purchase cost
rainfall at
Davenport,
a place of
la.,
expressed in inches, was: 1.6,
3.7, 3.6, 3.2, 2.4, 1.8, 1.6.
?
1.6, 2.2,
What
was the
rainfall for the year ?
The monthly
5.
4.8, 5.3,
7.4,
What was :
was:
6.7,
6.9,
4.9,
3.2,
was
3.5,
4.6.
?
rainfall at
Winnemora, Neb.
(scant),
1.1, 0.9, 0.8, 0.9, 1.0, 0.6, 0.2, 0.2, 0.3, 0.5, 0.7, 1.2.
What was 7.
6.1,
the yearly rainfall
The monthly
6.
was
rainfall at IMobile, Ala. (heavy),
4.5, 4.2,
the annual rainfall
The monthly
rainfall at Darjiling, India (excessive),
1, 1.5, 2, 6, 8, 16,
the annual rainfall
?
?
16, 16, 16, 6, 0.5, 0.5.
What
was
SUBTEACTION OF DECIMALS From
115.
9.25 take 7.075.
^^ there are more decimal places in the subtrahend than in the minuend, annex ciphers until they have the same number of places.
9.250 _ „_-
—
^
EXERCISE
58.
— WRITTEN
1.
From
1.25 take 0.15.
7.
From
25.25 take 2.525.
2.
From
7.75 take 1.95.
8.
From
37.18 take 9.189.
3.
From
14.2 take 4.92.
9.
From
1.25 take
4.
From
14.2 take 4.92.
lo.
From
-^
5.
From
39. take 21.689.
ll.
From
^-f^-^
12.
From ^i^
6.
From 500
take 9.32.
EXERCISE 1.
tein,
ash, 2.
lbs.
In 100
100
If in
take j^-^.
take
wheat bran there are 15.4 water.
is
lbs. of
water,
If in
100
milk there are 4.32
of
is
is
is
water,
lbs. of fat, 3.34
cream there are 23.8
how much water 97
there ?
and the
there?
4.12 lbs. of protein, 3.92 lbs. of sugar, 0.53 the balance
pro-
5.8 lbs. of
lbs. of fats,
How much water
how much water
lbs.
^7.
lbs. of
of protein, 5.7 lbs. of sugar, .74 lbs. of ash, is
^^. -^.
— WRITTEN
62.9 lbs. of carbohydrates, 4
and the balance
balance 3.
lbs. of
59.
take
is
lbs.
of fat,
lb. of ash,
there
?
and
PRACTICAL ARITHMETIC
98 4.
If in
100
lbs. of
timothy hay there are 13.2
lbs. of
water, 4.4 lbs. of ash, 7.4 lbs. of carbohydrates, 2.5 of fats is
there 5.
and the remainder
is
protein,
how much
lbs.
protein
?
If in
100
lbs. of
red-clover hay there are 15.3
lbs.
of water, 6.2 lbs. of ash, 62.9 lbs. of carbohydrates, 3.3 lbs. of fats,
and the
rest is protein,
how much
protein
is
there ?
Nuts contain the following amounts water in each pound. lining
The
of
refuse
and
refuse represents the shell and
MULTIPLICATION OF DECIMALS EXERCISE
60.
— ORAL
Read the following: .225, 2.25, 22.5, 225. does moving the decimal point one place to the affect the value of a number ? 1.
2.
Read:
How
.3720, 37.20, 3720.
How right
does moving the
decimal point two places to the right affect the value? 3.
Read:
.973, 973.
How
does moving the decimal
point three places to the right affect the value
?
Moving the decimal point one place to the right has the effect of multiplying tlie number by 10, two places 116.
by 100, three places by 1000,
etc.
117. To multiply by 10, 100, 1000, etc., move the decimal point as many places to the right as there are ciphers in the multiplier, annexing ciphers at the right to com-
plete the required
number
if
EXERCISE
necessary.
61.
— ORAL
Read the following: 675, 67.5, 6.75, .675. does moving the decimal point one place to the left the value of the number ? 1.
2.
Read: 22.70, 2270.
point two 3.
How
How affect
does moving the decimal
places to the left affect the value ?
Read:
325, .325.
How
does moving the decimal
point three places to the left affect the value 99
?
PRACTICAL AKITHMETIC
100 118.
Moving
the decimal point one place to the left has
number by one-tenth
the effect of multiplying a
(0.1),
two places by one one-hundredth (0.01), three places by one one-thousandth (0.001), 119.
To
etc.
multiply by 0.1, 0.01, or 0.001
mal point as many places
move
the deci-
to the left as there are decimal
places in the multiplier, prefixing ciphers
if
necessary to
complete the required number of decimal places.
EXERCISE Multiply
49.68 by 10, by 100, by 1000.
2.
6297.3 by 10, by 100, by 1000.
3.
9.6847 by 10, by 100, by 1000.
4.
429673.0 by 10, by 100, by 1000.
5.
84910.0 by 10, by 100, by 1000.
6.
49.68 by 0.1, by 0.01, by 0.001.
7.
6297.3 by 0.1, by 0.01, by 0.001.
8.
9.6847 by 0.1, by 0.01, by 0.001.
9.
0.429673 by
84910 by
0.1,
0.1,
Multiply 32.482 by 2 thousandths
32.482 3
97.446
— WRITTEN
1.
10.
120.
62.
:
by
by
0.01,
0.01,
by 0.001.
by 0.001.
3.
x 3
are 6 thousandths, the 6
is
written under the thousandths.
8 hundredths X 3 are 24 hundredths, which equals 2 tenths and 4 hundredths. The hundredths are written under
hundredths and the 2 tenths are to be added to 4 tenths x 3 are 12 tenths, which with 2 tenths are 14 tenths, which equal 1 unit and 4 tenths. 2 units x 3 are 6 units, which with 1 unit equal 7 units. 3 tens x 3 are 9 tens. tenths.
:
DECIMAL FRACTIONS
101
Multiply 'S2A82 by 0.3.
121.
Multiply by 3 as
0.3
were a whole number, the product for the thousandths in the multiplicand and an addi-
9.7446
tional place to indicate that the multiplicand has
32.482
pointing off
3
if
places
it
in
been multiplied by tenths.
The product then has
4 decimal places.
To
122.
multiply decimal fractions multiply as with
whole numbers.
Point
off as
many
places as there are
decimals in the multiplier and multiplicand together.
If
the product does not contain as man}'^ decimal places as are required, prefix
enough ciphers
to
make
the required
number.
EXERCISE
63.
— WRITTEN
Multiply
x
8.
0.236 by 8.93.
15.
184.2
9.
0.259 by 0.247.
16.
214.86x45.64.
10.
349 by 0.46.
17. 37.55
132 by 2.47.
ii.
4.39 x 0.74.
18.
873.0 x 0.675.
5.
13.2 by 24.7.
12. 5 .6
19.
214.76 x 1.25.
6.
0.132 by 247.0. 13. 35.16 x 5.75.
20.
87.136 x 0.0042.
7.
9.06 by 1.24.
21.
897.28x2.009.
1.
96.0 by 0.3.
2.
9.6
3.
0.96
0.3.
4.
by
0.3.
by
14.
.056.
50.05x0.0095.
EXERCISE 1.
x
64.
0.098.
x 0.00025.
— WRITTEN
on the ear weighs 70 lbs. and of cobs, what is the weight of a bushel of
If a bushel of corn
each pound 0.2
is
shelled corn? 2.
If in 1 lb. of corn stover there is 0.6 lb. of stalks,
PRACTICAL ARITHMETIC
102
0.3 lb. of leaves, and 0.1 lb. of shucks,
how many pounds
of each are there in 2000 lbs. of stover?
commercial
If in 1 lb. of
3.
phosphoric acid, 0.025
how many pounds
potash,
A
4.
lb.
of
How many pounds
?
of each
?
Saturday grocery order was
housekeeper's
follows:
nitrogen, and 0.035
of each are there in 100 lbs.
of such commercial fertilizer in 2000 lbs.
fertilizer there is 0.08 lb. of
lb. of
as
roast at f0.18 a pound, 3 lbs. rice at.
6 lbs.
$0.0825 a pound, 1 pk. sweet potatoes at $0.25 a peck, .5
lb.
tapioca at $0.08 a pound,
$0.19 a pound, 10
Find
graham
1.25
flour at
lbs.
cheese at
$0.03 a pound.
total cost.
The average wheat
5.
is
lbs.
yield to the acre in Great Britain
33.9 bus., in the United States 14.5 bus., in India 9.2
bus., in Russia 10.2 bus.
Russia grows 39,215,686
acres,
the United States 33,766,233 acres, India 16,847,826 acres.
per acre in the United States and Russia
If the yield
were brought up to that of Great Britain by
and
selection
tillage,
world's wheat crop
what would be the increase
were
sufficient, the yield per
acre there might be equal to that in Great Britain.
would the
At
mile? 8.
The
height.
high
total yield of India
What
7.
?
does
it
What Round
is
then be
What
?
cost to travel 198 miles at 2.5 cts. per
2.25 cts.? distance
to the
?
If the rainfall in India
6.
skilful seed
At
3.75 cts.?
round a wheel is 3.1416 times its the distance round a wheel 4.75 feet
a 28-in. wheel ?
DIVISION OF DECIMALS Divide
123.
by 110.00, 140.00 by 10 cts., $75.00 by 15 cts. Compare the
$40.00
$75.00 by 115.00, results.
We
have seen that United States money
decimal fraction,
$1 and 10
e.^.,
are
changed to
is
written as a
written $1.10.
United States money when the
In the division of divisor is represented
cts. is
by
cents, both divisor
and the division
cents,
is
and dividend performed as
with integers.
Divide 8.75 by
124.
3.5
25)87.5 'j'g
12.5 12.5
To
2.5.
changed to the integer 25. changed to 87.5. Dividing as in United States money, 87 -=- 25 = 3, with a remainder of 12. Adding .5 to the remainder gives
by 10
is
8.75 multiplied by 10
is
2.5 multiplied
12.5 for a
new
partial dividend.
Therefore, the quotient
12.5
-=-
25
= .6.
is 3.5.
divide a decimal fraction, multiply both dividend
and divisor by 10, or such multiple of 10 as shall make the divisor an integer; then divide as in United States
money.
EXERCISE 65.— WRITTEN Find the quotient
of
:
1.
7.75 -=-25.
3.
7.75 -=-.25.
5.
7.75 -.0025.
2.
7.75-^2.5.
4.
7.75^.0-25.
6.
7.75^.00025.
103
: :
PRACTICAL ARITHMETIC
104 7.
17280-4-125.
8.
17280^-12.5. 125.
9.
17280
',-T-
1.25.
xi.
17280 h- .001 25.
10.
17280
4- .125.
12.
17280
^- .0125.
Divide 10.10 by 10, divide 100.100 by 100, divide
Compare
1000.1000 by 1000.
these results.
In preceding pages you have seen that moving a figure
one place to the right in
its
period decreases
point one place to the left decreases a divides the
number by
10, 100, 1000, etc.,
to the
its
value
In like manner, the removal of the decimal
tenfold.
tenfold, or
Hence, to divide a decimal by
10.
remove the decimal point
left as there are
necessary,
number as
many places When
ciphers in the divisor.
add ciphers to complete the required number
of places.
BXEBCISB Find the quotient
66.
—WRITTEN
of
1.
3725.4 4-70.
4.
810.18 4-9000.
2.
309.45 4-1500.
5.
810.18 4-0.009.
3.
132.4^4000.
6.
7325.1 4- 1.045.
126.
When
there
is
a remainder after using
all
the
annex ciphers to the dividend and continue the division. For ordinary affairs in busi-
figures of the dividend,
ness
it is
not necessary to carry the division further than
four or five decimal places.
EXERCISE
67.
— WRITTEN
Find the quotient of 1.
92323.15
2. 3.
6.275.
4.
281.85 4-3.85.
281.8585 4-8.85.
5.
87.912 4-4.07.
725.406 4-6956.
6.
0.375
-f-
-5-
.25.
DECIMAL FRACTIONS 7.
105
106
PRACTICAL ARITHMETIC
:
REVIEW PROBLEMS The
2.
107
different items of cost to build a stave silo 12
in diameter
and 21
ft.
high are as follows
:
ft.
hauling rock
f 3, hauling sand $1, cement 4.75 barrels at f 2.85 per barrel, putting in concrete foundation, 1 man, 4 days at 11.25 a day, lumber
ber $3, nails 25 lbs. at 3
hoops $21.95, bolts 45 gasoline,
and brush
lum-
|5, staves 128.84, hauling cts.,
cts.,
10
nails
small
lbs. at 3|
bolts
30
cts.,
cts.,
tar,
tar paper 2 rolls at •tl.37o,
!i5l.40,
carpenter 6 days at #1.75 a day, labor 2 days at $1 a
What was
day.
the total cost of building the silo?
If a field of cotton yields
3.
and each poiuid yields .314 of seed
and how many pounds
To make
4.
chufas 2.3 lbs. of grain, grain,
when on sweet
on sorghum 3.70 grain
of
were
seed cotton
lbs. of
how many pounds
of lint are there
1 lb. increase in
on peanuts required 1.77
4793
lb. of lint,
?
weight in pigs pastured
lbs. of grain,
when pastured on
when on cow-peas
3.07 lbs. of
potatoes, 3.13 lbs. of grain,
lbs. of grain.
required
How many
when
more pounds
when on chufas than when
How many more when on cowpeanuts? When on sorghum than When on sorghum than when on
on peanut pasturage? peas than Avhen on
when on peanuts
?
sweet potatoes?
The following
5.
is
the average yield of wheat per
acre in the principal wheat-growing nations of the world
Great Britain 33.9 bushels, Germany 28.6, France 20.8, Hungary 18.4, Austria 19.6, United States 14.5, and Russia,
10.2.
How many
acres
would
it
require in each of
the other countries mentioned to produce as as
is
produced on 1 acre in Great Britain?
much wheat
:
108 6.
PRACTICAL ARITHMETIC
The following shows
the cost and benefit from spray-
ing Irish potatoes for several years in
Year
New York
REVIEW PROBLEMS and the balance
of fats,
is
109
how many pounds
water,
water are there in 1000 lbs. of fresh cow-peas
In buying redtop grass seed at 13.7
10.
when only 77 what
is
pound
a
cts.
good live the price paid per pound for good seed ?
With redtop
11.
?
in every 100 lbs. is
lbs.
seed at 8.54
cts.
a
11 lbs. of good seed in every 100 lbs.,
of
seed,
pound containing what is the price
per pound of the good seed?
With
12.
blue-grass seed at 14 cts. a
60 lbs. of good seed in every 100
lbs.,
pound containing what is the price
per pound of the good seed ?
With
13.
the price per
live seed to the
pound
of the
With timothy
14.
hundred
of
cts. a pound containing hundred pounds, what is
blue-grass seed at 10
good
.4 lb. of
good seed ?
grass seed containing 96 lbs. per
good seed bought
at $1.60 a bushel,
what
is
the price paid per bushel for good seed? If a
15.
cow produces 7446
lbs. of
milk in a year and
1 lb. of milk produces .059 lb. of butter, of butter does the
27
How much
of feed, 17.
of
cow produce, and what
if
she ate 12.4
cts.
worth each day?
Another cow gave 3400 lb.
lbs. of
of
milk, and each
butter.
a profit with butter at 27 cts.
was 11.2 18.
worth at
does the butter cost per pound in value
milk produced .0406
make
is it
a pound?
cts.
16.
how many pounds
cts.
If 1
if
Did
pound cow
this
the cost of feed
a day?
pound
of cotton-seed
of nitrogen, .018 lb.
meal contains .0618
of potash, and. .028
lb. of
lb.
phosphoric
:
PRACTICAL ARITHMETIC
110 acid,
how much
a ton, or 2000
of each of these fertilizing materials does
lbs.,
of cotton-seed
meal contain?
"What
is
the ton of cotton-seed meal worth for fertilizing at 18
cts.
and 5
cts.
a
pound
for nitrogen, 4 cts. for phosphoric acid,
for potash? 19.
If 1
pound
of cotton-seed contains .031 lb. of nitro-
gen, .013 lb. of phosphoric acid, .012 lb. of potash, what is
the ton of seed worth at the same prices for fertilizing
materials as in problem 18? 20.
The following
are the plant-food constituents which
a farmer sells from his farm in the products
named
REVIEW PROBLEMS round steak, in which do in tenderloin or in
I
23.
If for
niucli
more
?
Loin Cut op Beef
I can
purchase .03
protein do
I
lb. of
obtain in 70
protein in
cts.
worth of
I obtain
most
my money ?
In the following dairy products these amounts of
protein
may
be purchased for 10
cheese .1631b., whole milk .110 lb.,
How
?
In which of the above articles do
?
protein for 24.
cts.
how much
oysters,
oysters
10
get most protein for the money,
round steak
A Good
111
cream .034
lb.
How much
cts.:
lb.,
butter .004
skimmed milk
protein in each
lb.,
.20:5
may
I
obtain for 75 cts.?
LEGUMES pound of vetch hay contains .17 lb. of nitrogen, how many pounds of nitrogen are there in 2879 lbs. Each pound of alfalfa contains .143 lb, of vetch hay? 25.
If each
of nitrogen.
alfalfa?
How many
Each pound
pounds are there
in 2879 lbs. of
of red clover contains .123 lb. of
PRACTICAL ARITHMETIC
112
How many
nitrogen.
Each pound
clover?
pounds are there in 2879 of cow-pea
lb. of
hay contains .166
nitrogen.
How many pounds are there in
pea hay?
What
2879
red
lb. of
lbs. of
cow-
the value of the nitrogen in each of
is
the above instances at 19
pound?
cts. a
If 5953 lbs. of velvet-bean hay are grown on an and in every pound of this hay there is .0221 lb. of nitrogen, how many pounds of nitrogen are gathered by 26.
acre,
the crop, and what 27.
is it
worth at 18
If there is .024 lb. of
hay, and 3000 lbs. of
h.a,j
are
cts.
a
nitrogen in 1
made on an
pound? lb. of
acre,
cow-pea
what
will
be the value of the nitrogen collected by the crop, with nitrogen worth 18
cts.
a pound,
trogen in the hay there .3 lb. of 28.
for each
if
pound
in the stubble
is left
Crown Jewel
dug
potatoes
yielded 170 bus.,
in
dug
Virginia 80 days at
planting, the same variety gave 255 bus.
93 days
the
?
Hebron potatoes dug in Virginia at 101 planting showed an increase of 136 bus. over
Beauty
days after
after
What was
average increase daily during the additional period
those
roots
nitrogen?
after planting
29.
of ni-
and
of
dug 80 days
after planting.
What was
the average
increase per day during the additional time? 30.
Using
acre, at
from 2.09 field.
nitrate of soda
on clover, 300
lbs.
to the
§2.66 a hundred pounds, the yield was increased to 2.8 tons per acre,
Did the use
gain or loss per acre
valued at 19 a ton in the
of the fertilizer ?
pay ?
What was
the
COMMON FRACTIONS EXERCISE
71.
— OEAL,
How many weeks in a month ? One week is equal what part of a month ? Two weeks are equal to what part of a month? Three weeks are equal to what part of a month ? 1.
to
One week is equal to what part of two months? One week is equal to what part of three months ? 2.
Two weeks are Two weeks are equal 3.
equal to what part of two months ? to
what part
of three
months ?
4. Three weeks are equal to what part of two months Three weeks are equal to what part of three months ?
part called?
what
two equal
If a unit is divided into
5.
is
127.
is
one
If a unit is divided into three equal parts,
one part called
One
what
parts,
?
or
more
If into four, six, ten ?
?
of the equal parts of a unit
is
called
a Fraction. 128.
A fraction is expressed by two numbers,
ten above the other, with a line between them
fourth 129.
is
expressed thus,
|-,
:
\,
part of these fractions shows the is
e.g.,
one-
\.
Read the following
which the unit
;
one writ-
\,
Jg,
^^q,
number
gV-
What
of parts into
divided?
The number which shows
into
113
how many
parts a unit
:
PRACTICAL ARITHMETIC
114 is
divided
f,
6
called the Denominator
is
;
e.g., in
the fraction
the denominator and shows that a unit has been
is
divided into six equal parts.
Which is greater, ^ or | ? What does the number above the line indicate ? The number which shows how many parts are 130.
is
called
tlie
Numerator
e.g.,
;
in the fraction
3
|^,
taken is
the
numerator and shows that the fraction contains three of four equal parts.
The numerator and denominator
131.
Terms
are called
the
of a fraction.
A
132.
is
numerator
whose
fraction
denominator
less
is
than
called a Proper Fraction; e.g., |, ^, |,
its
^,
are proper fractions.
A proper fraction is always less than a unit. 133. A fraction in which the numerator is equal greater than the denominator tion;
e.g., |, |, ^,
fraction 134.
is
A
together
is
is
to or
called an Improper Frac-
An
are improper fractions.
improper
always equal to or greater than a unit.
whole number and a fractional number written called a
Mixed Number
;
e.g., 3|,
1^ are mixed ,
numbers.
BXBECISE 72.— OBAL Select proper fractions, improper fractions, and mixed
numbers from the following *•
-^*
3' F' 6' 9"
2 "*
-t
3 "*•
15
IS
3
2 0'
15^'
f' 3-
4'
1 34 1^ 5' '^¥' 14"
1
''e'
2''
la
-'"2' 5"
J
5
5 4'
c
IflS 2_5. Q2 9 '#' ^Y' •''"?' TO-
^°-
8.
16' 5' 25-
10'
n
**•
a
^-
20
19' 2_8
?9'
3'
2'
9
15 Q 1 5 6 ? ' ^^2' IV 19 .£;i 16
'5"' ''2' 24-
:
COMMON FRACTIONS EXERCISE
73.
115
— WRITTEN
Write as common fractions or mixed numbers 1.
Thirt3^-one tenths.
2.
Fifty-six elevenths.
3.
Eight-nineteenths.
4.
Seven-fifteenths.
5.
Eight one-hundredths.
6.
Ninety and three-fourths.
7.
One hundred and
8.
Seventy-seven and six-tenthsi
9.
Five hundred
forty-five forty-sixths.
tentlis.
10.
Twenty-five
11.
Nineteen and seven twenty-firsts.
12.
Twenty-one and eighteen nineteenths.
13.
One hundred
tliirty-sixths.
twenty-five and one hundred twenty-
four one hundred twenty-fifths.
EXERCISE
1.
V-
COMMON FRACTIONS EXERCISE
How many How many How many How many
1. 2. 3. 4.
77.
117
— ORAL
twelfths in one unit
?
twelfths in two units
?
twelfths in one-half unit
?
twelfths in one-third unit
5.
What
6.
Does changing ^^
?
true of the value of ^2 ^"^ true of the terms of the second fraction ?
value
is
2 ^
What
is
*o ^^^ lower terms, ^, change the
?
EXERCISE
Change the following
78.
— WRITTEN
to lower terms
1.
"•
21'
2 4'
^•
7'•
IS
li.
24
19
-6JL
R **• 9 ^-
TO
•^""
139.
A
fraction
is
reduced to
:
its
2T' 60' Tf¥"8''
102'
la. "rt-
10 8 li l± 111' ^1' YO22 11 IS. ?t' 6 6' 9 6*
Lowest Terms when
the terms are prime to each other.
To reduce mon to both
a fraction to lowest terms, select factors com-
terms, and cancel.
h
:
COMMON FRACTIONS To change
1 to 24ths, multiply both numerator and de8 = 1x8
nominator by 8
To change
3x8
2-i'
multiply both numerator and de5 X 3 ^ 15
| to 24ths,
=
nominator by 3
To change 1| ^|
8x3
24'
to 24ths, multiply both
nominator by 2
=
10 X 2 12 X 2
^
numerator and de-
20 24'
common denominator
In reducing fractions to a
143.
119
they are changed to Higher Terms.
EXERCISE 82.— "WRITTEN
Reduce to similar 1 ^-
1 42'?-
3 *
^-
12' IZ-
*
fractions -9-
21' 7'
ii ^0"
2 1-
EXERCISE Reduce
to fractions
^-
1
?' ^' 10-
"•
2'
S"'
12-
o "*
3 5'
4
2
T' 3-
*•
8'
5'
K
6
^-
'SO'
5 °-
5
_9_
10-
n'•
3
S'
°-
9'
S-
°-
"5'
J: t' TT1(J'
20-
— WRITTEN
having a L. V. D.
3_
1
1
83.
:
6.
?05_
_e
15' 15"
EXERCISE
— WRITTEN
improper fractions and reduce to
Change
to
1.
18f
12-1,
84.
L'.
5.
682^ 45}1.
2.
2V„36,V
6.
42l|,
3.
72^, 26^\.
7.
Sh%,2A^\.
4.
24|,
8.
16g\, 2111.
3(11.?.
61ff.
C. D.
ADDITION OF FRACTIONS KXEROISE
85.
— DEAL
How many tenths in ^ + ^^? How many fifths? How many How many twelfths in ^^ + 1^2 '
1. 2.
fourths ? 3.
How many
4.
To
the fractions
+
2
1
is
How many
|^?
+ 1?
fractions,
+ 1?
1
l
ones?
what terms
of
1+1?
+ J?
•
To what kind
6.
+
sums of these are added?
How much
5. 3
sixths in ^
find the
fractions
of
must those above be
changed before they can be added?
Add|,f,3^.
144.
The
First find the L. C. D.
L. C. D. is 5
x 2 x3x2
Eeducing each fraction to higher terms with 60
mon
denominator, 12
^ 48
5x12
60
X
4
ff
have,
6
Add
The sum
9x5 ^45
X 10 ^ 50
6x10
+ 1^ + 11 = Jg^.
145.
By
we
= 60.
for a cohj-
12 x 5
60
Eeducing
60
J^ to a mixed number gives
+ 6f of 3 + 6 = 9. 31
finding the L. C.
tions to higher termsj
T>.
we
of
get
^ and J^j
-J-
and changing these
+ |-i = ff-
120
frao-
COMMON FRACTIONS
121
Changing |J to a mixed number gives 1^^. Uniting the sums, 9 + l^j = lO^ij.
To add
fractions, reduce to similar fractions having the L. C. D., and add the numerators, placing the sum over the common denominator. The answer should al146.
ways be reduced
to lowest terms.
EXERCISE
SUBTRACTION OF FRACTIONS How much is f + |^? How much is | — ^? How much is f + ? How much is | — ^^? How much is | — yj^? How much is ^ + ^^
147.
-^-^
'
To
subtract fractions they must,
changed
to
similar fractions.
of the subtrahend
as
or 1^-
addition, be
from the numerator of the minuend
obtain the numerator of the difference,
- iV
in
Subtract the numerator
e.g.,
f—
to
iV = t^
COMMON FRACTIONS 4.
123
PRACTICAL ARITHMETIC
124
A normal child weighs at birth 7| lbs., at 1
4.
year 20|
What is the difference between at 2 years 26J lbs. weight at birth and at end of first year ? What is the difference between its weight at end of first year and end
lbs.,
its
of second year
At
5.
?
birth a normal child measures in height 20|
What
at 1 year 29 ins., at 2 years 32-| ins.
ence between
What end
is
its
height at birth and at end of
ins.,
the differ-
is
first
year
?
the difference between its height at birth and at
of second year?
6.
The organs
water, as follows
cord
-1^,
lungs
human body
of the
bones
:
^,
muscles
How much
r^^^^.
^y^',
are composed of
brain and spinal
more water
there in
is
In brain than in muscle ?
muscle than in bone ?
In lungs
than in muscles? 7.
The organs
human body
of the
loro' brain
How
y-J^.
:
in bone than in each of the other organs 8.
The head
measures
of
a
20|- ins., at 3
are composed of
bones \^, muscles 2 |o' ^^^S^ much more mineral matter is there
mineral matter, as follows
named ?
normal child at 6 years years 19|
ins., at
of age
2 years 19^
Find the difference in measurement between the head child 6 years old
and that
of a child 3 years old
;
between
and a 2-year-old child; between
a 6-year-old child
ins.
of a
a 3-
year-old child and a 2-year-old child. 9.
The average boy
average girl of 8
is
of 8 years is ISy'g
48^^^ ins.
What
is
i'^^- ^^^^'
^^^^
the difference in
their heights? 10.
The average
boy 99|^.
What
girl of
is
14 weighs
the difference
?
100^ lbs., the average
.
MULTIPLICATION OF FRACTIONS EXERCISE 1.
How much
cents ? •
I of
I
is
93.
^ of 6 inches
4.
5.
In example 4 the result
3.
6. 7.
8.
How much How much How much
149.
of
^of|? iofif?
12?
inches are there in a foot
inches in
is
what part
yard?
is I
of |
is
-|-
of ^ dollar?
is
| of
?
In J of
foot?
|
foot?
|-
of a foot?
of | dollar?
I
^
of ^g dollar?
|- ?
its
When
value.
by another, the number
denominator decreased, 150.
is i
Multiplying any number by another number larger
than 1 increases plied
is
e.ff.,
one fraction
of parts as
multi-
increased, but the value of the fraction
2x3 = 6.
Multiply I by 1
I of f = 2 X ^ or
-^
=1
x ^
=J
of
|^
|.
is
= ^.
of |.
Hence, | multiplied by |
= |.
= f off _ i of + = -?~ Jj = 5 times Jj, or |f of I
Multiply I by | 1
152.
is
shown by the
iof| = i.
151.
^ of 10
of 9 dollars?
^
?
?
How much How many How many
2.
— ORAL
To
of
7
2
multiply a fraction by a fraction, find the 125
:
COMMON rRACTIONS 155.
To
number, regard
common
;
tlie
wliole
number
as
and multiply the terms
or indicate the multiplication factors.
EXERCISE Find the product 1.
and a whole an improper frac-
find the product of a fraction
tion with 1 as its denominator,
together
127
of
96.
— ORAL
and cancel the
128 7.
PRACTICAI, ARITHMETIC
DIVISION OF FRACTIONS How many
158.
many
times
Since ^ 1,
is
is
times
contained in
^ contained in 1?
times
or |, four times, |
1,
or I, ^ of four times, or
How many
is
-t
| contained
is
Since ^
is
^
^ contained in 2?
is
| contained in 2?
contained in
times
is
2,
2.
f
?
|
is
contained
times.
is
or |, eight times, | is contained
f times.
f contained in 2?
|
is
contained
of 8 times, or | times.
EXERCISE 1.
in 1
times
How many in 2, or |,
|-
times
in 2, or |, | of 8 times, or
contained in
is
times.
in 1, or |, one-third of 4 times, or
How many How many
How
| contained in 1?
99.
— DEAL
How many times is ^ contained in 1? | in How many times is | contained in 1?
1?
| in 1?
inl? 3. 4.
How many times is ^ contained in 2 ? J in 2 ? | in How many times is ^ contained in 3? in 3?
2?
-f
159.
When
the product of two numbers
equal to
is
1,
each of the two numbers is called the Reciprocal of the other, e.g.,
3
X 1^=
1.
the reciprocal of the reciprocal of
Hence, 3 3. |-,
is
the reciprocal of ^, and ^
Again, ^
and
|-
is tlie
129
Xy = |-| = l. reciprocal of
Hence, |-.
-|
is is
.
PRACTICAL ARITHMETIC
130
To
160.
same
multiply by the reciprocal of a number
by that number.
as to divide
Hence
is
the
to divide a
whole number by a fraction, or a fraction by a whole
number, or a fraction by a fraction, multiply by
its re-
ciprocal.
161.
Divide | by f we have seen,
Since, as
f
is
contained in
tained in IJ-j-
or
162.
1-|
1,
|-
1,
j- is contained in 1, seven times, i of seven times, or times. If i is con-J
times,
it
will be contained in |, ^ of f, or
Mixed numbers should be reduced
possible, use cancellation in the process.
BXEECISE Find the quotients 1.
or
to improper
fractions before performing the division.
When
^
times.
of
:
100,
-OEAIi
COMMON FRACTIONS 3| of 71-^61
off 9^J^-off^i.
16. 17.
18. 19.
EXERCISE 1.
240-Jj^|of|. 3|ofl|^iofi.
— WRITTEN
normal child of 7 years weighs
If a
child of
102.
131
years weighs 54|
8
monthly increase
lbs.,
49^- lbs.,
what
and a
the average
is
weight?
in
measurement of and child a of 8 years lias a chest measurement 23J ins., of '2-l|- ins., what is the average monthly growth in chest 2.
If a child of 7 years has a chest
measurement? 3.
year weighs 20|
If a child of 1
10 years weighs 6Q^ lbs., what in
is
lbs.,
and a child of
the average yearly increase
weight? 4.
A
merchant buys a
$250.50, silks
^5^125. 75,
discount of ^ of the
bill
of
goods
bill for cash.
:
cotton goods
He
notions -¥75.80.
What
receives
a
does he pay for
the goods? 5.
A man
food of a
at
man
hard muscular labor requires 1^ times the moderate muscular work. If a man at
at
hard work consumes
how much
11-|
roast beef
is
ounces of roast beef at a meal, required for a
man
at
moderate
work?
man
moderate work requires | the amount of food required for a boy from 10 to 12 years of age, and 6.
If a
the food of a
at
man
at
moderate work for supper consists of
3 ozs. of bread, | oz. of 2 ozs. of cake, a
how much
boy of 12 years 7.
If the
man
of
butter, 3 ozs. of bananas, of these foods is required
and
by
age?
requires 5 times the
amount
of food
:
PRACTICAL ARITHMETIC
132
required by a child of 6 years of age, foods
is
how much
required for the 6-year-old child
of these
?
COMPOUND AND COMPLEX FRACTIONS
An
163.
a
indicated multiplication of a fraction
Compound
Fraction,
e,.g.^
f
of f or
| x f
is
is called
a
compound
is
sometimes
fraction.
An
164.
indicated division of a fraction 2
called a tions,-
They
Complex Fraction,
e.g., -2-
and are read f divided by
and I are complex
^ and
|-
frac-
divided by
5.
are solved as are other examples in division of frac'
tions.
EXERCISE
103. — "WRITTEN
Reduce to simple fractions 12 1.
3
^\'
:
COMMON FRACTIONS EXERCISE
104.
— OEAL
Find what part the second number 1.
133
is
of the first
PRACTICAL ARITHMETIC
134
Dried beef
15.
at
#1.80 per dozen cans costs how much
per can?
A boy has 50 cts.
16.
10
cts. for a tablet.
A
17. it
He spends 30 cts. for a book, and What part of his money has he left?
boy's spending
for a fielder's glove.
money
What
is
$1.60.
He
spends |
of
does the glove cost?
18.
If a half-ton of coal costs $4. 50, what will 5 tons cost?
19.
If the food required
expressed as 100 parts,
by a man
how many
at
moderate work
is
parts are required by
the following? a,
man
at light
work requiring
-^^ of
the food of
man
at
moderate work. h,
woman at
moderate work requiring ^ of the food of man
How many
20. a,
at
moderate work. parts are required
by the following?
of the food of a
man
at
child 2 to 5 years requiring ^ of the food of a
man
at
child 6 to 9 years requiring
-|
moderate work. b,
moderate work. c,
child at
d,
under
2 years requiring
A
21.
boy can walk
goes 4 miles.
when
how
of the food of a
man
moderate work.
man at hard muscular work a man at moderate work.
22.
-^-^
How
requiring 1^ of the food
| of a mile
of
while an automobile
far will the automobile
have gone
the boy has walked 5 miles? If four
long will
two boys?
boys can it
mow
the school lawn in 1^ hours,
take one boy?
How
long will
it
take
COMMON FRACTIONS
How many
168.
16| is
cts.,
12|
same
of a dollar?
J of 1 dollar
is
by any number multiplied by that number.
cents in ^ of a dollar?
^ of a dollar
is
^ of a dollar multiplied by any number by that number.
as 12| cts. multiplied
The part
170. is
cts.
How many
cts., therefore,
the
|^
therefore, | of a dollar multiplied
the same as 16| 169.
is
cents in
135
of a
number which
will exactly divide
it
number.
called an Aliquot Part of that
by ^ dollars, ^ than to multiply or divide by 12^, 16|,
It is often easier to multiply or divide dollars, or ^ dollars
or 334 cts.
EXERCISE 1.
What
2.
At
106.
— ORAL
will 18 pineapples cost at 16^ cts. apiece?
12|
cts.
a yard,
what
will 12 yards of
gingham
cost? 3. 4.
At 33J cts. apiece, what will 15 blank books cost ? At 25 cts. each, what will 16 pairs of stockings cost? EXERCISE
107.
— WRITTEN
1.
40
is
what part
of 100?
7.
621
is
what part
of 100?
2.
60
is
what part
of
100?
8.
87-1 is
what part
of
100?
3.
80
is
what part
of 100?
9.
66|
is
what part
of
100?
4.
75
is
what part
of 100?
10.
83|
is
what part
of
100?
5.
37|
is
what part
of 100?
ii.
is
what part
of
100?
6.
31^
is
what part
of 100?
12.
41f 58^
is
what part
of
100?
REDUCTION OF DECIMAL FRACTIONS 171.
terms:
Express as .4, .04,
common
.004, .0004.
fractions and change to lowest
:
PRACTICAL ARITHMETIC
136
Express as common fractions and reduce to lowest terms
.
.25, .025, .0025.
common fractions and reduce
Express as
to lowest terms
.300, .00003. 172.
To
reduce a decimal to a
common
fraction, write
the figures of the decimal for the numerator, with 1 and as
many
number
ciphers as there are decimal places in the decimal for the denominator,
and reduce
this fraction to
lowest terms.
EXERCISE Reduce numbers: 1.
to
common
108.
— WRITTEN
fractions in lowest terms or to mixed
COMMON TRACTIONS 175.
If the
137
denominator of a common fraction has other
prime factors than 2 or
5,
cannot be completed.
In such cases
the division of the numerator it is
customary to
carry out the decimal to the fifth place and to place a plus
sign after the decimal, thus 24.28978 +.
PRACTICAL ARITHMETIC
138
the outer circle in
all
cases where
it is
Multiply the numbers at
49-112.
ber in the outer 113-176.
numbers
p from
Subtract the nuinbei* in
33-48.
at
each number
b, e, g, I
by each num-
circle.
Divide each number in the outer 6, c, g,
and
circle
by
the
i,
EXEECISE
HI.
— WRITTEN
Express as decimals, carrying the division to the place in cases of inexact decimals 1.
in
possible.
fifth
:
if-
2. 3. 4. 5.
EXERCISE REVIEVi^
112.
— WRITTEN
PROBLEMS
number?
1.
160
is
f
2.
144
is
j^ of
3.
160
is
1^
of
4.
180
is
|-
of wliat
5.
364
is
^ of what number?
6.
In repairing the waste pipes of a house 4 pieces
needed,
— 3^
the total
of vs^hat
ft.,
number
what number?
what number?
9|
number?
ft.,
of feet
41
and 17| needed? ft.,
ft.
long.
are
What
is
:
REVIEW PROBLEMS 7.
A
six-sided chicken yard
on another, 51 on another, side,
1 yL
and 4 rods on the sixth
is 3| rods on one side, 41 on another, 2| on the fifth
If
How many
side.
fence will be required to enclose 8.
139
rods of
it ?
an apple tree bears 2678 apples and J drop, and
wormy, what fraction of the apples good? How many apples are good?
^ of the remaining are originally present
is
If the trees are
sprayed to prevent worms, only about -^ will be wormy. What will the fractional gain from spraying be? How many apples are gained? 9.
What
the cost of spraying 197 apple trees for
is
black rot at S^ 3 times?
cts. a tree for
Adding
1-| cts.
each application, spraying
to cover cost of arsenite of lead
used to prevent the codling moth, what
is
the cost?
According to the Arkansas Experiment Station, | of lbs. of pork, and the same area in corn produced 104 lbs. What fraction 10.
an acre of peanut pasture produced 312
of the value of
peanuts as a pork producer
is
possessed by
corn ? 11.
Corn
at different stages of
and dry matter in each
COKN PER Acres
100
Fully tasselled
....
Fully silked Kernels watery to full milk Kernels glazed
....
Ripe
What
growth contains water
ton, as follows
100
Acres
Dry Matter PER 100 Acres
90 tons
82 tons
8 tons
129 tons
113 tons
15 tons
163 tons
140 tons
23 tons
161 tons
125 tons
36 tons
tons
102 tons
40 tons
11-2
fraction of the corn
Water per
is
dry matter in each period?
PRACTICAL ARITHMETIC
140
How much
greater is the fraction representing dry matter " ripe " than " fully tasselled " ?
A
12.
many corn
bushels of shelled corn will
is
13.
How
crib of corn holds 10,976 lbs. of ear corn.
grain and 56 If it requires
how many
acres will
lbs. of
it
yield
shelled corn
6| acres of corn to require to
it
fill
^ of the ear
if
make fill
a bushel?
a 93-ton
silo,
a 60-ton silo?
good roads to a farm increase What would this amount to its value about f 9^ an acre. on a 67-acre farm? 14.
It is estimated that
15.
Divide the number 81 into 2 parts such that ^
the
first shall
16.
A
piece of
man by working work
of
be f of the second. in 11|^ days,
7|-
hrs. a
day can complete a he work
how many hours must
per day so that he will complete the work in 15 days? 17.
If a
boy can do |
as
much
will he require to complete the
as a
work
working the same number of hours
man, how many days
in the above problem, as the
man?
CREAMING 18.
In skimming cream from shallow pans in the usual
way, about ^500 of the skimmed milk
is
butter
fat.
Milk
skimming usually contains j^^q butter fat. What fraction of the original butter fat is lost in skimming? before
cow produces 256 lbs. of butter how much is lost in skimming? What is 19.
23
cts.
20.
If a
fat in a year, its
value at
a pound?
In setting milk in deep pails and using better skim-
ming methods, the skimmed milk
is
only g^^ butter
fat.
EEVIEW PROBLEMS
What
fraction of the original butter fat
What
many pounds? 21.
When
22.
How many
What
What
fat.
pounds?
fraction
is
-^
cow
If a
is
butter
How-
skimmed milk
is
fraction of the butter fat
is
is
What
used,
is its
value?
saved by the separator that
by the shallow-pan method? What fraction that is lost by deep setting? 23.
lost?
is
value?
hand separator
a
only g-j^ butter lost?
141
is
is losti
thus saved
in a year gives 6278 lbs. of milk of which
fat,
and
-^-^-^
of this
amount be
lost in sepa-
PRACTICAL ARITHMETIC
142 rating,
and there be an increase
of J
in weight in the
amount remaining (due to water, salt, etc., used ing the butter), what will be the butter yield?
How many
24.
cows will a dairyman need
mak-
in
in order to
save enough butter in a year, by the use of a separator, to enable
him
to
pay
for a
Use
|65 separator?
the facts
given in problems 18, 19, and 21. In one herd the average of butter fat per cow
25.
was 285.62
containing ^
cow
fat,
were
converted into butter
all
what would be the amount?
in the herd
much 26.
If this
lbs.
gave 439.37
lbs.
of
butter
The fat.
best
How
butter does that equal?
Assuming that
in
problem 23
becomes skimmed milk and that
it
be
-I
of the
^q^q
q"
whole milk
butter
fat,
and
that f of the cream becomes buttermilk containing ^^ of butter fat, what is the loss in butter fat? What is its
equivalent in butter
?
27. The cost of feed to produce 100 lbs. of milk in New York was as follows from 19 different cows: f .62, |.61,
$.46, 1.55, 1.49, $.89, $.82, f.62, $1.48, $.77, $.70, $1.07, $.74, $.85, $.75, $.81,
average cost per pound 28.
The
$.59, $.53, $.44.
What was
the
?
cost for each
pound
of butter fat
was $.115,
$.155, $.18, $.225, $.175, $.16, $.13, $.16, $.17, $.14, $.12,
$.26, $.125, $.14, $.185, $.21, $.27, $.15, $.225.
was the average cost 29.
of butter fat per
If a tree 9 ins. in
lumber as one 18 the smaller tree
is
of the larger tree,
pound
diameter yields only
ins. in
What
?
-|
as
much
diameter, and the lumber of
worth only | as much per foot as that what is the difference in the value of
KEVIEW PROBLEMS two such and
it is
cts. a
butter
fat,
one yields 132
ft.
of
lumber
foot?
composed
If 1 lb. of butter is
30.
is
trees, if the smaller
worth 1|
143
of j.^^-^ watei-,
|||
how much
salt
-gf^^ curd, and the balance salt,
there in 16 lbs. of butter?
A
31.
and
hayseed mixture consists of 3 parts red clover
How many
7 parts tall oat grass.
pounds
of each are
needed for 27 acres, using 35 lbs. to the acre?
Another mixture
32.
4 parts,
Using 40
meadow
is
fescue 2 parts, and red clover 1 part.
the acre,
lbs. to
red top 3 parts, orchard grass
how many pounds
of each
kind
of seed are needed for 29 acres?
A
33.
good pasture mixture
is
Kentucky blue-grass
2^-
parts, white clover 1 part, perennial rye 3 parts, red fescue 1 part, red top
many pounds
2^ parts.
of each are
34. If, in a score
Sowing 35
card for judging butter,
points are given for perfect
and J^
color,
for salting,
the acre,
lbs. to
needed for 26 acres
what
flavor,
^-^
of the total
^\ for grain, ^g- for
will be the numerical value
assigned to each in a score card of which the total of points is 100
A
35.
carcass
|-
alive
less
;
weighs 312
what
is
lbs.
and the dressed
the weight of the dressed
?
What
36.
number
?
hog when
carcass weighs
how
?
is
the difference in cost of a 2-2-50 (2
lbs.
of bluestone, 2 lbs. of lime, 50 gallons of water) and a
Bordeaux mixture with lime at 1^ cts. a pound, bluestone at 6| cts. a pound ? Using 150 gallons to the 6-4-50
acre,
what
is
the difference per acre in the cost of these
two mixtures?
PRACTICAL ARITHMETIC
144
In an Arkansas orchard 6 apple trees sprayed
37.
to
prevent the bitter rot yielded 8674 sound apples and 989 diseased ones; on 3 unsprayed trees 188 sound apples
and 4244 diseased ones. What fraction was sound in each case? Reduce to similar fractions for comparison. How many times greater is the yield of sound apples when sprayed than when not sprayed
Two
38.
?
cows, Glista and Belva, were very similar in
outward appearance, age, and weight. Glista required 21 cts. worth of feed to produce 1 lb. of butter fat. Belva produced 1
What
lb. for 15|- cts.
fraction of the
feed required by Glista was sufficient for Belva
Seven samples
39.
of clover seed sold per bushel (60 lbs.)
for: 15.50, §5.25, 15.00, 14.75, $4:.15, .$4.00,
They
?
contained, respectively:
55^,
4^5^^^,
and 13.50.
55y2_.^
55^,
48,
and 27-^\ lbs. of good seed to the bushel. What was the price paid for a bushel of good seed in each case? 52^3j_
Concrete
40.
is
made
of
cement, sand, and aggregate
(coarser material, gravel, crushed stone, etc.) in quanti-
of each material are required for
ploying this mixture, to
4000
Another mixture often used
41.
make 4000
lbs. of
how much
43.
what
is 1
concrete
?
Em-
to 2J to 5. is
needed
how many
pounds
concrete?
of each ingredient are needed to crete
lbs. of
of each material
Using the quantities 1 to 3
42.
How many pounds
part to 2 parts to 4 parts.
ties of 1
to
6,
make 4000
lbs. of con-
?
If the entire corn plants is
shucks,
the weight of grain, if
2^0"
on an acre weigh 6800
lbs.,
cobs, stalks, leaves, and
of the plant be ears,
and
of these | be grain
KEVIEW PROBLEMS and \\ be and J^ shucks ?
and \ cobs leaves,
A
44.
stover,
;
145
and of
this
3-penny standard wire nail
is
4-penny nail IJ ins., a 5-penny nail 1| nail 2 ins., an 8-penny nail 2|
May
a 10-penny nail 3 ins.,
ins.,
ins.
there for
is
every pennyweight increase
stalk,
is
ins.
17, tgoS.
Mis.
Phlla.
.'
, .
(MUi&Cliestiiiit
Sts.)..
AM
[lhavb
Baltlmoro ((!uQ(lnSts.)+ Relay .....,....> Hanover ..** DoTScy
.
9.0 11.5
^
Jessup
iS-8
10 pennyweights
Annapclls+ Annapolis
If it is desired
a
board
|-in.
to nail
a
to
IJ-in.
board with as long a nail as
.arr.
.
17.9
but not allow the
come nearer than
nail to
^^g-
going through both
of
in.
how long
pieces,
a nail can
Ive,
Laurel
£
Muirkirlc. Beltsville
5
17.9 19.4 ai.3
5 38
24-9 27.1 29-9 33-4
5 54
ton
J+lv. 40.0
Station
X
Rockville Gaithersburg
Boyd
...
BrunswicK +..
Weverten Harper's Fernr+
46.
Martinsburg +
Ill
....
i%-in.
piece to a f-in. piece, with a
3-penny
.
nail,
how much
the nail extend
v.
. . .
North MoUDtsun
a
nailing
. .
will
beyond the
Cherry Run+
Hancock +
Sir John's
Run
Woodmont Orleans Road Baird....
<
Magnolia
Paw Paw Patterson Creek
In nailing a
47.
to
-J-in.
a 1-in. piece, with
penny
nail,
how much
through the wood ? will
it
project
piece
Cumberland +
92.7 9S.6 103.0 106.5 114.2 121.6 127.6 137-0 142.6
AM •6.51
t7io 725 738 IS
AM
804 fsao 820 644 A M 653 714 $ 729 5 147s 740 '52.9 752 159-8 807
$
Okonoko Green Spring
wood?
AM
56-5 fits 69.1 82.8 S9.8
".
WashlnEton June
Kemeysville
?
542 546
V^ 003 6 H/attsvllle 4ao 625 I ng- jKev Hsioii) g ar.
Branchvtlle
Shenandoah Juno+
be used
tsoo 516 523 528 532 538
.arr,
AnnapolisJunctlon.lve, Savage
wash possible
1*1
.Ive.
An n»poll« June $
45.
long, a
a 6-penny
ins.,
between 3 pennyweights and ?
-^
West 33d Street liiberty Street
fraction of an inch in-
crease in length
1\
New Vork
and a 20-penny nail 4
What
|
S
163.1 168.0 172.8 178.3 185.1 192.2
{arrive
8 14
82s 836 848 903 9 20
A H
a 5will
the nail lack of reaching
In using a 6-penny
beyond the wood?
nail,
In
how much
each
of
the
?
PRACTICAL ARITHMETIC
146
above cases what will be the result tersunk
-jJg
The
48.
145
on page
table
far
is
Annapolis
from Baltimore
it
Junction
a reproduction of a
to
distances
Washington?
Washington
to
?
From
Washington
Ferry to Cumberland?
Harper's
tinsburg to Cumberland?
49.
is
in miles.
Harper's Ferry?
nolia
the nail be coun-
and Ohio time-table showing the
Baltimore
between stations
How
if
in. ?
to
Mar-
Annapolis Junction to Mag-
?
What would
be the cost for each of these
dis-
tances at the following rates per mile, which are charged
by some railroads: 2 If a
50.
farm
is
|^
cts.,
2^
cts.,
in corn,
^f
2|
cts.,
and 3^
in wheat,
-^^ in
in pasture, and the remaining 5 acres
1^ in oats, -^-^ pied by houses, other buildings,
how many
the farm, and
A
51.
daughter
man
caught
53.
j-
fish
A
as
many
occu-
the size of
is
acres are in each crop?
son ^ of his estate, to one daughter the remainder, amount-
What was
Walton caught
52.
what
clover,
is
his
to
|, to the other
ing to f 3268.
many
left
etc.,
cts.
|
the value of the estate? as
many
as Vernon,
fish
as
whose catch
Clara,
who
63.
How
is
did Walton catch? horse
is
worth 7 times the buggy.
of the value of the horse
is
What
part
^^ the value of the horse and
buggy? 54.
It
is
estimated that about 1700,000,000 are
lost
annually in the United States through insect and fungous diseases
;
|
of
What amount
this
could be
prevented by spraying.
could be saved by spraying?
:
ACCOUNTS AND BILLS 176. 177. 178.
A A A
Debt
is
Debtor
that wliich one person owes to another.
who
a person
is
Credit is that wliich
owes.
due one person from
is
another. 179.
A Creditor
180.
An
181.
A
the
is tlie
Account
is
person to
a record of debits
Balance of an account
sums of the debits and
182.
and
A
is
the debt
and
is
due.
credits.
the difference between
credits.
Bill describes the
goods sold by giving quantity
price.
183.
The Footing
184.
A
A
whom
of a bill
is
the total cost.
Receipt acknowledges the
payment
of a bill.
by the creditor's writing the words " Received Payment " and his signature. bill is
receipted
ORDERING GOODS
185.
Hendersonville, S.C, Sept. 10, 1908.
Chisholm, Ward & Co., Market and Madison Sts., New York, N.Y.
Dear me by
Sirs
:
Please find enclosed 18.37, for which send
express the following items 147
148
Catalogue No.
PRACTICAL ARITHMETIC
;
ACCOUNTS AND BILLS complete
as a
it
and write
bill,
149
a receipt indicating its
payment.
cts.
|7
Cereals: 1 bbl. flour
2.
10
;
@3 @ 10
corn meal
lbs.
cts.
4 pkgs. breakfast foods cts.
10
;
tapioca
lbs.
@7
Sugars
3.
:
cut loaf sugar cts.
10
;
lbs.
@9
rice
lbs.
cts.
25
lbs.
@
10
lbs.
;
10
lbs.
cts.
1
;
graham hominy
flour
@3
@
3J cts. pkg. corn starch 10
@ 15
2 lbs. macaroni
@
granulated sugar
cts.
;
cts.
:
6 cts.
3
;
5 lbs.
;
@
2 lbs. pulverized sugar
@ 5J
brown sugar
@
10
cts.
Canned vegetables
4.
peas, 6 cans
;
;
cts.
cans@ f 1.50
a dozen;
tomatoes, 12 cans
@ $ 1.35
corn, 6
$ 1.50 a dozen
;
10
a dozen.
Canned
5.
2 cans
ries, 6.
2 lbs.
fruits
@
25
cts.
fruits
@
cts.
prunes, 5 lbs.
@
;
19
raisins, 2
Lima
cts.
cts.
dried black beans, 1 quart, 10
:
@ 15
beans, 5 quarts
cts.
beans, 1 peck, 75 cts.
;
split peas, 2 quarts
Canned meats
:
ham, 2
8.
lbs.
@ 30 9.
cocoa, 10.
cts.
;
salmon, 2 cans
Beverages
^
lb.
@ 88 cts.;
Sundries
:
lbs.
@
coffee, 1 lb.,
:
1
Orleans molasses, 60
;
cts.
Dried vegetables dried
;
;
Dried 13
;
plums, 2 cans
:
apricots, 2 lbs. 7.
@ f 3 a dozen cher@ 25 currants, lbs. @ 15 @ 15 cts.; evaporated
peaches, 6 cans
:
cts.
@
20
35
30
dried white
;
@ 10 cts. cts.
;
tongue, 2
cts.
cts.;
tea, 1 lb.,
75
cts.;
chocolate, 1 lb., 35 cts.
gal. cts.
vinegar, 25 ;
cts.
baking soda, 2
;
1 lbs.
cream of tartar, 1 lb., 50 cts.; baking powder, i lb. cts.; salt, 25 lbs., 25 cts.; white pepper,
gal.
New
@ 8 cts. 1 lb.,
@ 50
54
cts.
DENOMINATE NUMBERS How many
187.
inches are there in 1 foot
Express
?
2^ feet as feet and inches.
A
concrete
number wliich represents one kind of unit is Number e.g., 2^ ft. is a simple number.
called a Simple
A
188.
ent units a
;
number which is expressed in Compound Number, e.ff., 2 ft. 6
concrete called a
is
differins. is
compound number. Concrete numbers denoting units of measure
189.
called Denominate Numbers, e.g.,
ft.
2|-
is
are
a denominate
number.
A
190.
denominate number composed of units of one
denomination 2^-
ft.
called a Simple Denominate Number,
e.g.,
a simple denominate number.
is
191.
is
A
denominate number composed of units
than one denomination
is
Number,
ins.
e.g.,
2
ft.
6
of more
called a Compound Denominate is
a
compound denominate
number. 192.
derived
A is
unit of measure from which other units are called
a Standard Unit;
standard unit of money, the pound weight, the yard 193.
The
is
e.g., is
a standard unit of
the dollar
is
a
a standard unit of
measure
of length.
process of changing the unit of a denominate
number from one denomination 150
to another without chang-
;
DENOMINATE NUMBERS ing the value
called Reduction,
is
changing 1 yd. to 36
e.g.,
change be from a
If the
194.
ins.
higher to a lower denomination, the process
Reduction higher, duction,
36
ins.
it
from a lower to a called Ascending Re-
is
changing
e.g., is
Descending
called
is if
;
yd.
1
to
descending reduction
changing 24
ins. to 2 ft. is
ascend-
ing reduction.
UNITS OF LENGTH
195.
A
line has length only.
Meas-
ures that are used in measuring
measures.
lines are called Linear 196.
_
TABLE OF LINEAR MEASURES
= 1 foot (ft.) 3 feet or 36 ins. = 1 yard (yd.) 5|^ yards, or 1Q\ ft. = 1 rod (rd.) 320 rods, or 5280 ft. = 1 mile 12 inches (ins.)
(mi.)
The folio-wing abbreviations are to represent commonly used
also feet
:
and
" to
represent inches.
EXERCISE 1.
2.
114.
How many
in 5 ft.?
In 10
— ORAL
inches are there
ft.?
How many
3 yds.?
'
feet are there in
In 7 yds.?
—
151
:
PEACTICAL ARITHMETIC
152
How many feet are there in 2 rds. ? How many inches are there in 2 yds. ?
3.
4.
197.
Reduce 12 yds. 2
Since 3
36
ft.
+2
= l yd., = 38 ft.
Since there are 12
ins.=456
ins.
466
In 2
ins. in
ins.
+8
a foot, in 38
ins.
?
3 ins.
ft.
?
8 ins. to inches.
in 12 yds. there are 12
ft.
f t.
ft.
In 4 rds.
=464
ft.
x3
ft.
there are 38 x 12
Hence 12
ins.
= 36
ft.
yds. 2
ft.
8 ins. =464 ins.
To reduce
compound denominate number to lower units, multiply the number of the highest denomination by the number of units required to change to the 198.
a
next lower denomination, and to the product add the number of units of this denomination given. Proceed in like
manner with
this result
obtained until the number
and each successive
result
reduced to the required
is
denomination.
EXERCISE
Reduce
115.
— WRITTEN Reduce
to inches:
to feet
5.
2 mis. 15 rds. 6
6.
3 mis. 30 rds. 15
7.
25 rds. 10
8.
3.875 mis.
1.
2 yds. 2
2.
4 rds. 2 yds. 1
3.
25 rds. 12
4.
I
9.
Measure the length, width, and height
ft.
6 ins.
ft.
4
ft.
ins.
rds.
room, and express as
feet, as inches, as
ft.
4
ft. ft.
ins.
of your school-
yards, as rods, and
as fraction of a mile.
EXERCISE 1. 2.
116.
— ORAL
How many feet in 24 ins. ? How many yards in 30 ft.?
In 36 ins.? In 48
ft. ?
In 18
In 36
ins.
ft. ?
?
DENOMINATE NUMBEKS 3.
4.
How many rods in 33 yds.? How many rods in 11 yds.?
199.
Reduce 250
feet,
with 10
6 = number of yards, = 6 yds. 2 ft. 10 ins. 200.
number
ft.,
J^ of 250
remainder.
ins.
To reduce
In 66 yds.?
In 77 yds.?
In 23 yds.?
In 99 yds.?
ins. to yards, feet,
Since 12 ins. equal 1
witli
2
153
and inches:
= 20 = tlie number of ft. = 1 yd., { of 20 =
ins.
Since 3
Hence, 250
remainder.
ft.
a denominate
number
to an equivalent
of higher denomination, divide the given
ber by the
number representing the
ins.
units of
num-
the next
Proceed with this and each succesmanner until the required denomiThe last quotient with the remainders nation is reached. will be the required compound denominate number. higher denomination.
sive quotient in like
EXERCISE
117.
1.
Reduce 950
ins. to feet.
2.
Reduce 496
ins. to feet,
3.
Reduce 8966
4.
Reduce 375
5.
Reduce 42,560 yds.
6.
Reduce
ins. to yards.
ft.
to rods
35'6|^ rds.
and yards.
to rods
and
miles.
to miles.
METRIC UNITS OF MEASURE
201.
In
— WRITTEN
many
foreign countries and to an increasing ex-
country, another system gf measures called
tent in our
own
the Metric
System
is
used.
10, as are decimal fractions,
This system
and
is
is
founded upon
simpler and easier for
purposes of computation than are other systems.
PRACTICAL ARITHMETIC
154
METRIC LINEAR MEASURES
202.
= 1 centimeter <^cm.) = 100 mm. = 1 decimeter (dm.) = 1000 mm. = 1 meter (m.) 1000 m. = 1 kilometer (km.)
10 millimeters (mm.) 10 centimeters (cm.) 10 decimeters
The meter yard.
It
= 100
is
the unit of measure corresponding to the
39.37
is
cm.
ins. long.
EXERCISE
118.
=
.62138 mi.
-ORAL
part of a meter
is
1 centimeter? 3 cm.?
2.
What What
part of a meter
is
1 millimeter? 6
3.
What
part of a meter
is
100 millimeters? 500 mm.?
4.
Measure the length, width, and height
1.
room, and express as meters 203.
A
;
of
mm.? your
school-
as centimeters.
REPRESENTATION OF MAGNITUDES
clear conception
often gained
is
km.
1
of
the relative sizes of numbers
by representing the numbers by
lines, let-
ting the length of the line bear direct relation to the size of
the number,
e.g.,
the approximate amount of wheat
produced in 1900 was: United States 520,000,000, Russia 400,000,000, France 300,000,000 bushels.
\
in.
Letting a
long represent 50,000,000 bushels, a line 1^
would represent the yield 2| ins. that of the United 50
UNITED STATES RUSSIA
FRANCE
100
150
ins.
line
long
of France, 2 ins. that of Russia,
States, thus: 800
260
300
350
400
4B0
500
:
DENOMINATE NUMBERS EXERCISE
119.
155
— WRITTEN
Represent the coal production of the following counLet { in. equal 2n,000,000 metric tries in metric tons. The United States was as follows production tons. The 225,000,000, the United Kingdom 225,000,000, Germany 155,000,000, Austria-Hungary 37,500,000, and France a 1.
:
over 25,000,000 metric tons.
trifle 2.
Represent the
duction
100
following
the
of
silk pro-
90
countries, letting ^ in. rep-
pounds:
resent
1,000,000
China
14,000,000, Italy
7,000,000,
Japan
7,000,000,
Turkey, France, Spain, and India together 3,000,000 lbs. 3.
Represent the cotton letting
production,
The United
in. 40
bales
1,000,000
equal
{
50
States 10,250,-
000, India 2,250,000,
SO
China 20
1,250,000, 4.
Egypt
Represent
1,165,000.
the
corn
production in 1898, ^ in. representing 100,000,000 bushels. of the
The
production
10
ssMay
34
83
Fig.
United States was 2,100,000,000
a
that of other
countries about 700,000,000. 204.
clearly
Change in a quantity from time to time may be shown by arranging, side by side, the lines repre-
PRACTICAL ARITHMETIC
166 senting the
may be May
varying magnitudes so that they
readily compared
;
thus, the highest temperature for
22d, at a given place, was 75 degrees, the
23d 80
de-
and the Rejiresenting the temperature by ver-
grees, the 24th 85 degrees, the 25tli 96 degrees,
26th 76 degrees.
1 degree
tical lines,
=
mm.,
1
and connecting the tops
at equal distances apart,
of these lines,
This
on the preceding page.
we have
figure
A
The
is called a Curve.
vertical lines are unnecessary, the curve alone being sufficient to picture the facts.
I860
1870
1880
1890
190O
soot iu
I «D = O
700
600 500 400
g
300
^
200
1
100
—
Curves showing the relative increase in population and in wheat production in the United States, wheat and population both expressed in
Fig. B.
millions.
EXERCISE 1.
120.
— "WRITTEN
Interpret in words the meaning of the curves shown
in the above figure. 2.
in
The maximum
May
in 1894,
37
price of corn per bushel in Chicago
during 9 years was as follows 55
cts., in
cts., in
1898, 35
1895, 29 cts.,
cts., in
:
In 1893, 38
1896, 25
cts., in
in 1899, 40 cts., in 1900, 58
cts.,
1897, cts..
DENOMINATE NUMBERS
Show
in 1901, 65 cts. 2
mm.
represent 1 cent.
157
hj
these values
a curve, letting
Place the lines representing years
1 cm. apart.
The maximum
3.
in Chicago in 1905
wheat per bushel
v^holesale price of
was
ruary 11.24, March
as follows: Januarj^ 11.21, Feb-
April
11.19,
May
fl.l8.
11.14,
June 11.20, July 11.20, August 11.15, September 10.95, October 10.92, November |!0.92, December |0. 90. Show the changes in price by a curve, letting 1 cm. represent 1 Place the lines representing months 1 cm. apart.
cent.
SURFACE MEASURE
is
205.
A
206.
If a surface is flat
surface has two dimensions. Length and Width.
and has four square corners,
it
called a Rectangle.
A
207.
rectangle with four equal sides
is
called
a
Square.
The
208. is
unit of surface
is
foot
is
is
it
of a surface
1.
A
rectangle
is
6
ft.
121.
is
1
ft.
if it is
is
square
long.
A
1 yd. long.
expressed by the number
2
ft.
— ORAL
long and 1
square feet are there in
square feet
A
contains.
BXEECISB
many
is
square inch
1 in. long.
a square each side of which
The Area
209.
of square units
is
each side of which
a square
square yard
A
a square.
a square each side of which
wide? 3
its ft.
wide? 6
How How many
wide.
ft.
surface? ft.
wide?
PRACTICAL ARITHMETIC
158 2.
How many
whose 3.
How many
whose 4.
square centimeters are there in a square
sides are 6 cm. long? 7 cm.
How many
are 8 rods
210.
square inches are there in a square
sides are 5 ins.? 6 ins.? 8 ins.? 10 ins.? 12 ins.?
?
?
9 cm.
?
18 cm.
?
square rods in a school lot whose sides ? 11 rods ? 13 rods ?
9 rods
SQUARE MEASURE
=1 9 square feet = 1 30^ square yards = 1 160 square rods = 1 640 acres = 1
144 square inches (sq.
ins.)
square foot (sq.
ft.)
square yard (sq. yd.) square rod (sq. rd.) acre (A.)
square mile (sq. mi.)
METRIC SQUARE MEASURE 100 square rnillimeters (sq.
mm.) =
1 square centi-
meter 100 square centimeters
=1
(sq. cm.)
square deci-
meter
(sq.
dm.)
100 square decimeters
=
1 square meter
=
=
2.4711 A.
(sq.
10,000 sq. m.
1 hectare
m.)
:
DENOMINATE NUMBERS EXBBCISB
Reduce
to square inches
1.
13
2.
19 sq. rds. 7 sq.
3.
26 sq. rds. 6 sq.
4.
I sq. rd.
5.
^
Reduce
:
m. to
sq.
to square yards
6.
130
ft.
7.
2 sq. mis. 80 sq. rds.
ft.
8.
8 A. 5 sq. rds. 29 sq. ins.
9.
5.47 A.
cm.
10.
Measure the area of
11.
— WRITTEN
122.
sq. yds. 5 sq. ft.
sq.
159
sq. rds.
12 sq. yds.
86.4 sq. m. to sq.
tlie floor,
and
mm.
eacli of the four
walls of your schoolroom, and express as square feet
;
as
square yards.
EXERCISE
Reduce
123.
— WRITTEN
to higher denominations
1.
6740
2.
984
3.
540
ft.
7.
12,346 sq. rds.
sq. yds.
8.
39,271 sq. rds.
9.
3240 sq. cm.
4.
22,160 sq.
sq. ins.
5.
9678
sq. ram.
6.
6782
sq. ins.
:
sq.
cm.
SURVEYORS' MEASURES 211.
Surveyors in measuring use a Chain consisting
of 100 links
212.
;
its
length
is
4 rds., or 66
ft.
TABLE OF SURVEYORS' LINEAR MEASURE
=1 link (1.) 25 links = 1 rod (rd.) = 1 chain (ch.) 4 rods = 100 80 chains = 1 mile (mi.) 7.92 inches
1.
PRACTICAL ARITHMETIC
160
TABLE OF SURVEYORS' SQUARE MEASURE
213.
=1 =1 acres = 1
16 square rods
square chain (sq. oh.) acre (A.)
10 square chains
640
mile=
1 square
36 sections
square mile (sq. mi.)
1 section (sec.)
=1
BXEECISE
township. 124.
— WRITTEN
1.
Reduce 1560
2.
Reduce 960
3.
Reduce 67,820
4.
Reduce | mi.
5.
Reduce 60
6.
Measure the distance around your school yard.
press in chains
rectangular,
;
sq. yds. to chains.
sq. chs. to acres. ins. to chains.
to chains.
chs. to feet
in links
how many
fraction of an acre
;
;
to inches.
in feet
;
in rods
square chains does
in yards.
;
it
Ex-
equal ?
If
What
?
MEASURES OF VOLUME
A
214.
body that has length, width, and thickness
is
called a Solid. If the rectangles
215.
squares, the solid 216.
is
The number
forming the faces of a
solid are
called a Cube. of solid units that a
body
contains
is
called the Solid Contents or Volume.
EXERCISE 1.
How many
125.
— ORAL
cubic inches are there in a rectangular
solid 1 in. long, 1 in. wide,
and
1 in.
thick
?
)
DENOMINATE NUMBERS
How many
2.
cubic feet are there in a solid 1
wide, and 1
1 ft.
What
the
is
ft.
name
How many
3.
thick
How many
?
ft.
long,
cubic inches
Name such
and
How many
thick?
1 yd.
cubic
a solid.
IIIIIIIIIII'
217.
UNITS OF VOLUME, OR CUBIC MEASURE
=1 =1 feet = 1
1728 cubic inches (cu. ins.)
cubic foot (cu. ft.)
27 cubic feet
cubic yard (cu. yd.
1^ cubic
bu. (approximately)
METRIC CUBIC MEASURE
218.
1000 cubic millimeters 1000 cubic centimeters
1000 cubic decimeters
EXERCISE
Reduce
?
of such a solid?
cubic yards are there in a solid 1 yd.
long, 1 yd. wide, feet ?
161
to cubic inches
1.
10 cu.
ft. 14.5
2.
46 cu.
ft.
126.
cubic centimeter (cc.) cubic decimeter (cdm.)
cubic meter (cbm.)
—WRITTEN
:
cu. ins.
149 cu.
=1 =1 =1
ins.
cu. yd.
3.
-^
4.
I cu.
ft.
PRACTICAL ARITHMETIC
162 5.
45 cu. yds. 18 cu.
6.
8 cu. yds. 16 cu.
7.
29 cu. yds. 12 cu.
8.
15 cu. yds. 1234 cu.
9.
72 cu. yds. 25 cu.
ft.
10.
15 cu. yds. 16 cu.
ft.
ft. ft.
425 cu.
ft.
1-J
15 cbm. 5 cdm. 10
12.
300 cbm. 150 cdm.
cc.
cu, ins.
ins.
Reduce to cubic centimeters 11.
ins.
:
13.
200 cbm. 125 cdm.
14.
275 cbm. 165 cdm. 15
cc.
EXERCISE 127.— "WRITTEN Reduce
to units of liigher denominations
:
1.
12,865 cu. ins.
4.
4256 cu.
2.
924 cu.
5.
98,764 cu. ins.
3.
6573 cu.
6.
325 cu.
7.
How many
many 8.
ft.
ins.
cubic feet?
How many
How many
ins.
ft.
cubic yards in your schoolroom
?
How
Cubic inches? cubic centimeters in your schoolroom?
cubic meters
?
DRY MEASURE
219.
2 pints (pts.)= 1 quart (qt.)
= 1 peck (pk-) pecks = 1 bushel (bu.)
8 quarts
4
A
bushel contains 2150.42 cubic inches.
The dry quart contains
A
67.2 cubic inches.,
Heaped Bushel, which equals about 1^ Stricken Bushels,
:
:
DENOMINATE NUMBEKS
163
used in measuring potatoes, apples, and other large vege
is
tables, also for lime, coal,
and other bulky substances.
EXERCISE
How many
1.
In
1
— ORAL
pints in 5 qts.?
In 7 qts.?
In 2 pks.
?
In 1 bu.
?
In 2 bus.?
bu.?
2.
128.
How many
quarts in 3 pks.?
In 3 bus.?
In 12 bus.? 3.
pks.? 4.
How many
bushels in 20 pks.?
In 25 pks.?
In 36
In 16 qts.?
How many
pints in 1 bu. 2 qts. 1 pt.?
EXERCISE Reduce
129.
to pints
— WRITTEN Reduce
to higher units
1.
5 bus. 3 pks. 5 qts.
4.
2254
qts.
2.
5 bus. 2 pks. 3 qts. | pt.
5.
3360
pts.
3.
.625 pk.
6.
4800 pks.
:
PKACTICAL ARITHMETIC
U'A
Reduce the following to fractions of a bushel. both as decimals and as common fractions 7.
-f^
pt.
8.
Get a bushel
11.
qt.
f of
9.
I pk.
can
make
pints,
and pecks
to see
the most accurate estimates at sight.
LIQUID MEASURE
220.
4
=1 =1 quarts = 1
gills (gis.)
2 pints
4
A
2 pks. 8 qts.
sand or grain and a quart measure,
and practise estimating quarts,
who
10.
Express
pint (pt.)
quart (qt.) gallon (gal.)
gallon contains 231 cubic inches.
31^
gals, are usually •considered a barrel,
and 2
barrels a
hogshead.
METRIC LIQUID MEASURE
221.
=1 =1 deciliters = 1
10 milliliters (ml.)
10 centiliters 10 1 milliliter 1 gram.
= 1 cubic centimeter.
centiliter (cl.) deciliter (dl.) liter (1.)
1 milliliter of water weighs
:
DENOMINATE NUMBERS EXBBCISB
— ORAL
130.
How many gills are there in 6 pts. ? In 10 pts. ? How many gills are there in 5 qts. ? In 8 qts. ? How many pints are there in 8 qts. ? In 12 qts. ? How many quarts are there in 60 pts. ? In 45 pts. ? How many milliliters are there in 3 1.? How many
1. 2. 3. 4.
5.
cubic centimeters in 7
1.
?
EXEBCISE
Reduce
131.
to units of lower
1.
12 gals. 2
2.
25 gals. 1 qt. 1 pt. 2
3.
I
4.
165
— WRITTEN
denomination
qts. 1 pt. gis.
gal.
I gal.
:
5.
14 gals. 2
6.
45
qts. 1 pt. 1 gi.
gals. 2 qts. 1 pt. 3 gis.
7.
.225 gal.
8.
J_. gal.
Reduce 9.
12 liters to deciliters.
With come
a pail of water
10.
-^
liter to milliliters.
and pint and quart measures, be-
familiar with all of these units.
EXERCISE Reduce
132.
— WRITTEN
to units of higher denomination
:
1.
145 pts.
8.
I
2.
424
gis.
9.
1 qt. 1 pt. to
3.
380 pts.
10.
786
4.
1984
gis.
11.
6.7 gis. to decimal of gallon.
5.
1286
qts.
12.
29 cu.
6.
1254
pts.
13.
1728
7.
-j-9j
14.
7| gals, to decimal of barrel.
deciliter to
liter.
gi. to fraction of quart.
decimal of gallon.
qts. to bbl.
ft.
and
fraction.
to gallons.
pts. to
hogsheads and fraction.
PRACTICAL ARITHMETIC
166
MEASURES OF WEIGHT
222.
Avoirdupois Weight
= 1 ounce (oz.) 16 ounces = 1 pound (lb.) 100 pounds = 1 hundredweight (cwt.) 20 hundredweight .= 2000 lbs. = 1 ton (T.) avoirdupois pound = 7000 grains. 16 drams (drs.)
1
A
cubic foot of water weighs 62.42 pounds.
of 2000 lbs. is sometimes called a Short Ton, the Long Ton being 2240 lbs. The long ton is used in measuring
The ton
coal at the mines.
500 cu.
ft.
of
hay
in loads, or
400 cu.
ft.
of
hay
in the
223.
mow
=
1 ton (approximately)
METRIC UNITS OF WEIGHT
Kilo
im^
=1 10 centigrams = 1 10 decigrams = 1 1000 grams = 1
10 milligrams (nig.)
centigram (eg.)
decigram (dg.)
gram
(g.)
kilogram (kilo or k.)
:
.
:
DENOMINATE NUMBERS
A
gram weighs 15.432 grains
equals the weight of a
it
;
167
cubic centimeter of water. 1
pound
= .45+
EXERCISE 1. 2. 3.
4. 5.
kilogram.
133.
— DEAL
How many ounces are there in 6 lbs. ? In 9 lbs.? How many ounces are there in 5 cwts. ? In 7 cwts. ? How many ounces are there in T. ? In 8 cwts. ? How many pounds are there in 44 ozs.? In 100 cwts.? How many tons are there in 60 cwts. ? In 100 cwts.? BXBECISE
134.
— WRITTEN
Reduce 1.
3 cwts. 21 lbs. 6 ozs. to ounces.
2.
10 T. 50 cwts. 15
3.
lbs. to
pounds.
5.
4. 5 I T. to pounds. .375 T. to hundredweights.
6.
^Q T. to pounds.
7.
17 cwts. 15
8.
2 T. 10 cwts. 25 lbs. to pounds.
9.
.675 cwt. to pounds.
10.
.5
lbs. 3 ozs.
10 dg. to milligrams.
to ounces.
T. to hundredweights.
EXERCISE Reduce
g.
135.
11.
21 lbs. 6 ozs. to grams.
12.
26 g. to grains.
— WRITTEN
to units of higher denominations
1.
2500
ozs.
4.
5275
lbs.
7.
15,674 cwts.
2.
9546
ozs.
5.
4250
ozs.
8.
2654
grs. to lbs.
3.
1056 mg.
6.
5420 mg.
9.
5460
grs. to g.
PRACTICAL ARITHMETIC
168
Tie up packages of sand or grain of various weights,
10.
and practise
lifting
them
until
you can judge weight with
some accuracy.
MEASURES OF TIME
224.
= = 24 hours = 7 days = months (mos.) =
60 seconds (sees.) 60 minutes
12
1
minute (min.)
1 hour (1 hr.)
1 day (da.) 1
week (wk.)
1 year (yr.)
" Thirty days hath September, April, June, and November, All the others thirty-one
Except the second month alone, Which hath but four and twenty-four Till Leap Year gives it one day more."
The common year has 365 days, or 52 weeks and 1 day. The leap year has 366 days. Years whose numbers are divisible by 4
A
and not by 100, or by 400, are leap years.
decade consists of 10 years
;
a score, 20 years, and a cen-
tury, 100 years.
EXERCISE 1.
How many
mins.?
136.
— ORAL
seconds are there in 3 mins.?
In 15 mins.
?
In 15 mins. 20
sees. ?
In 10
DENOMINATE NUMBERS
How many
2.
In 6J hrs.
minutes are there in 2
In 8^ hrs.
?
4.
In 6 hrs.
hrs. ?
?
?
Howmany hours inS days? How many days in 2 wks. ?
3.
169
In
4i-
In
5|-
days? In 5| days? wks.
In 5 wks.
?
?
In 5 days?
How many
5.
days in 2 years?
EXERCISE Reduce
137.
— WRITTEN
to units of lower
denomination
In 2 leap years?
Reduce
to units of higher
denomination
:
:
1.
6 hrs. 25 mins. 10 sees.
5.
2460 mins.
2.
10 days 5 hrs. 12 mins.
6.
142.2 hrs.
3.
f day. 867 days.
7.
89,764 sees.
8.
|-
4.
hr. to fraction of a da}'.
Practise estimating a second and a minute until
9.
you can do
so with
some accuracy.
ANGLE MEASURE 225. line,
A
Circle is a plain surface
bounded by a curved
the circumference, every point of which
is
equally
distant from a point within, called the Centre. 226. circle
A
straight line
drawn through the
from one point in the circumference
centre of a to another
called the Diameter of the circle. 227.
A Section
228.
The diameter exactly
229.
One-half the diameter
of the circumference
is
called an Arc.
divides the circle. is
the Radius.
is
J
PRACTICAL ARITHMETIC
170 230.
meet
is
231.
The
called
A
said to
is
Perpendicular to the other the line
AB
pendicular to the line line
so
A
which cuts anmaking with it two
equal adjacent angles
line, e.g.,
AB with the
made
is
lines that
an Angle.
line
other line
be
two
difference in the direction of
line
C
B CB. The two angles made by the CB are equal. Each of the angles is
per-
called a Right Angle,
e.g.,
the angles
and ABB are right
The
232.
of a circle
Degrees.
ABQ
angles.
circumference
is
measured
in
There are 360
degrees in a whole circum^08ti—
^
I
a
Lo
ference.
Degrees are not
uniform
of
length,
but
vary with the circumference of the
circle, e.g., the cir-
A measures
360 degrees as does
cumference of the also
the
circle
circumference of the circle B.
Degrees are
divided into minutes and seconds. 233.
TABLE or ANGLE MEASURE
=1 60 minutes = 1 360 degrees = 1
60 seconds (")
EXERCISE 1.
How many
(')
degree (°) circle.
— ORAL
degrees are there in a circumference?
In a half circumference?
cumference?
138.
minute
In I circumference?
In
cir-
DENOMINATE NUMBERS one line
If
2.
many many
is
171
drawn perpendicular
to another,
degrees are there in each angle so made?
how
How
degrees in the two angles?
How many
3.
What
is
degrees are there in a right angle?
the difference between a right angle and an
angle of 60°?
Of 90°?
Of 120°?
Of 100°?
What part of aright angle is 45°? 30°? How many minutes in 6°? 8°? 24°? How many seconds in 3'? 5'? 1°, 6', 6"?
4. 5. 6.
EXERCISE
Draw an
1.
grees
— WRITTEN
angle of 45 degrees
;
90 degrees
;
120 de-
180 degrees.
;
Reduce 40°
2.
139.
20' 20 " to seconds.
Reduce 43,200" to degrees. Draw an angle having number of degrees found. 4. Determine the number of degrees of " pitch " of 3.
the
some roof that
is
accessible to you.
COUNTING
234.
= 1 dozen (doz.) = 1 gross (gr.) 12 gross = 1 great gross (g. 20 things = 1 score. sheets of paper = 1 quire. 12 things
12 dozen
24
EXERCISE 1. 2.
many 3.
A A
140.
gr.)
— ORAL
crate contains 492 eggs;
how many dozen?
single card contains 24 hooks
and
eyes.
gross are there on 48 cards?
How many
years are three score and ten?
How
PRACTICAL ARITHMETIC
172
ADDITION AND SUBTRACTION EXERCISE
141.
— ORAL
Add: 1.
4.
12 13
ft.
1 in.
ft.
9 ins
2.
120° 14' 12" 10° 15' 30''
7 days
1 hr.
3.
8 days 12 hrs.
.
5.
20 rds. 4 yds. 1
ft.
10
ft.
rds. 1 yds.
12
lbs.
5
16
lbs.
9 ozs.
ozs.
in.
6 ins
.
235.
16
lbs.
4
25
lbs.
3 ozs.
ozs.
18 lbs 12 07S ; T^ FQ 1, oy IDS. i-v ozs.^ or
—
^
60 lbs. and 3 ozs.
Addition and subtraction of compound numbers is performed in the same manner as with simple numbers,
Til
the only difference being that units of •
compound numbers have a varying
1
scale
of value, while with simple numbers the scale is uniformly ten.
Add
the numbers of eacb denomination separately, then
reduce the sums to the highest units possible.
EXERCISE
142.
— WRITTEN
Add: 1.
12
lbs.
12
ozs.
18
lbs.
10
ozs.
4.
13 bus. 3 pks. 5
qts.
25 bus. 4 pks. 4
qts.
9 bus. 1 pk. 2.
73 rds.
54 bus. 2 pks.
5.
18 gals. 1 qt.
1 qt. 1 pt. 1 qt.
1 pt.
68 gals. 1 qt. 25 gals. 3 qts. 1 pt.
13
gals. 1 qt.
1 pt.
::
DENOMINATE NUMBERS BXBRCISB
143.
173
— OBAIi
Subtract 1.
15
ft.
9 ins.
9
ft.
4 ins.
3.
27 T. 12 cwts. 11 lbs.
2.
1 T. 10 cwts. 10 lbs 236.
4.
.
150°
16'
16"
100°
8'
10''
3 yds. 31
ft.
1 yd.
ft.
2
6 ins.
Subtract:
45 bus. 3 pks. 1
In the first right-hand colhave 1 pt. to be sub39 bus. 1 pk. qt. 1 pt. tracted from pt., which is impossible. Taking 1 qt. from the quarts column and changing it to pints gives 2 pts. 1 pt. subtracted from 2 pts. leaves 1 pt. Completing the subtraction the remainder is 6 bus. 2 pks. 1 pt. pt.
qt.
^^^ we
Increase when necessary number representing any denomination by taking one
Subtract as simple numbers. the
unit from the next higher denomination.
BXBRCISB
144.
- WRITTBN
Subtract 1.
12 hhds. 10 gals. 3 qts. 10 hhds. 50 gals. 1
2.
50 yds.
8 ins.
30 yds. 10 ins 3.
76 mis. 8f rds. 19 mis. 9 rds.
5.
.
25 rds. 3 yds. li
ft.
10 rds. 1 yd.
ft.
237.
4.
qt.
2
DIFFERENCE BETWEEN TWO DATES
Find the difference between the dates March 6 and July 4:
Yes.
:
DENOMINATE NUMBERS Multiply 30
239.
185
Opt.
The product
gals.
X
6
30 gals. 3 Qts. 1 pt.
185 gals. Iqt.
by
gals. 3 qts. 1 pt. 1 pt.
175
=6
6.
pts., or
qts., or
5 gals, and 1
^^g^
^^^^^
185
is
^gO
and 1
gals,
3
+
6
x 30
6
qt.
g^jg.
qts.
g
x 3
gals.
g^^l3_
^
qt.
Multiply separately the number representing each de-
Reduce each product to units of the next higher denomination and add to the product of that nomination.
denomination.
EXERCISE
147.
— WRITTEN
Multiply
by
1.
15 bus. 3 pks. 2
qts.
2.
56
61
96.
3.
4 T. 25 cwts. 10
4.
46 mis. 3
5.
121
6.
46
7.
15 m. 6 dm. 8 cm. by 25.
8.
25
9.
18 g. 4 dg. 6 eg. by 12.
ft.
lbs.
ins.
4
ft.
by
by
lbs. 9 ozs.
3 dl.
by
28.
34.
gals. 2 qts. 1 pt.
1.
by
27.
by
ozs.
8.
by
12.5.
.34.
10.
2 sq. mis. 80 sq. rds. 6 sq. yds.
11.
3 sees. 50 A. 7 sq. chs. by 364.
12.
15 cu. yds. 19 cu.
ft.
108 cu.
by
ins.
.245.
by
2.75.
DIVISION
EXERCISE
148.
— ORAL
Divide: 1.
12
ft.
2.
35
lbs.
6 ins. by
14
ozs.
2.
by
7.
3.
54 gals. 3 qts. by
4.
60
ft.
by 12
ft.
3.
PRACTICAL ARITHMETIC
176 5.
108 yds. 3
6.
54° 20' 36" by
7.
25 hrs. 30 mins. 20
8.
144
9.
48 bus. 2 pks. 3
qts.
174 yds. by 6 yds.
11.
136 yds. 2
12.
154 bus. 3 pks. 2 Divide 25
4 )25 gals. 6 gals.
by
by
sees,
sq. ft. 72 sq. ins.
ft.
9.
6.
10.
240.
by
6 ins.
ft.
by
by
3.
5.
qts.
by
qts.
4.
1\
by
\ of 25
1 pt.
1 qt.
4. gals.
1 remainder.
pts.
qts.
pts.
9.
gals. 2 qts. 1 pt.
2 qts.
10.
= 1 qt. and 2 qts. remainder. = 5 pts. ^ oi 5 pts. = 1^ pts.
+2
qts.
2 qts.
=6
1 gal.
=
6
=4
gals,
=4
qts.
pts.
with
qts.
4
^ of 6 1 pt.
+4
Divide separately the number representing each denomination.
If there is a
remainder, reduce
it
to the next
lower denomination and add to the number representing that denomination. 241.
Divide 18
lbs. 6 ozs.
18
lbs.
8
lbs.
= 256 = 128
262
ozs.
^ 131
by
8 lbs. 3 ozs.
+ 6 ozs. = 262 + 3 ozs. = 131 ozs. = 2.
ozs.
ozs.
ozs.
ozs.
In order to divide one compound number by another,
both compound numbers must be reduced to simple numbers of the same denomination. 242.
when is
Observe that in division of denominate numbers the divisor and dividend are concrete, the quotient
abstract,
e.ff.,
131
ozs. is
contained in 262 ozs. two times.
:
DENOMINATE NUMBERS EXERCISE
149.
— WRITTEN
Divide 1.
245 mis. 120 rds. by
2.
945
3.
2 lbs. 7 ozs. 14 grs.
4.
12 yrs. 6 mos. 5 days by 2 yrs. 4 mos. 5 days.
5.
32 gals. 2 qts. by 5 gals. 1
6.
10
7.
15 m. 8 dm. 6 cm. by 10 m. 2 cm.
8.
25 g. 3 dg. by 12 g.
9.
6984
ft.
1.
6 ins.
3 dl. 5
ins.
by
cl.
8.
12.
by
by 2
1.
5.
qt. 1 pt.
1 dl.
by 127.
10.
8 A. 25 sq. rds. 3 sq.
11.
1155
sq. rds.
10
sq.
EXERCISE
ft.
Is.
150.
by
by
9.5.
2.5.
— WRITTEN
177
PRACTICAL ARITHMETIC
178
and how many hundredweight do they many tons and fraction? Solve problems based on lines
2-10.
No.
How
equal
?
2
10 as
to
in
1.
11-20.
If
the numbers in columns
«,
b,
represent
c
respectively miles, rods, and yards,
how many
yards do
the numbers in each line 'equal?
Rods and
fraction?
Miles and fraction If the
21. feet,
and
equal
?
numbers
in line 1 a,
inches, respectively,
Feet and fraction
?
c
b.
represent yards,
how many
inches do they
Yards and fraction
?
Solve each other line as in No. 21.
22-30. 31.
?
If the
numbers
in line 1 a,
represent bushels,
c
5,
and quarts, respectively, how many quarts do they equal? Pecks and fraction ? Bushels and fraction? pecks,
Solve each other line as in No. 31.
32-40. 41.
If the
numbers
in line 1 a,
5,
e
represent respec-
and days, how many days do they Years and fraction? Centuries and fraction?
tively centuries, years,
equal? 42-50. 51.
Solve each other line as in No. 41.
If the
numbers
tively hours, minutes,
they equal 52-60. 61.
?
in line 1 a,
c represent respec-
Minutes and fraction
?
Hours and
fraction ?
Solve each other line as in No. 51.
If the
numbers
tively barrels, gallons,
they equal? 62-70.
J,
and seconds, how many seconds do
in line 1 a,
i,
e
represent respec-
and quarts, how many quarts do
How many
barrels
and fraction?
Solve each other line as in No. 61.
REVIEW PROBLEMS numbers
If the
71.
tively square
in line 1
represent respec-
a, b, e
and square
miles, acres,
square rods do they equal ? miles and fraction
179
how many
rods,
Acres and fraction
Square
?
?
72-80.
Solve eacli other line as in No. 71.
81-90.
If
each number in a represents grams,
how many
pounds does each equal ? 91-100.
many
each number in a represents meters,
If
inches does each equal
101-110.
111-120.
does each equal
If
many grams
yards
how
?
each number in a represents yards,
If
many meters
How many
?
how
?
each number in a represents pounds,
how
does each equal?
EXERCISE
151.
— WRITTEN
Review Peoblems If a
1.
man
and plants 4
bu3's
it in
A dairyman
producing 80
pint bottles, ^ of
3.
Two
seed corn at
$2 a
bushel,
how many acres can be planted how much will it cost to the acre ?
bottles of each size are
quart cans.
lbs. of
qts. to the acre,
with this seed, and 2.
373
gals, of
milk delivers ^
in quart bottles.
it
of
How many
needed for one delivery
?
bushels of peaches are preserved and kept in
Allowing
-J
for shrinkage,
how many
cans
are needed? 4.
quarts.
A
barrel of vinegar
How many
is
sold, half in pints, half in
of each are sold?
PRACTICAL ARITHMETIC
180 5.
boxes. 6.
Twenty bushels of garden peas are How many boxes are required?
In building a fence 80 rds. long, 4 boards high, with
boards 16
ft.
long and posts 8
every point where a board
pounds of tenpenny to the pound ? 7.
Wind
is
ft.
apart, using 2 nails at
What
nails will be needed, allowing 69 nails
with a velocity of 1 mile an hour (barely
is
8.
With is
the square
lb. to
the pressure of such a wind on a tight '
board fence 1 rd. long, 5
pressure
ft.
high
?
a velocity of 8 miles (a pleasant wind) the
.32 lb. to the square foot.
What
With
the pressure
a velocity of 80 mis. an is
32
lbs. to
the press-
is
ure on the fence mentioned in the last problem 9.
how many
nailed to a post,
observable) exerts a pressure of .005 foot.
sold in quart
?
hour (a hurricane)
the square foot.
What
is
the
pressure on the fence of problem 7? 10.
If
each tea bush yields 3 ozs. of tea each year,
many bushes 11.
If a
how
will be required to yield 18 lbs.?
pound
of tea will
make 400
cups,
how many
tea plants will be needed to furnish 1 cup each day for a
year for each 12. is its
13.
A
of a family of nine
square piece of land
is
?
81 chs. on a side.
What
perimeter?
A
city block
on one side 14.
member
?
is
625
ft.
How many
How many
on a
side.
How many
chains
square chains in a block?
acres are there in a rectangular enclos-
ure 1 mi. long and
-I
mi. wide?
'
REVIEW PROBLEMS 15.
on one
A rectangular side.
How
farm contains 100 A.
long
16.
Reduce 2482
17.
At i960
181 It is
80 rds.
the other side?
is
sq. rds. to square chains.
a mile, what
is
the cost of
making a road
4 mis. and 43 chs. long? 18.
At $4.90
a square chain,
what
the cost of 27 A.
is
43 sq. rds. of land? 19.
What
The pressure is
of the air is 14 lbs. per square inch.
the air pressure on a table top 38"
x 76"?
The longest day in Stockholm is 18 hrs. 30 mins., London 16 hrs. 32 mins., in Paris 16 hrs., in Boston 15 in hrs. 16 mins., in Washington 14 hrs. 62 mins. How much 20.
longer
the longest Stockholm day than that of each of
is
the other cities?
The shortest day in Stockholm is 5 hrs. 54 mins., London 7 hrs. 44 mins., Paris 8 hrs. 10 mins., Boston 8 hrs. 58 mins. How much shorter is the shortest Stockholm 21.
day than that 22.
of each of the other cities
How many
cubic feet of dirt must be
digging a ditch 18" wide,
many 23.
14'
What
holds
will 6'
A
deep
it
6" deep, 79
rds.
moved
long?
in
How
excavate a cellar 18' long,
at f.42 per cubic yard of dirt?
bushels will a bin hold
if
it is 5'
wide,
?
wagon bed
how many
10',
8" long,
3'
wide, and 19" deep
How many bushels will it added? How much with a 9-in.
bushels?
hold with a 6-in. top-box
top-box?
to
cost
3" deep
How many
7' long, 4'
25.
2'
cubic yards?
wide and
24.
?
:
PRACTICAL ARITHMETIC
182 26.
must such
a
How
27.
to hold
3|-
A
28.
many
weighs 80
If a bushel of soft coal
wagon
deep a bin
7'
long, 4' 7" wide
solid piece of timber 8"
cubic feet
must be
built
x 9" x
16' contains
how
?
lbs., of
hemlock 25.53
of ash 39.19 lbs. of the
What
above woods of the
is
lbs., of
47.44
rd., 1 ft. in
size
The following
Of
weighs 87
1 A., 1
table
of cedar lbs.,
mentioned in problem 28?
soil of 1 sq. yd., 1 ft. in
depth?
lbs.,
white pine 21.72
the weight of a piece of each
If a cubic foot of soil
weight of the
31.
deep
tons of soft coal?
of hickory 58.8-1 lbs., of pitch pine
30.
how
A cubic foot of seasoned mahogany weighs 65.1 lbs.,
29.
42.7
lbs.,
bed be to contain 1 ton?
ft.
in
lbs.,
what is Of 1
depth?
the sq.
depth?
shows the number of pounds
of
the three important elements of plant food in a ton of
four different soils
REVIEW PROBLEMS Plant Food
183
PRACTICAL ARITHMETIC
184
Through how many degrees does the hour hand
40.
of a clock pass
3.30 P.M.
From
?
From 12
from 6 A.M. to 3 p.m.?
M. to
9 p.m. to 10 p.m.?
Through how many degrees does the minute hand
41.
pass from 6.15 to 6.30?
From
5.45 to 6?
THREAD AND CLOTH 42.
A
calico cloth 27 ins.
wide
is
warp are there
of
made with 64
How many
wise threads (warp) to the inch.
length-
linear yards
in a piece of calico 3| yds. long?
In a
square yard of calico?
Cloth made with 84 crosswise (filling) threads to
43.
the inch has
28
ins. 44.
how many yards
of filling in 3 yds. of cloth
wide?
A
ference.
standard wrapping reel
How many
times will
is it
4
ft.
6 ins. in circum-
turn in wrapping 840
yds. of thread? 45.
A
cloth 30 ins. wide with 80 " ends " (lengthwise
threads) to the inch has 46.
open in
-^
A
in. is
the total 47.
has
cloth 30 ins. wide consists of alternate close and
stripes.
What
The
The open
close stripes, | in. wide,
number
number
weighs I
in cloth 28 ins.
What
is
wide ? filling to the inch
to the yard ?
gentleman's oz.
1-in. stripe.
of ends per inch ?
Cloth made with 84 threads of
A
have 60 ends
have 96 ends in a
stripes
the average
how many
48.
how many ends?
cotton
How many
handkerchief
18" X 18"
can be made from 450
cotton, not allowing for waste?
lbs. of
REVIEW PROBLEMS 49.
A lady's handkerchief
many can be made from 450 50. ties
A
185
lbs. of
cotton
?
Bagging and
bale of cotton weighs 500 lbs.
weigh 25
This cotton loses
lbs.
How
one-fourth smaller.
is
f-^
during the
making the warp and filling threads. many handkerchiefs can be made from the bale process of
How if
a
handkerchief weighs | of an ounce? 51.
The warp threads
in a handkerchief
weigh .43
oz.
The filling threads in same handkerchief weigh .32 oz. How many pounds of cotton will be used for warp threads and how many pounds for
52.
Wilbur Wright
of
filling
Ohio
threads
is
?
reported to have flown
on his aeroplane, in France, on Aug.
8,
1908, a distance
What was
of 3 kilometers in 1 min. 46 sees.
the rate in
miles per minute? 53.
A
man
purchases 2520
corn and feeds 2 qts.
lbs. of
and 1 pt. three times a day to his horse. the corn last? 54.
A
(56
tomers taking 2
55.
A
=1
corn
dairyman produces 50
this is delivered to
taking 1
lbs. of
gals, of milk.
customers taking 1 pt. each,
qts.
qt. each.
How long
Half of ^-^
to cus-
remainder to customers
each, the
How many
will
bu.}
customers are there?
quart of beans weighs 80 ozs.
How many pounds
are there in a bushel of beans ? 56.
For a grain bin 6'xl5|^'x5' how much carbon
di-sulfide will be required to kill weevils, allowing 1 lb.
to every
1000 cu.
29^ per pound ?
ft.
of space?
What
will this cost at
MEASUREMENTS 243.
A
plane figure having four straight sides
is called
a Quadrilateral.
244.
A
plane figure having four straight sides and
opposite sides parallel
A
quadrilateral which has
opposite sides parallel 246.
angles 247.
A is
A
A TRAPEZOID only one pair of
its
called a Trapezoid.
parallelogram the angles of which are right called a Rectangle.
plane figure bounded
having three angles
A Rectangle 248.
is
its
called a Parallelogram.
A PARALLELOGRAM
A QUADRILATEBAL 245.
is
The
line
is
bj-
three straight lines and
called a Triangle.
A Triangle
Base and Altitude
upon which a figure seems to
called the Base. 186
rest
is
MEASURKMENTS 249.
The perpendicular
the highest opposite point 250.
The
252.
around 253.
is
called the Altitude.
Polygon
its
Diagonals.
Equilateral Triangle
Diagonals 251.
distance between the base and
straight lines joining the opposite angles of a
parallelogram are called
by straight
187
is
the
name given
to
Isosceles Triangle
any figure bounded
lines.
The Perimeter
of
a
polygon
the
is
distance
it.
A triangle whose three sides are equal,
is
called an
Equilateral Triangle. 254.
an
A
triangle,
two
of
whose
sides are equal,
is
called
Isosceles Triangle.
Right Triangle 255.
A
Obtuse Angle
Acute Angle
triangle having
one right angle
is
called
a
Right Triangle. 256.
Angle.
An
angle less than a right angle
is
called an Acute
PRACTICAL ARITHMETIC
188
An
257.
angle greater than a right angle
called an
is
Obtuse Angle.
EXERCISE 152.— ORAL
What
1.
is
the perimeter of a square lOJ
on a
ft.
side?
What
2.
which are
What
3.
are 10, 12,
on a side
What
5.
is
the perimeter of a rectangle
and 6^
ft.
two
sides of
respectively?
the perimeter of a quadrilateral whose sides
and 8 inches?
6,
What
4. ft.
is
12|^ ft.
is
the perimeter of an equilateral triangle 25
?
is
the perimeter of a triangle whose sides are
21ft., 3|ft., and 6 ft.? 6.
A
What 7.
is
one side
;
ins.,
The base ft.
of
an
isosceles triangle is 12
What
is
ft.
;
the perim-
the length of each of the equal
?
BXEECISE 1.
ins.
another IJ times this number of inches. the length of the third side ?
eter is 42
sides
120
triangle has a perimeter of
measures 30
How many
153.
— ORAL
square inches are there in a rectangle
10 ins. long and 1
How many inches figure 2.
are
in.
wide?
rows of square there
in
the
?
How many
rows
of
square inches are there in a rectangle 10 ins. long and 2 ins. wide inches are there in a
row ?
?
In two
How many square rows ? How many
:
MEASUREMENTS
189
rows of square inches are there in a rectangle 10
and 3
10
ins. long,
10
In finding the area or surface of a rectangle,
we
wide
258.
of the surface in
number
will give the is
are, as
In a rectangle 10
?
?
must think
row
square inches in a row?
square inches are there in a rectangle
5 ins. wide
ins. long,
ins.
long
?
How many
3.
How many
wide?
ins.
In three rows
ins.
of times the square inches in one
to be taken, e.g.,
may be
rows of square inches, which
if
a square measures 10
rows
seen, 10
ins.,
there
of square inches of 10 sq. ins.
each, or 100 sq. ins.
Hence, the area of a rectangle equals the product of the length by the width.
EXERCISE
154.
—ORAL
State the areas of the following rectangles 1. 2.
3.
X 10
5 ins.
4
ft.
10
X
ft.
6i
X4
4.
8 ins.
ft.
5.
9
ft.
6.
ins.
x
7.
7 ins.
ft.
8.
4
3 m. X 1^ m.
9.
1 yd.
ft.
X 61
EXERCISE 1.
What
is
8|- ins.
155.-
X 9 X 6
ft.
ins.
ins.
x 10
ft.
-ORAL
the re-
lation of triangle a to
rectangle 2.
A?
What
tion of
is
the rela-
triangle
rectangle
h
to
B?
What is the relation of triangle c to (7? From the above, what is true of the area of 3.
a triangle
?
:
:
PRACTICAL ARITHMETIC
190 4.
Give the areas of the following triangles
height 6
ins.
;
base 9
height 12
ins.,
4ft.; base 3ft., height 3
The
259.
ins.
:
base 4
base 3
;
ft.,
ins.,
height
ft.
area of a triangle equals J the product of the
base by the altitude.
EXERCISE
156.
— WRITTEN
State the areas of the following triangles
Base 45
ft.,
altitude 30
ft.
2.
Base 16
ft.,
altitude 12
ft.
3.
Base 87
ft.,
altitude 28
ft.
4.
Base 40
ft.,
altitude 26
ft.
5.
Base 67
ft.,
altitude 55
ft.
1.
260.
If
you
CLit off
gram X
\
^^
^e of
of
area of the
the
second
the triangle a from the parallelo-
X and
place the line ho so that
exactly coincides with de, what kind
have
figure first
figure
you ? What is true as compared with the
?
EXERCISE
157.
— ORAL
Give the area of the following parallelograms
261.
The
1.
Base 12
ins.,
height 9
2.
Base 14
ins.,
height 6 ins.
ins.,
height 12
ins.
3.
Base 18
4.
Base 15 m., height 6 m.
5.
Base 17
ins.,
height 17 ins.
area of a parallelogram
uct of the base by the height.
ins.
is
equal to the prod-
:
:
MEASUREMENTS EXERCISE
158.
191
— "WBITTEN
Find the areas of the following parallelograms 1.
Base 18.4
2.
Base 17|
ins.,
height 9.2
height 16.5
ft.,
ins.
ins.
3.
Base 34 m., height 20 cm.
4.
Base 16
5.
Base 171.4
6.
Base 3.75
7.
Base 35 m., height 9 cm.
8.
Base 345.2
6 ins., height 12
ft.
ft.,
ft.,
height 34.9
height 4.25
rds.,
ft.
4 ins.
ft.
ft.
height 6 yds. fj
-X
262.
d^
you cut the trapezoid
If
X through
and place the two sections so that the cide, what kind of figure have you ? Is the area of the
XI How How
high
9
long is
is
it?
lines cf
the line ef
and df coin-
second figure the same as the area of the figure
To
made
froin the trapezoid?
find the area of a trapezoid,
what
dimensions must be given?
EXERCISE Find the area
159.
— ORAL
of the following trapezoids
1.
The
parallel sides are 10 ins.
and 12
2.
The
parallel sides are 6 ins.
and 4
3.
The
parallel sides are 12 ins.
and 9
height 6
ins.
ins.,
height 4
ins.
ins.,
height 8
ins.
ins.,
:
:
PKACTICAL ARITHMETIC
192
The parallel
4.
The
263.
two
sides are 16 ins.
area of a trapezoid
parallel sides multiplied
EXERCISE Find the area
height 9
equal to the
sum
ins.
of the
— WRITTEN
of the following trapezoids
and 180
Parallel sides, 96 rds.
2.
Parallel sides, 45 rds.
3.
Parallel sides, 120
4.
Parallel sides, 60
5.
Parallel sides, 135.5 m.
6.
Parallel sides, 62 yds. It has been
circle is
ins.,
by J the height.
160.
1.
264.
is
and 12
ft.
rds.,
and 95
and 90
ft.,
height 108 rds.
rds.,
height 64
height 40
rds.
ft.
m. and 90 m., height 44 m. and 34 m., height 110 m.
and 80
yds., height
112^ yds.
found that the circumference
of a
approximately 8^ times the diameter. of circles with the following
Find the circumference diameters 1.
7 ins.
4.
21
ins.
7.
0.7 m.
10.
45
ft.
2.
14 ins.
5.
77
ins.
8.
14 cm.
11.
84
ft.
3.
49
6.
0.28 in.
9.
14.7 cm.
12.
105
265.
ins.
To
ft.
find the circumference of a circle, multiply the
diameter by 3^, or more accurately by 3.1416.
EXERCISE
IBI.
— WRITTEN
Find accurately the circumferences cles;
also find their
of the following
approximate circumferences.
the difference. in results
by the two methods.
1.
Diameter 16
ft.
4.
Radius 9
2.
Diameter 21
ft.
5.
Radius 12 m.
3.
Diameter 19
ft.
6.
Radius 45
ft.
rds.
cir-
Note
:
:
MEASUREMENTS EXERCISE Find the diameters
—WRITTEN
162.
of
193
circles
having the following
circumferences 1.
426
ft.
4.
1400 rds.
7.
318 m.
2.
218
ft.
5.
1676 yds.
8.
164 m.
3.
670
ft.
6.
115.6 rds.
9.
92.45 ins.
266.
If
you divide the
shown
circle
in the figure
by
many
cutting the line ah, then cutting each half circle into small triangles by
cutting each
along
radius,
it
will be seen that
the
many
trian-
gles joined, as
is
suggested in figure
y, will
approximate in area a parallelo-
gram with a length equal to one-half the circumference of the circle and a height equal to the radius of the circle. The area of a circle is found by multiplying one-half the circumference by the radius, or by multiplying the square of the radius by 3.1416. EXERCISE Find the areas
163.
— WRITTEN
of circles with a
1.
Circumference of 242
ft.
7.
Diameter of 77
2.
Circumference of 110
ins.
8.
Diameter of 35 m.
3.
Circumference of 154
ft.
4.
ft.
Diameter of 49
rds.
Circumference of 96 yds.
10.
Diameter of 146
ft.
5.
Circumference of 3.75
ft.
11.
Diameter of
6.
Circumference of 18 yds.
12.
Diameter of 54
9.
|^
ft.
rds.
:
PRACTICAL ARITHMETIC
194
EXERCISE Find the areas
of circles
1.
8 ins.
3.
4
2.
10
4.
16
ins.
164.
— WRITTEN
having a radiugr of
ft. ft.
5.
9
m.
7.
4 rds.
6.
8 m.
8.
5 rds.
SOLIDS 267.
A
dimensions,
solid has three
— Width,
•
Length,
and Thickness. 268.
A
solid that has six rectangular sides or faces
is
called a Rectangular Solid. 269. 270.
A A
solid that has six square faces is called a Cube.
cubic inch
is
a solid, the faces of which are each
What
one inch square.
is
a cubic
foot?
What
is
a
cubic yard?
BXEECISE In a solid 12
1.
how many rows
165.
— ORAL
ins. long, 1 in.
wide, and 1
of cubic inches are there?
cubic inches are there
in. thick,
How many
?
SI Figure
1
I'igure 2
Figure 2.
many
3
In a solid 12
Figure 4
ins. long,
2 ins. wide, 2 ins. thick,
how
How many
rows
layers of cubic inches are there
?.
MEASUREMENTS
195
of cubic inches are there in one layer
inches are there in one layer are there in 2 layers
layer
layers are there
How many
?.
How many many
ins.
ins. long,
How many
How many
12
ins. Avide,
How many
?
How
12
ins. thick,
how
rows are there in a
cubic inches are there in one row?
cubic inches are there in 12 layers
how many
row
?
?
cubic inches are there in a layer
In a solid 4
how
rows are there in one
cubic inches are there in one
layers are there ?
layer?
5.
wide, 2 ins. thick,
How many
?
cubic inches are there in two layers
many
cubic inches
cubic inches are there in one layer
In a solid 12
4.
How many
?
cubic
?
In a solid 12 ins. long, 12
3.
many
How many
?
ins. long,
?
How many
?
4 ins. wide, and 4
ins. thick,
cubic inches are there in the length of the
How many rows of cubic inches in the width? How many cubic inches in each layer ? How many layers in the solid? How many cubic inches in the solid? solid?
In examples
example
its
7,
8,
answer
all
the questions
by 5
by
In a solid 4
7.
In a solid 2 ins. by 3 ins. by 12 ins.
8.
In a solid 6
To
a solid
made
in
5.
6.
271. iis
6,
ins.
ins.
find the
by
ins.
8 ins.
volume
6 ins.
by 10
of a cube,
? ?
ins. ?
we must
think of
it
having a length equal to the number of units in
length and a width equal to that of the rows of cubic
units in its width,
and a thickness equal
of layers of cubic units in its thickness.
to the
number
PRACTICAL ARITHMETIC
196
The volume
272.
of a rectangular solid equals the prod-
uct of the three dimensions similarly expressed.
BXBBCISB
How many
1.
and 9
How many
2.
ft.
3.
4J
ft.
4.
long, 2
How many
5.
long, 9^ 6.
2|" by 8". 7.
A
ft.
5|- ft.
long,
deep contain?
cubic yards of soil will be excavated in ft.
long, 2
ft.
wide, and 3
liters of air are
m. wide, and
The box
high?
ft.
gallons of water will a tank
a ditch 12
How many
deep?
wide, and 4
wide, and 2^
making
ins.
cubic feet of masonry are there in a wall
ft.
How many
— WRITTEN
cubic inches are there in a box 16 ins.
long, 8 ins. wide,
120
166.
3
ft.
deep?
there in a room IS^ m.
m. high?
of a one-horse express
wagon
is
T
2" by
3'
Find the capacity.
two-horse farm wagon
is
11'
6" x
3'
x
10^".
Find the capacity.
THE CYLINDER 273.
A
cylinder
having for
its
circles joined
is
a solid
ends two equal
by a uniformly
curved surface, called
its lat-
eral surface.
274.
A
cylinder
may
be
seen in the form of a rectangular solid with a length equal
to the length of the cylinder, a width equal to one-half
:
:
MEASUREMENTS
197
the circumference of the circular base, a thickness equal to the radius of the circular base.
275.
Hence, to find the volume of a cylinder, multiply of square units in the base by the height.
the number 276.
may
The
lateral surface of a cylinder
be seen in the form of a rectangle,
with a length equal to the circumference of the circular base
and a width equal to
the height of the cylinder. 277.
Hence, to find the area of the
lateral surface
of
vjy
multiply
a cylinder,
the length of the circumference of the circular base by the height of the cylinder.
EXERCISE 167.— WRITTEN Find the volume
of the following cylinders
1.
Area
of base 126 sq. ins., height
2.
Area
of base 72 sq. ins., height 44.56 ins.
3.
Area
of base 81 sq. ins., height 16 fins.
4.
Area
of base 84 sq. ins., height
EXERCISE Find the
168.
16|
42|
ins.
ins.
— WRITTEN
lateral surfaces of the following cylinders
1.
Circumference of base 40
ins.,
height 45
2.
Circumference of base 24
ins.,
height 25 ins.
3.
Circumference of base 66|
ins.,
4.
Circumference of base 14f
ins.
ins.
height 27
ins.
height 641
ins.
PEACTICAL MEASUREMENTS PLASTERING, PAINTING, PAVING 278.
In estimating labor of
and paving, the square yard
latliing, plastering, painting,
is
taken as the unit.
In mak-
ing estimates for plastering, one-half the areas of doors,
windows, and other openings area,
and the result expressed
EXERCISE 1.
What
2.
If the
3.
25
What What
cts.
169.
— ORAL
the perimeter of a room 12
is
x 14
ft.?
the area of the ceiling?
room
at
a square yard? 170.
— WRITTEN
In this exercise exclude closets, and
windows
1.
ft.
will be the cost of plastering this
EXERCISE
for
total
to the nearest square yard.
room is 8 ft. high, what is the area of the making no allowance for the openings in them?
4 walls,
4.
is
deducted from the
is
To
make no allowances
or doors.
plaster 100 sq. yds. of surface requires 1 barrel
of lime, 3 barrels of sand,
and
1 bushel of hair.
Find the
amount of these materials required to plaster each bedroom of the house shown in the two accompanying diagrams, also living room, dining room, and kitchen. 2.
What
will it cost to lath
and plaster the
room, kitchen, and dining room of
pulp plaster at a cost of 60
cts. a
198
tlie
lower
square yard
?
living
floor with
PRACTICAL MEASUREMENTS
To
3.
lath
and plaster the i bedrooms
with ordinary plastering will cost 25 yard. Estimate the cost. floor
Pitch 10
4.
of the cts.
upper
a square
ft.
Estimate the number of gallons of paint required
to give
two outside
wide, 18
700 sq.
300
199
sq.
ft. ft. ft.
coats to a house 32
high, the of
surface.
ft.
long, 32
ft.
gable ends of the roof forming
One
of surface, 2 coats.
gallon
of
paint covers
PRACTICAL AEITHMETIC
200 5.
At f 1.25
a gallon,
what would be the
cost of paint-
ing this house? 6.
cement, 0.44 cu. yd. of
It requires 1.16 barrels of
sand, 0.88 cu. yd. of gravel to
make
a cubic yard of con-
Pitch 8
How much
Crete.
basement 3 ins. 7.
cement will
floor of a
house, 21
it
ft.
ft.
require to concrete the
x 18
ft.,
to a depth of
?
If 1 cubic
yard of concrete costs $3.31, what
be the cost of material in the
last
problem?
will
PRACTICAL MEASUREMENTS
201
CARPETING Carpets
279.
Brussels
are
usually
and velvet
1
carpeting
yd. is
or
| yd.
|
yd.
wide.
wide and
is
usually sold with a border varying from 22 to 27 ins. in width. Ingrain carpets are 1 yd. wide. Matting is usually 1 yd. wide.
Linoleum and oil-cloth are sold by The short loops of wool seen in Brussels carpet are made by the use of wires over which the wool is thrown in weaving. The number of wires the
square yard.
(usually between 5 and 10 to the inch) used in weaving varies with the price of the carpet
and the
fineness of the
wool.
EXERCISE 1.
How many loops of
171.
— OBAIj
wool are there in a piece of 5-wire
Brussels carpet | yd. wide and 5 ins. long? 2.
How many
loops of wool in an 8-wire Brussels car-
pet I yd. wide and 5 ins. long 280.
In determining the number of yards of carpet
required
number found,
?
for
a
the
floor,
of strips should be
the fractional part
of a strip being regarded as
a full strip.
Often
it
is
necessary to allow for match-
I
I
ing and shrinking; 3 inches are also allowed on each
end
of each strip for turning in.
Borders are
corner, hence the perimeter of the
length of border required
;
see figure.
room
fitted at
indicates
each the
:
PRACTICAL ARITHMETIC
202 If a floor is 12
ft.
wide and the carpet f yd. wide,
it
will
Since | strip cannot be bought, 6 strips require 5^ strips. must be bought. If the room is 18 ft. long, it will require 6 strips 18
ft.
matching the
long, or 36 yds. figure, 9 ins.
ing one, since
If 9 ins.
must be added
must be allowed
for
to each strip, except-
not necessary to allow for matching the
it is
Three inches additional must be allowed for turning under. If a 22-in. border is used, only 3^|- strips of carpet are actually used, but 4 strips must be bought. first strip.
BXBBCISE 1.
How many
2.
The room
— ORAL
ft.
f yd. carpeting are required to wide?
14
ft.
strips of
room 12^
carpet a
172.
is
How many
long.
yards, without
border, are required, allowing 12 ins. for matching? 3.
A
room
12
is
ft.
x 18
How many
ft.
strips of | yd.
carpeting are required? 4.
How many
yards allowing ^ yd. for matching?
EXERCISE Find how many yards
173.
— WRITTEN
of carpet are
needed for the
fol-
lowing rooms
X 18 ft. 6 ins.: use 27-in. carpet, allow matching and use border -I yd. wide.
1.
for
15
ft.
9 ins.
use carpet 1 yd. wide, and allow ^ yd. for matching, turning in, and shrinkage. 2.
16'
3.
The
X
18'
:
living
room and
diagram on page 199 1^
:
hall of the house
shown by
use a 10-wire body Brussels carpet
yd. wide, with 22|-ins. border, which requires 9 ins. for
matching and turning 10
cts.
in,
and
a yard extra for making.
costs 11.50 a yard, with
PRACTICAL MEASUREMENTS 4.
8^
ft.
The dining room X
if
What
the rug
will
covered with an Axminster rug,
is
What
a square yard.
How much
when
the rug 5.
$1
10|^ ft. at
the rug?
is
6.
a quart
cts.
comes only
in 2-yd.
What
cost?
7.
floor is
The bedrooms ins.
?
around the rug
ft.,
the stain cost-
covered with linoleum which
and 4-yd. widths
at f 1 a square yard.
are carpeted as follows
plain ingrain carpet 1
lowing 6
room
?
The kitchen is its
the price of
each side of
laid in the centre of the
1 qt. of stain is sufficient for 125 sq.
ing 50
is
floor space is left at
cost to stain the floor
it
203
j'd.
:
No. 1 with
wide, strips lengthwise.
on each width for turning in and 3
each width for shrinkage after
it is
cut,
what
is
ins.
Al-
on
the cost
at 63 cts. a yard, allowing 3 cts. per yard additional for
making? 8.
34
cts. 9.
Bedroom No. Bedroom No.
at 21 cts. a 10.
2 with China matting 1 yd. wide at
a yard, strips lengthwise? 3 with Japanese matting 1 yd. wide
yard?
Bedroom No. 4 with
wide at 25
cts.
Sanitas washable carpet 36 ins.
a yard, strips lengthwise?
PAPERING Wall paper
281.
the
roll.
yds.
A
usually 18 ins. wide and
single roll
is
Borders are from 3
made
for
is
sold
by
8 yds. long, a double roll 16
ins.
upward
in width.
made for borders, since no allowance Some paper-hangers measure the matching.
Deduction is
is
is
not
surface above the base-board, and
deduct for windows
PRACTICAL ARITHMETIC
204
and doors, allowing also
is
| roll for each
door or window.
customary to find the number of square feet
It
in
the walls and ceiling, deduct for doors and windows, and divide
by
70, to find the
number
EXERCISE 1.
How many
174.
of double rolls required.
— OBAIi
square feet of wall paper are there in
a
single roll? 2.
How many
square feet of wall paper are there in a
double roll? 3.
If a
how many
room measures 12
ft.
single rolls of wall
x 12
ft.
and 9
ft.
high,
paper will be required,
making no allowances? 4.
How many
double
rolls are
required for the same
room? 5. 7|^
Allowing for 2 windows 6
X 4
ft.,
how many
ft.
x
3 ft.
and a door
square feet are there left to be
papered? 6.
How many
this deduction, 7.
making no allowance
How many
How many
for
double rolls?
BXBECISE 1.
making matching?
single rolls are required after
rolls of
175.
— WRITTEN
paper will be required to paper
the living room of the house
shown
in the diagram on
page 199, the base-board 9" wide, there being 3 windows 3' 7'
X x
window
6'
x
one fireplace
6',
1
4',
alcove not papered
6',
7'
x
6',
and
?
a.
Estimate accurately by the number of square
h.
Estimate, allowing
-|
1 door
roll for
each opening.
feet.
PRACTICAL MEASUREMENTS
205
Estimate by dividing total number of square feet by
c.
70, after deducting for the doors
and windows.
How much will the paper cost at 50 cts. a double roll ? c above.) How much will it cost to paper
2.
(Use answer
the ceiling at 20
moulding cost 3.
6 7
ft. ft.
30
cts.
What
?
will picture
a foot, no allowance for openings?
a double roll and the ceiling paper, 20 cts. a double
with no border, but with picture moulding at 2J
a foot,
7
3-|
a double roll
The dining room has 2 windows 6 ft. x 3 ft., one, X 6 ft., one opening 6 ft. x 7 ft., and two doors x 4 ft., buffet not papered. If the wall paper costs
cts.
roll,
at
cts.
how much
cts.
the total cost?
is
Each bedroom has 2 windows 6 ft. x 3 ft. and 1 door ft. X 3 ft., ceilings and closets not papered. 4.
Find the cost
a double 5.
roll,
bedroom No.
of
picture moulding IJ
Find the
cost of papering
wall paper at 30
a double
cts.
3 with paper at 25 cts. cts. a foot.
room No. 4 with sanitary border at 2
roll, 4-in.
cts.
a
yard, ceiling papered at the same price.
MASONRY AND BRICKWORK
282.
Brickwork
is
usually estimated by the thousand brick.
The unit of measure for walls built of Twenty-two bricks of common size
stone
reckoned for each cubic foot of wall.
measure
8x2x4 ins.
The mortar
ness between bricks.
A
and equals 24| cubic
feet.
stood to be 25 cubic
feet,
is
laid in
the perch.
mortar are
Common
occupies \
in. in
brick thick-
perch measures 16^' x 1|'
In practice a perch
is
X
1'
under-
:
PRACTICAL ARITHMETIC
206
It requires for each square foot of wall
1 brick in thickness.
7 bricks,
if
the wall
is
15 bricks,
if
the wall
is
2 bricks in thickness.
22 bricks,
if
the wall
is
3 bricks in thickness.
In estimating work, deductions are not usually made for openings of less than 100 sq.
ft.
In estimating
area.
materials, deduct for openings.
BXERCISB 1.
How many
long, 5
thick 2.
ft.
178.
— ORAL
required for a wall 10
bricks are
2 bricks thick
high, 1 brick thick ?
?
ft.
3 bricks
?
How many
bricks are required for a wall 1 brick
thick, for a cellar 10
ft.
x 12
ft.,
ings?
not allowing for open2
bricks
bricks thick
How
3.
thick?
3
perch
of
?
manj'^
stone are required for a wall
50 4
To
is 1, 2, 3,
high, 1
ft.
or 4 bricks thick.
EXERCISE
2.
ft.
number of bricks required for a wall, mulnumber of square feet by 7, 15, 22, or 29 accord-
ing as the wall
many
long, 10
thick?
find the
tiply the
1.
ft.
ins.
If a cellar is 18'
x
177.
24'
— WRITTEN
x
9',
bricks are used in walling
How many
it
inside dimensions,
how
2 bricks thick?
perches of stone are required for the
walls of a cellar 18'
x
24'
x
9',
6", the wall 18" thick?
PRACTICAL MEASUREMENTS Find
3.
207
cost of construction in problems 1
and 2 with and labor 13.00 per M, allowing no
M
bricks at $8.50 per
deductions for openings, stone costing 118.00 per perch
and f 1.50 per perch
How many
4.
bricks will be required to wall a house
wide outside, and
36' long, 30' cellar,
for labor.
34'
high, including the
No
the wall to be 2 bricks thick?
allowance for
openings.
The
5.
X
6" X
30',
3'
X
and rear walls
cellar
common
are of
1^', 2
brick, the
6'
x
windows 6' x 3'. What is the M ? Of the labor at $3 per
cord of wood
128 cu.
=
ft.
is
8
ft.
long, 4
16 cu.
cord.
1
EXERCISE
A
What ft.
ft.
8
is
windows
cost of the brick
ft.
178.
ft.
ft.
wide, and 4
=1
ft.
high.
ft.
high.
is
there
cord foot.
— ORAL
long, 4
ft.
wide, 2
is it?
wood
of
pile
long, 4
is
wide, 4
How many
high.
ft.
wood
pile of
part of a cord
A
2.
96
2
WOOD MEASURE
283,
1.
3',
M?
at 18.45 per
A
problem 4
dimensions being 36'
1 door
the openings
9',
of the house of
cellar
cords are there? 3. ft.
Another
long, 4
ft.
pile is
wide, 4
12 ft.
in the pile?
EXERCISE 1. ft.
How many
long, 16
ft,
How much wood
high. 179.
— WRITTEN
cord feet are there in a pile of
wide, 12
ft.
high?
wood
96
::
PRACTICAL ARITHMETIC
208
How many
2.
X
16-1- ft.
Hi
X
long, 25
ft.
ft.
ft.?
Find the number
3. ft.
cords can be piled in a woodhouse 12
wood 100 Find the number of
of cord feet in a pile of
wide, 25
high.
ft.
cords.
BOARD MEASURE 284.
Lumber
285.
The
which less
were
bought and sold by Board Measure.
is
unit of Board Measure
wide, and 1
1
ft.
long, 1
than 1
in.
in thickness are
is
1
in.
the Board Foot,
in. thick.
number
thick are
of board feet in them,
e.g.,
feet.
EXBBCISE Find the number
in.
wide, 2" thick, contains 20 board
sold according to the 1'
Boards
reckoned as though they
Boards more than 1
thick.
a board 10' long,
ft.
is
of
180.
— OEAIj
board feet in the following
1.
10 boards 1" x 12" x
2.
3.
4.
10 boards 2" x 9" x
10boardsl"x|"xll'.
5.
10 boards 1^" x 6" x
10 boards 1" X f" X
6.
10 boards If" x 9" x 14'.
8'.
18'.
EXERCISE
Find the number
181.
10'. 8'.
— "WRITTEN
of board feet in the following
1.
12 planks 3" x 8" x
2.
14 planks 2|" x 9" x 18'.
3.
18 planks 1^" X 12" x
12'.
4.
24 planks If" x 26" x
16'.
5.
60 planks If" x 4" x
6.
How much
12'.
12'.
flooring 18' long, 4"
wide, If" thick
:
PRACTICAL MEASUREMENTS must be bought
room
to floor a
the flooring cost at
|60 per
M
18'
x
12'
209
What
?
will
?
ROUND LOGS 286.
Round
logs are sold
by the number of board feet find the number of board
To
that can be cut from them.
feet in a log, subtract twice the diameter in inches
the square of the diameter
the
number
;
|^
of the
from
remainder will be
of board feet in 10 linear feet of the log.
Find the number
board feet in a log 18' long, 12" in
of
diameter. 122
_
= 144 - 24 = 120 = 63 63 = 113.4 board feet. (2 X 12)
|l of 120 If of
EXERCISE Find the number
182.
— WRITTEN
of board feet in the following
1.
In a log 12' long, 10" in diameter.
2.
In a log 18' long, 15" in diameter.
3.
In a log 14' long, 18" in diameter.
4.
In a log 15' long, 22" in diameter.
MEASURING TEMPERATURE 287.
Temperature
mark
commonly measured
in this coun-
by Fahrenheit's thermometer.
try in degrees
degree
is
is
the 212-degree
placed at the
mark
The
32-
freezing-point of water,
at the boiling-point of water.
The
between the freezing-point and the boiling-point Another thermometer divided into 180 equal degrees.
interval is
used in
many
other countries and in most scientifc work
:
PRACTICAL ARITHMETIC
210 is
the Centigrade, with zero at the
freezing-point, 100
Below zero is indicated by Above zero is indicated by the
degrees at the boiling-point.
—
the -(-
sign.
sign or by no sign.
EXERCISE
183.
— ORAL
Unless otherwise stated, Fahrenheit degrees are to be understood in the following
problems
When
1.
degrees,
the temperature of the air
how much above
When
2.
much below
water
is
at
boiling
is
it?
freezing
normally 98.6 degrees.
A
40
180 degrees, how
The body temperature
3.
is
is it?
of a person
is
temperature of 99
degrees or more indicates fever.
What
is
the range between normal temperature and fever temperature? 4.
A
body temperature
approaching death.
of 108 degrees usually indicates
What is the range between normal tem-
Only rarely does the body below 92 degrees and life continue. What
perature and the death point?
temperature is
fall
the range of temperature 5.
How many
?
degrees Centigrade equal 180 degrees
Fahrenheit? 6.
How many degrees
Fahrenheit equal
1
degree Centi-
grade ? 7.
How many
Fahrenheit?
degrees
Centigrade
equal
1
degree
PRACTICAL MEASUREMENTS BXEECISE
184.
C;
211
— 'WRITTEN
1.
Change 10°
2.
Devise a rule for changing from Fahrenheit to Centi-
F. to
change 10° C. to F.
grade.
Devise a rule for changing Fahrenheit ?
from
3.
Centigrade to
LONGITUDE AND TIME BXEECISE 1.
The
185.
earth appears to be
— ORAL If it
flat.
were really
what would be true concerning the time
flat,
of sunrise on
every part of the earth's surface? 2.
What would be true of sunset under the same What are the facts concerning the time of
ditions? rise 3.
and sunset upon different parts
Which
Why?
city has sunrise
first,
consun-
of the earth's surface?
New York Why?
or Chicago?
Chicago or San Francisco?
What
upon the earth have sunrise at the places have noon at the same time? What places have midnight at the same time? 4.
same time?
288.
A
places
What
meridian
is
an imaginary
and south from pole to
pole.
line
running north
All places upon the same
meridian have their midday or noon at the same moment, i.e.,
they are touched by the vertical rays of the sun at
the same time. 289. is
The
distance east or west from a given meridian
called Longitude.
PRACTICAL ARITHMETIC
212
EXERCISE 186.— ORAL 1.
Through how many degrees does the earth
from sunrise until the sun
is
rotate
in the zenith?
Through how many degrees does the earth rotate from sunrise to sunset ? Through how many degrees does a point upon the earth pass in a complete rotation ? 2.
3.
in 1
Since the earth turns on
day
24 hours, through
of
turn in 1 hour 290.
its
axis through 360 degrees
how many
degrees does
it
?
Longitude
is
The meridcommonly reckoned are
measured by degrees.
ians from which longitude
is
two, one of which passes through Washington, D.C., one
through Greenwich, England.
The given meridian from which longitude
291.
erally reckoned is
is
called the
Prime Meridian.
is
gen-
Longitude
reckoned east and west of the prime meridian to 180
degrees.
West longitude
"W." and
east longitude
by the
EXERCISE 1.
When
before
it
it is
designated by the
is
187.
letter
letter
"E."
— ORAL,
sunrise at Baltimore,
how long
will
it
be
sunrise at a place 15 degrees west of Balti-
is
more? 30 degrees west? 45 degrees west? 2.
When
before 3.
it is
it is
noon
noon
at St. Louis,
at a place
If I travel eastward, will
or too fast
?
If I travel
too slow or too fast
?
how long
15 degrees west of
my
will
it
be
St. Louis?
watch become too slow
westward, will
my watch
become
:
:
PRACTICAL MEASUREMENTS 292.
Since the earth turning upon
213 axis once in 24
its
hours, passes through 360 degrees in that time, the follow-
ing table
may
be deduced
Longitude
Timb
360° corresponds to 24 hours. 15° corresponds to
1 hour.
15' corresponds to
1 minute.
15" corresponds to
293.
Two
1 second.
1° corresponds to
4 minutes.
1'
4 seconds.
corresponds to
What
places are 40° 15' 30" apart.
difference in time
is
the
between them ? Since places 16° distant
15 )40°
30"
15'
from each other have a
dif-
ference of 1 hr. in time, and
2 hrs. 41 mins. 2 sees,
since places 15' apart have a
difference of 1 min. in time,
and since places 16" apart have a difference of 1 sec. in time, jig- of the numbers representing degrees, minutes, and seconds will give the difference in time in hours, minutes, and seconds.
BXBRCISB 1.
The
188.
— WRITTEN
difference in longitude between
46 degrees, 20 minutes, 35 seconds. in
What
is
two places
is
the difference
time? 2.
Washington
is
77°
3'
from Greenwich.
the difference in time?
The longitude
of the following cities
Washington,
77°
New
74°
York,
Paris,
3'
2° 20'
is
0"
W.
3"
W
22" E.
What
is
:
PRACTICAL ARITHMETIC
214
San Francisco, 122° 24' 15" W. 116° 27' 30" E. Peking, Constantinople,
28° 59'
Berlin,
13° 23' 43" E.
E.
Find the difference in time between
294.
3.
Washington and Peking.
4.
New York
5.
Washington and Constantinople.
6.
New York
7.
San Francisco and Berlin.
The
ri
on 30
and Paris.
difference in time
What
30 mins. 25 sees. 5 hrs.
and San Francisco.
mms. oc lo -.
between two places
Since there are 15 times as
sees.
,
r
number representing the
BXBBCISE
^.
,
of
and seconds of time, 15 times
difference in time will give the
189.
difference in time
16 mins. 24 sees.
many
mmutes, and seconds
difference of longitude in degrees, minutes,
The
5 hrs.
longitude as there are hom's, minutes,
1.
,
.
degrees,
'-
the
is
the difference in longitude?
is
What
is
and seconds.
-WRITTEN
between two places
is
10 hrs.
the difference in longitude?
Find the difference in longitude between the following places and Greenwich, the difference in time being: 2.
Athens, Greece,
1 hr. 34 mins. 54.9 sees. E.
3.
Calcutta,
5 hrs. 53 mins. 20.7 sees. E.
4.
Chicago,
5 hrs. 50 mins. 26.7 sees.
5.
St.
6.
What
Petersburg, is
the
W.
2 hrs. 1 min. 13.5 sees. E.
difference in
Petersburg and Chicago?
longitude between
St.
PRACTICAL MEASUREMENTS 7.
When
Chicago. 8.
it
is
What
Wlien
it
San Francisco.
is
noon is
at
Greenwich,
it
215 6.09 A. jr. at
is
the longitude of Cliicago?
6.09 a.m. at Chicago,
What
is
it is
3.50 a.m. at
the difference in longitude?
STANDARD TIME 295.
To use the exact sun time for each place brings many complications that another method has
about so
been devised by which the world
is
divided into 24 time-
Standard Time Map belts, all places
within the same belt using the same time.
The time meridians
of the time-belts of the
are those of 75°, 90°, 105°, and 120°, as
accompanying map.
Canada are divided south.
is
United States
shown
in the
Accordingly, the United States and into four belts extending north
and
All places in the same belt have the same time
regardless of their exact longitude.
In practice, these
PRACTICAL ARITHMETIC
216
do not have regular boundaries
belts
but the points of
;
change are determined rather by the position of important
Time determined
cities.
in
this
manner
is
known
as
Standard Time.
EXERCISE 1.
New 2.
When
it
noon
is
190.
— OEAL
Greenwich, what time
at
York, estimating the longitude at
When
Chicago ?
New
6 a.m. at
it is
At Denver
'
At
?
is it at
New York
York, what time
San Francisco
as 75"? is it at
?
EXERCISE 191.— WRITTEN 1.
What
is
the difference between standard and local
time at Chicago ? 2.
The longitude
of Pittsburg is 80°
2'
0".
What
is
the difference between standard and local time there? 3.
What
time at
the difference between standard and local
is
New
Orleans, longitude 90°
The longitudes
3'
28.5"
?
Richmond, Denver, and 90° 15' 15" W., 77° 26' 4" W., Boston are respectively 104° 59' 33" W., 71° 3' 30" W. At what time, standard, 4.
of St. Louis, :
will
an
time signal sent from Washington at
electric
noon reach them ?
At what
local time ?
REVIEW PROBLEMS EXERCISE 1. is
7 2.
How many ft.
long, 2
If a
— WRITTEN
barrels of water will a trough hold,
if it
wide, 16 ins. deep?
windmill pumps 2 gals, and 8
and pumps 4 if
ft.
192.
hrs. in a day,
qts.
how many cows
each cow consumes 1.5 cu.
ft.
each minute
will it supply
of water daily?
;
REVIEW PROBLEMS
How many
3. if
pounds of water does each cow consume
one gallon weighs 8.35
A
4.
pound
Sowing 16
lbs.
How many
What is
5.
lbs.?
of timothy seed conta,ins 1,170,500 seeds.
the acre
?
217
to the acre,
how many
seeds are sown to
seeds are there in an ounce
?
the value of a rectangular field 23 chs. 2 rds.
17 Iks. 6 ins. long by 17 chs. 3 rds. 18 Iks. 7 ins. wide at
137.50 an acre?
There are 15 steps on the
6.
12", the rise
What
7|-".
:
hills
;
3d, seed
ordinary seed 136 lbs.
What was
that of No. 2?
hills.
llw. 1-t ozs., best
seed 172 lbs. 8 ozs.,
What was
the average yield per
10
ozs.
the increase in yield from seed No. 1 over
Of seed No.
2 over seed No. 3
Sprayed grapes yielded 4
Unsprayed grapes yielded was the gain per row 9.
2d, seed
;
from the very poor
yields for each 100 hills planted with these seed were:
poor seed 75
8.
?
seed from the best hills to be found
1st,
from ordinary
hill?
is
In raising Irish potatoes three grades of seed were
7.
The
tread
carpet cost
sufficient stair
Avill
a yard, allowing Jq extra carpet for the pro-
at 62 cts.
jection of the tread
used
The
hall stairs.
in
?
lbs. 5.8 ozs. to
the row.
1 lb. 1.5 ozs. to the row.
What
pounds from spraying?
Sprayed grapes yielded 3
than unsprayed grapes.
lbs. 4.3 ozs.
What was
more per row
the difference in
yield on 17| rows ? 10.
Western Yellow Pine
measured
1.2 ins. in
diameter
in Colorado, 20 years old, ;
at 80 years, 2.9
;
at 40, 4.9
at 50, 6.8; at 60, 8.6; at 70, 10.2; at 80, 11.7; at 90,
12.8; at 100, 13.8;
at 110, 14.7;
at 120, 15.5.
What
PRACTICAL ARITHMETIC
218
was
How much
circumference at each of these ages?
its
did the diameter increase from the fourth to the
How
decade ?
fifth
How much
mucli the circumf ereiice ?
did
both the diameter and the circumference increase from the eleventli to the twelfth decade? IX.
An
ordinary milk pail
is
llj
ins. in
top; another pail has an opening only 7
What
is
the difference in the areas of the openings?
seven billion bacteria
fall into
other pail in the same time
Planting 7
many pounds 13.
ozs.
of
the milk in the
how many would
15 mins., at the same rate
12.
fall into
tomato seeds to the
are needed for 19 A.
Sowing
the
acre,
how
?
3 pks. of cow-peas to the acre,
Bordeaux mixture
If
first pail in
?
bushels of seed are needed for 40 A. 14.
diameter at the
ins. in diameter.
how many
?
consists of 5 lbs. of bluestone,
5 lbs. of lime, and 50 gals, of water.
Applying
this to
potatoes at the rate of 150 gals, of mixture to the acre, for each application,
many
and making 3 applications:
gallons will be needed on 40 A.
barrels?
c.
pound?
d.
What What
will the bluestone
?
6.
a.
How
How many
cost at
will the lime cost at \\ cts. a
6
cts.
a
pound?
To produce 1 T. of oats requires 376 T. of water. How many cubic feet of water are needed? How many barrels? How many hogsheads? How many quarts? 15.
16.
To produce
Solve for 17.
all
a ton of wheat requires 338 T. of water.
the items of the last problem.
To produce
a ton of dry matter, the average crop
plant requires 325 T. of water.
Solve as in problem 15.
REVIEW PROBLEMS 18. cts.
A man
customers 1
sells 7
pt.
219 each of syrup at 5
a pint, 9 customers 1| qts. each at 10 cts. a quart, and
13 others 1 gal. each at 35
cts.
How much
a gallon.
a
gallon did he average for his syrup? 19.
A
sec. ?
At
20.
crete
horse moving at 2:40 gait, moves
What made
a 3-nnn. gait?
At
the cost of materials for
is
of 1.16
@ 75
of sand
At
a 2: 10 gait?
bbls.
of
cement
far in 1 ?
cu. yd. of con-
1
@
how
a 4-min. gait
|2, 0.44 cu. yd.
0.88 cu. yd. of gravel
@
75 cts. ? If 20 posts 6" X 6" at the bottom, 6" x 8" at the top, and 7' long, can be
cts.,
made from
what
will
of 0.16-in. steel wire
@3
1 cu. yd. of concrete,
the materials cost per post? 21. cts. a
22.
Adding
6 cts. for 28
pound, what
A
ence?
well
If
it
is
is 7 ft.
ft.
the total cost for materials per post? in diameter.
contains 6
ft.
Wliat
of water,
circumfer-
is its
how many
gallons
are there? 23.
A
tree has a circumference of 12
diameter? 24.
The
its base, its
If 8
ft.,
what
is
What
ft.
triangular end of a house gable
and 16
ft.
is its
the diameter?
from the base
is
37
line to apex.
on
ft.
What
is
area in square feet?
25.
A
triangular garden has a base of 90
altitude of 75 26.
What
12
deep and has a diameter of 8
cistern
the volume of the cistern? it
and an
fraction of an acre
is
is
ft.
What
A
of water will 27.
ft.
ft.
is it?
How many
ft.
gallons
hold?
The water
pipes on a house measure 13 ins. outside
220
PRACTICAL ARITHMETIC
circumference.
There are 200
What
ft.
of piping
on the house.
is the surface of this piping ?
28.
How many
cubic feet are there in a cylindrical
How many in diameter and 20 ft. deep? How much does the water in it weigh when it How many square feet in its outer surface, exis full? How many gallons of water does it clusive of bottom? tank 12
ft.
gallons?
contain for each foot in depth? 29.
a
How many
room 30.
17'
AVhat
diameter?
feet of picture
6" long and is
Of
moulding are needed
the length of the tire of a wheel 4 a wheel
for
9" wide?
9'
ft.
in
in diameter?
3^- ft.
Mr. Akers owned a rectangular piece of land, the north and south sides of which were each 42 rds. long. The east and west sides were each 38 rds. long. Two 31.
railroads cut off portions of
beginning at the
N.W.
it
point 14 rds. east of the S. all east of
the S.E. corner. the railroads.
by
cost ? 32.
one took
all
west of a
line
W.
corner.
The
other took
a line beginning at a point 12 rds. south of the
N. E. corner and running
off
;
corner and running S.E. to a
Draw
The
S.
W.
map
to a point 8 rds. west of of the land as cut off
railroad owners
their roads at
How much How much
a
$150 an
acre.
by
bought the land cut
How much
did
it
land was left in the tract ?
lumber
will be required for 80 rds. of
fence 4 boards high, each board 6 ins. wide ?
How much
will be required to make a tight board fence the same length and 5 ft. high, nailing the boards to two 2" X 4" scantling? No allowance for waste in either case.
lumber
33.
How many
yards of 27-in. velvet carpet with 22-in.
REVIEW PROBLEMS
221
border will be required to carpet a society hall 42 long, 36
ft.
Each alcove
end?
5
is
mate the amount with
ft.
deep and 20^
strips of carpet
wide.
ft.
Estimate with strips running crosswise.
35.
What
36.
How much
will carpet
and border
Esti-
running lengthwise.
34.
and
ft.
wide, having one rectanglar alcove at each
cost at $ 1.25 a yard
?
paper will be needed to paper the walls
windows 9| x 6 ft. and the pitch of the ceiling being 14 ft.? The alcove ceiling of this hall, there being 4
ceilings are papered, but the alcove walls are finished in
hard-wood panels, and require no paper. 37.
The paper
for walls costs 95 cts. per double roll,
for ceiling 25 cts. per double roll, picture
moulding 7
a foot, no moulding being used in the alcove. the cost 38.
Estimate in meters the height of Mt. Everest 29,002
Pikes Peak 14,111 Aconcagua 23,082 ft.
What number
ft.,
Mt. Blanc 15,744
of bricks
is
40.
How many
41.
walk
x 23
ft.
ft.?
cubic yards of concrete are required to
ins.
How many
high and 5
ft.
3 ins. inside diameter ?
cubic yards of concrete are needed to
a semicircular walk in front of a schoolhouse, the to be 4
ft.
3 ins. wide, 27
and the concrete 42.
and Mt.
a circular wall 8 ins. thick around the top of a well,
the wall to be 29
make
ft.,
needed for a wall 4^
high, 3 bricks thick, around an enclosure 14
make
is
?
ft..
39.
cts.
What
A
ft.
long on
to be laid 4 ins. thick
its
shorter side,
?
farmer uses a potato crate 19|" x 13" x 12" to
contain a bushel of potatoes,
60
lbs.
How much
does
PRACTICAL AKITHMETIC
222
exceed in
this bushel of potatoes
of dry measure
A
43.
A
44.
?
22" x llf" X 14|" contains how How many standard dry bushels ?
crate
such bushels
standard bushel
size the
?
tank of a spraying machine
is in.
half-cylinder resting on its convex side, 5 ins.
6|
height 3|
If it ins.
were shortened 5
ins.
46. in. in
What fraction
47.
depth.
What
The base
of
is
a,
circumference?
48.
of an inch in
and 20
silo
weighs 30
50.
its
sides,
in
what
it
ins., inside di-
be
of uniform
if
depth equals
1 qt.?
silo is
If
26
ft.
high,
if
?
AND SILAGE 16
ft.,
ft.
what
in diameter. is its
What
is
circumference?
tons, of a silo 10
a cubic foot of silage
ft.
in diame-
from such
a
lbs.
How many
tons of silage will this silo contain,
after it has settled, the silage is 5 feet
is
12-|-
the diameter of the can
Find the capacity, in
ter
49.
is
and increased
In the usual 50-qt. milk can, 1 qt. occupies .375
SILOS
its
What
ft.
?
45. The usual 40-qt. milk can is ameter. How many inches tall need ?
long and 2
without further curving of the
would the capacity be
diameter
the form of a
ft.
measurement.
inside
in diameter,
capacity?
many-
Find how many tons of
from the top
if,
?
silage a silo will hold, that
20 feet in diameter and 32 feet deep,
if
in such a silo
a cubic foot of silage weighs 40 pounds. 51. if,
How many tons
of silage will there be in this
after it has settled, the silage is 7 feet
silo,
from the top?
REVIEW PROBLEMS 52.
43 COWS be fed 37
If
how long 53.
In order that the silage its
30
deep.
ft.
each of silage per day,
will the contents of this silo last
insure
may
What it
enough
?
settle sufficiently to
preservation, a silo should
ameter must hold
lbs.
223
not be less than
di-
have to
silage
to
feed 25 cows 40 lbs. per
day for 185 days, silage
weighs 38
if
the
lbs. to
the cubic foot? 54.
of
How many
corn will
furnish
it
feed
a
acres
take to
35
of
pounds per day each
to
a herd of 32 cows for
150 days, each acre yielding 12 tons of silage
What must this silage,
if
?
be the diameter of the the height of the silo
foot of silage weighs 40 55.
The corn on
silo is
necessary to hold
32 feet, and 1 cubic
pounds?
a field of 18 acres
when ready
for
cutting arid shocking or for putting in the silo weighs 9 tons per acre, of which
shocking the corn, there
^
is
is
water.
If
by cutting and and
a loss in dry matter of ^^^,
by putting it in a silo there is a loss of dry matter of Jg-, what is the value of the feed gained by putting the crop in the silo, if the dry matter in silage
is
worth .71 of a
cent per pound ? 56.
How many
acres of corn will
it
require to produce
;
PRACTICAL ARITHMETIC
22-4
the silage to feed 18 cows 37- pounds per day for 184 days,
each acre produces 13 tons of silage corn?
if
DRESSMAKING
How many
57.
to
make
yards of 36-in. material will be required
a shirt-waist,
the tucked front measures 24
if
ins.
before tucking and the two backs 12 ins. before tucking the front length from shoulder measuring 18 ins. and two
backs 16
18
ins.
sleeves 16 ins. long before finishing and
ins.;
wide in the widest place?
found in pieces cut from
How many
58.
Cuffs, collars, belts are
See diagram.
strips.
yards of insertion will be required for
this waist for 4 strips the length of the front, 4 strips
one piece for the neck 12
for the back,
ins.,
and two
pieces for the sleeves 8 ins. each?
How many
59.
skirt of the top,
yards will be required for a nine-gore
same linen
and 15
ins.
each gore being 38
and allowing 1 60.
ins.
in. at
How much
gores average 5 ins. wide at the
if
wide
at
the
when
bottom, the
the top for finishing?
insertion will be required for
5 and 8 inches from the bottom of the skirt, for the 61.
bottom row average 13
At 50
cts. for
length of
finished with a 3-in. hem,
linen
ins.
and 15
if
two rows the gores
and second row 12 cts.
ins. ?
a yard for insertion,
1 doz. buttons at 10 cts., 1 bolt of tape at 5 cts., what will the dress cost? 62.
The
items cost
lining and finishings for a dress are called the
What
findings.
will findings consisting of the following
skirt 2 J yds. of waist lining at 15 cts., 6 yds. lining at 25 cts., 2 spools silk at 10 cts., 1 spool cotton :
REVIEW PROBLEMS 5
1 bolt braid 10
cts.,
and eyes 10
cts., 1
cts., 1
1 yd. featherbone
cts.,
shields 35 cts.
dress
5
cts.,
1
pr.
?
Find the
63.
card hooks
bolt silk binding 10
cost of a Panama-cloth
8 yds. of material at 89 cts. a
;
yard, with findings at price given in last
problem.
64.
What
professional
the
will
dress cost
shopper charges 10
if
a
cts.
on each dollar for buying the above materials and a dressmaker charges f 8 for
making the dress?
65.
If,
for the cotton skirt lining,
a silk lining be substituted which will
require 10 yds. of silk at 59
cts.
what
What
will the dress cost?
a yard, will
be the shopper's fee? 66.
Races are run at the
Olympic games
at
Athens
over distances of 100 meters,
400 meters, 800 meters, 1500 meters. in
How many
j'-ards
each of these distances C7.
The
best
time
these races prior to
was respectively 49|^ sees., 1
?
for
1908
10|- sees.,
min. 56
sees.,
and 4 mins. 5| sees. What was the speed per yard in each race
?
FOLD OF GOODS
PRACTICAL ARITHMETIC
226
Some
68.
races run
Public Schools' Athletic
the
in
League, high school events, are 100 yds., 440 yds., 880
and
yds.,
What
1 mi.
is
the diiference between these dis-
tances and those mentioned in problem 66
The time
69.
53
for these races
mins. 7|
sees., 2
Some Olympic
70.
24
1
ft.
in.
sees.,
What
sees.
?
records are
running high 6
;
was respectively 10|
and 4 mins. 59|
sees.,
was the speed per yard
?
ft.
running long jump
:
ins.; pole vault 11 ft.
2^
P. S. A. L. high school records for the same events
6 ins.
are respectively: 21
ft.,
5
6 ins., 9
ft.
ft.
9 ins.
By what
fraction does the P. S. A. L. high school record fall short of the 71.
Olympic record
in these events
The steamship
Lusitania, in July, 1908,
?
average speed of 25.01 knots an hour. 6086.7
What was
ft.
made an One knot equals
the average speed in miles per day?
The Lusitania covered the distance from Daunt's Sandy Hook lighthouse in 4 das. 20 hrs. and 15
72.
Rock
to
mins.
What is the distance? What is the speed per second
73.
of a grindstone 4 ins. in diameter,
of the circumference
run at 30 revolutions
per minute?
Allowing 5
74.
may
what
sq. ft. of floor space to each fowl,
the dimensions of a henhouse be to accommodate 100
fowls?
If
sion be?
one side be 14
With lumber
at
ft.
what
$15 per M, what
boards for sides and ends cost built square
?
When
will the other dimen-
built 14
if
ft.
5
ft.
wide?
will the
6 ins. high
when
How much
does
the extra light and ventilation secured by the narrower
form
of
house cost?
PERCENTAGE spraying mixture contains 98 parts water,
If a
296.
part lime, and 1 part bluestone,
how many
1
parts are there
How many hundredths of the mixture How many hundredths are lime? How many
mixture?
in the
are water?
hundredths are bluestone?
Of to
number
a
of seeds tested, one out of every ten fails
How many
grow.
fail
to gi'ow out of every
hundred?
How many
hundredths fail to grow? The number of hundredths of a number is commonly expressed by the term per cent. Out of 100 oak leaves examined, 60 were injured by
What
insects.
per cent were injured by insects
?
What
per cent were uninjured? 297. 8
%
is
The term per
cent is expressed
by the sign %,
e.g.,
read 8 per cent.
A
given per cent, or a given number of hundredths, of a number may be expressed as a whole number 298.
with the per cent sign, as a decimal, or as a tion, e.g., 1
per cent
per cent
may
may
be written
be written 8 %,
.08,
or
common
1 %, .01, or
j-f-iy
frac-
^-J-g-.
8
:
:
:
PRACTICAL ARITHMETIC
228 13.
125^%.
16.
2.25%.
19.
.4%.
14.
250%.
17.
6.4%.
20.
.04%.
15.
631%.
18.
9.34%.
21.
.004%!
299.
Express 25%, 2.5%, | %, as
common
fractions in
lowest terms
25%=TVu = i1
1 pi„ 'i JO
— iTo ~ ~i
EXBBCISB
1
TiriT-
194.
— "WRITTEN
Express as common fractions in lowest terms: 1.
12%, .12%.
6.
16f%, 1%.
11.
150%, .15%.
2.
25%, .25%.
7.
3.31%,
1%.
12.
625%, 6.25%.
3.
42%, .42%.
8.
621%, 1%.
13.
375%, 3.75%.
4.
55%, .55%.
9.
83^%, f%.
14.
5.
75%, .75%.
10.
121%,!%.
15.
1%, 1.2%. 1%, .05%.
300.
Express
|
%, ^%, j^^%,
as decimals of a per cent,
and as decimals
i%=.6%=.005. i
% = .2 % = .002.
t\%=.2%=.002. exercise
195.
— written
Express the following as decimals, and as decimals
of a
per cent 1-
\1o.
10.
^%.
11.
1%.
12.
^%.
:
fERCENTAGE 13.
^%.
15.
14.
i%.
16.
f%.
17.
T^%.
18.
Important per cents
301.
to be
= 15%. i = 20%. 1 = 60%. i = 16f%. 1 = 831%.
= 100%. = 50%. i = 33i%. f=66|%. i = 25%. 1
f%. 1%.
1%.
= 6|%. ^-, = 5%. 2^ = 4%. ^V = 2%. 1^0 = 1%.
J^=10%. 196.
1%.
20.
tV
= 371%. 1 = 621%. 87i%. t=
1
EXERCISE
19.
remembered
i=m%.
1
1
229
— ORAL
Find: 1. 2.
3. 4. 5.
% of 50. 25 % of 80. 60 % of 300. 121 % of 72. 16| % of 90. 10
6. 7.
8. 9.
10.
% of 48. 871 % of 72. 5 % of 125. 2 % of 200. 831 % of 96. 371
EXERCISE
197.
%
ii.
16|
12.
62-1 ^^ of 64.
13.
% of 10. 83^ % of 42« 5 % of 120.
i4.
15.
of 66.
60
— WRITTEN
Find:
%
75
2.
^%
3.
2.5%
of 2655.
10.
42%
4.
871
%
of 6424.
11.
§
of 2254.
12.
381%
of 5431.
6.
4% 1%
of 8243.
13.
4.5%
of 5240.
7.
831%
14.
8.9%
of 1872.
5.
302.
%
1.
of 1280.
of 5420.
of 9846.
The number
certain per cent
is
of
8.
66f
9.
4.2%
%
of 5432. of 2437.
of 8432.
of 9812.
which so many hundredths or a
to be taken
is
called the Base.
:
PRACTICAL ARITHMETIC
230
The number
303.
indicating
how many hundredths
of
the base are to be taken expresses the Rate or Rate Per Cent.
The
304.
result obtained
by taking the number
dredths of the base indicated by the rate
is
of hun-
the Per-
centage.
Find 9
%
of 50
50
is
.09
is
the rate.
is
the percentage.
4.5
Three kinds
305.
centage
is
in
which base and percentage are known and
to be found.
is
Those
3.
per-
to be found.
Those
2.
base
of problems occur in percentage:
Those in which base and rate are known and
1.
rate
the base.
is
in
which rate and percentage. are known and
to be found.
Case One.
306.
Given the base and the rate
to find
the percentage. In testing a certain ore iron.
How much
it
was found that 25
25
In testing an ore
How much Since
iron
29%
or
it
was found that 29
was there
-^
is
%
lbs.
of
it
was
Since
by taking
of it
was
|
iron.
in 469 lbs. of ore?
not conveniently used as a common
fraction, it is best to express it as a decimal, .29.
136.01
%
iron was contained in 496 lbs. of ore?
Hence 136.01
lbs.
was
iron.
469 x
.29
=
:
PERCENTAGE
Knowing
231
the base and rate to find the percentage.
Multiply the base by the rate expressed either as a com-
mon
or as a decimal fraction.
EXERCISE
%
1.
Find 5
2.
Find
3.
Find 10
4.
Find
of 80
4% %
of 40 of
6.
110
;
30; 75
% of 20 of 100 I %
Find 25 Find
40
;
— ORAL 200
;
180
;
;
160
20.
;
of 75; 125; 150; 175; 50; 25.
20%
5.
120
;
198.
90
;
70
;
860
;
;
10.
90; 65; 95; 100; 25; 5; 10.
;
;
40
;
200
EXERCISE
140
;
80
;
;
199.
60
;
;
12
;
8
;
10
;
4.
50.
— -WRITTEN
Solve the following, using the rate both as a decimal
and as a common fraction 1.
Find
7%
2.
Find
3.
Find
14% 6^%
4.
Find 19
of 425; of 67.3; of 526; of 9642; of 87.9.
5.
Find
6.
What
% 72 %
of 48.8; of 68;
of I
15%
is
of 99
;
;
of 7981.
of 128.64;
of 96.32;
of 32; of 38
of 125.6;
of 132
of J^
;
of
869
of 842. ;
of 7684.
of -^\ of If. fy of $5.20? of *13.50? of |75? of
;
of
;
;
;
$8764.75?
10.
What is 4 % of | of an acre of land ? What is 13% of 96 sq. ch^. 48 sq. rds. of land? What is 37% of 1 sq. mi. 168 sq. rds. of land? Find 129% of 76; of 128; of 7842.1.
11.
Find 300
12.
Find .3%
7.
8. 9.
%
of 84
;
of 78.2
of 782; of 6498.
;
of 3.
PRACTICAL ARITHMETIC
232 13.
Find .17%
of 6842; of 17; of 386.7.
14.
Find .06%
of 98; of 782; of 6428.
15.
A
of a mill
and sold 33^% of his share. part of the mill did he sell, and what part does
What he
still
307.
owned f
own? Case Two.
Given the base and the percentage
to
find the rate.
What
per cent of 85
Dividing 17 by 85,
^ of any number 20
%
17?
is
^=
we have
is
%
20
\.
of that number, therefore 17
is
of 85.
Since the percentage
by the
rate,
the rate
is
found by multiplying the base
may
found by dividing the
be
percentage by the base. _
What
per cent of 85
is
17.85?
^
85)17.85
Dividing 17.85 by 85,
I'^QO
85
Therefore, 17.85
21
%
is
we have
.21, or
.21
= 21 %.
21 hundredths, or
of 85.
85
BXEECISB
200.
1.
What
per cent of 50
2.
What
per cent of 1^.00
3.
Whatper
4.
— ORAL
25?
is
is
is
What
per cent of 172.50
is
3.
What
per cent of 96
6.
What
per cent of 122
Is $2.50?
$3.00? $15.50?
31?
is
10?
|125?
cent of 112.50
is
Is
6.1?
Is
Is
12.75?
Is
27? Is 9.76?
$17.40?
PERCENTAGE BXBECISB
— WRITTEN
201.
1.
What
2.
What per cent of 7862 is
3.
Wliatper cent
4.
Whatper
5.
What
6.
A man
per cent of 86
233
24?
is
Is 8?
18?
Is
1?
Is
7614?
cent of 848is 424?
Is
212?
per cent of 1
^
is
whose salary
is
Is
?
^? Is 7?
Is 96? Is
106?
Is .08?
f?
f 182 a month pays 126.40
is
and $5.28
his salary
remaining after his board
What
amusement.
for
Is
986? Is 12?
67?
of 7847
for board,
for
Is
is
per cent of
paid, does he
pay
amusement?
A
7.
time
workingman's day remaining hours in
^ of the
A
8.
declined
What
sleep.
What
given to sleep?
is
spends
per cent of his
per cent to other pursuits?
farmer held cotton bought of a renter; the price
12%, then
15%
rose
;
If a
What
he then sold.
cent did he gain on the transaction 9.
He
10 hours long.
is
per
?
merchant's scales weigh 14
ozs. for a
pound,
what per cent does the purchaser lose? If the retail
10.
3 ounces
and the
merchant's fair profit
scales are as in the
is
equivalent to
above example, what
per cent more does the buyer pay than
if
he were to buy
from wholesale houses?
What
11.
308.
per cent of a
Case Three.
number
is
33^%
of 6
%
of it?
Given the rate and the percentage
to find the base.
29 20
is
20
%
of
% = TW)
what number ?
or
h
29
is
therefore i of the base
;
the base
is
PRACTICAL ARITHMETIC
234 29 -H
20
%
-^
= 29
X f
by 5, or 145, or expressing and dividing we have,
or 29 multiplied
,
as a decimal
=
.20
=
.2,
2 )29.0 145.
The second method
is
preferable
when
the rate cannot
readily be expressed as a fraction.
Since the percentage base, the base
may
the product of the rate and the
is
be found by dividing the percentage
by the rate expressed
as a decimal.
EXERCISE 1. 2. 3.
4. 5.
5%
202.
— OBAL
10% of what number? 8 is 20% of what number? 25% of what number? 12 is 12^ % of what number? 75% of what number? 12.50 is 16|% of what? 33^% of what? 6 ft. 10 ins. is 66| % of what? 331% of what? 8
is
of
what number?
871-% of what?
6.
21
7.
16 gals. 4 qts. 2 pts.
ft.
7 ins. is
is
87-i-% of
what?
BXBECISB 203.— "WRITTEN 1.
44.1
is
105%
of
what number?
90%
of
what
number ? 60
is
96
is
6.
125% of what number? 75% of what number? 30% of what number? 18% of what number? 47 is 8% of what number? 20% of what number? 776 is 60% of what number? 83% of what number? 6 is 16% of what number? 90% of what number?
7.
87
is
2.
3. 4. 5.
.05
%
of
what number? 178 %
of
what number?
When
309. is
known
When
310.
The
311.
of 10
"Jo
235
added
sum
the base
as the
the remainder
PERCENTAGE is
the percentage is
to the percentage, the
Amount. is
subtracted from the base,
called the Difference.
rent of a farm
is
§68.20 and this
over the previous year.
is
What was
an advance
the rent the
previous year?
= rent the previous year. % = advance this year. % = ()8.20. 1% = .62. 100% = $62.
100 10 110
"Jo
r?
Hence, % 62 was the rent of the farm for the previous year.
A is
5
regiment returns from battle with 1197 men, whicli
%
less
than
the regiment
started with.
it
when
How many men
were in
the battle began?
100 6
% = nmnber started with. % = number lost.
95%
=1197.
1%=12.6. 100
To
% = 1260.
when the rate and amount are given, amount by 1 plus the rate expressed as a
find the base
divide the
decimal.
To
find the base
when
divide the difference
the rate and difference are given,
by 1 minus the
decimal.
EXERCISE 1. 2.
Amount Amount
110, rate 10
150, rate 50
;
;
204.
rate expressed as a
— ORAL
find the base. find the base.
23G 3. 4.
5.
PRACTICAL ARITHMETIC
Amount 75, rate 50 find the base. What number plus 7 % of itself equals 214 ? What number minus 10 % of itself equals 90? ;
EXERCISE
205.
— WRITTEN
PERCENTAGE EXERCISE
FARMING 1.
In 1900, 7.1
%
IN
206.
— WRITTEN
THE UNITED STATES
of the farms, or 407,012 farms, were
How many
between 10 and 20 A. in area. there in the United States then ? 2.
States
237
Of 29,285,922 working inhabitants in.
farms were
in the
United
1900, 10,438,217 were engaged in agriculture,
7,112,987 in manufacturing, and 1,264,735 in professional
What
service.
pursuits 3.
per cent was engaged in each of these
?
$3,560,198,191, the value of the farm buildings of
the United States, is
is
21.4
%
of the total
farm value.
What
the total farm value?
4. Of the 5,739,657 farms in the United States in 1900 54.9% were worked by their owners, 13.1% by cash tenants, and 22.2% by share tenants. How many farms were worked in each of these ways? 5.
In 1900, 1,366,167 of the 5,739,657 farms of the
United States were between
What per cent
of farms
1000 A. in area. 6.
50 and 100 A.
were of this
What
size ?
47,276 were over
In 1900 24.8% of the farms in the United States
farms of this
and 50 A.
size
were there?
How many United
States, 20.1
the same rate of increase,
be in 1910?
area.
How many
21.9% were between 20
were there of
In 1900 there were 9,349,922
in farming in the
At
area.
per cent did they constitute?
were between 100 A. and 175 A. in
7.
in
this latter class?
men and boys engaged
%
more than
how many
in 1890.
farmers will there
PKACTICAL ARITHMETIC
238
In 1894 there were
8.
2712 Agricultural
College
What was
students in the United States; in 1899, 5035. the per cent of increase for these five years?
The value
9.
of the fertilizers used
1899 was 149,099,939.
States in
If
in
the United
by home mixing
of
and more intelligent use 23 % of this could be what would be the saving to the farmers of the
fertilizers
saved,
United States?
IMPORTANCE OF GOOD SEED
A
10.
certain
number
heavy seed produced 12.5
tobacco plants raised from
of
lbs. of
tobacco; an equal num-
ber of plants raised from light
seed gave only 6.4
was the per cent
lbs.
of gain
What by the
use of heavier seed?
With
11.
ordinary
tobacco
seed yielding 816 lbs. of tobacco
per acre, and heavy seed yielding 29 the
on an
acre, if
8 cts. a pound, 12.
If a
more, what would be
number
heavy seed were used?
what
is
of
pounds
Tobacco
the gain in value
of gain
selling at
?
machine to separate heavy seed (see picture)
18 and the labor
costs
%
of such separation costs 5 cts. for
seed for an acre, what would be the profit per acre the first
year, supposing 7
13.
What would
A. were
to be raised?
be the per cent of profit the second
year on the same acreage?
machine the second year.
There
is
no cost for the
;
TERCENTAGE
239
by using only the best varieties and selecting the seed by the best-known methods, the corn crop of the United States might be increased 10 %, It is estimated that
14.
of corn
or 1116,662,647, in value.
What
is
the present value of
the corn crop?
What
15.
selection
its
value
the best methods of seed
if
Light and heavy seeds were tested for germinating
16.
power. seed
could be
were used?
was found that with
It
germinated, 88
onions, 38
%
the
lettuce,
44 % of the light
heavy seed germinated
of the light seed germinated, 85
What was
heavy.
of
%
of the
the per cent of increase of the heavy
seeds over light seeds in germinating power in each case ? If
17.
selected heavy cotton-seed yield
8.25% more
than ordinary cotton-seed, what will be the value of the increase in yield on 600 A., averaging
acre with the unselected seed,
|-
of a bale to the
when cotton
sells at
$56
a
bale? If
18.
cow-pea stubble plowed under increases the cot-
ton crop of the following year
was originally
|-
of a bale to
47%, and
tlie acre,
the cotton crop
what
is
the
money
value of the stubble to the farmer, witli cotton at $55 a bale? 19.
light
Heavy
cotton-seed produces better plants than does
seed.
On
yielded 1047| lbs.
20 rows at Lamar, S.C.,
lbs. of
What was
cotton
;
heavy seed
ordinary seed yielded 944
the per cent of gain
by the use
of
heavy
seeds ? 20.
On
another
trial,
heavy seed
gave 1164
lbs.
of
PRACTICAL AKITHMETIC
240
What would
cotton; ordinary seed 1075 lbs.
from the use
the gain
heavy seed amount to on a 500-acre plan-
of
tation averaging
of a bale per acre
-^
(500
?
lbs. equals
1
bale.) 21.
What would
11^
cts.
pay
to
per pound
be the value gained, with cotton at
What
?
could the planter afford to
have seed separated, and
still
make 12 % upon
the
investment ? 22.
Which
is
most economical
seed at 15.20 per 100
lbs.
clover seeds and only 38
Red
to buy, a.
clover
containing only 48.06% of real
them
of
alive
;
or
i.
Seed
at
with 46.24% of real clover seed, 27.5% or c. Seed at 17.20 per 100 lbs. with of which are alive
$6.10 per 100
lbs.
;
73.8% 23.
tained
real clover seed,
One
of
which are alive?
redtop seed at f 5.00 per bushel congood seed; another lot at fl.lO per
lot of
77.4%
89%
of
bushel contained 10.48% of good seed.
How much
cheaper?
was paid per bushel
Which was for
the
good seed
in each case?
PREVENTION OF PLANT DISEASES 24.
In using 1
oz.
of formally to 3 gals, of water as
a steep for oat seed to prevent smut, what per cent of
formalin 25.
(1 gal. of water weighs 8J lbs.)
used?
is
How many
pounds, of formalin will be needed for
25 A., allowing 1 gal. of mixture to each bushel of oats
and 2 bus.
of oats to the acre
will it cost
?
26.
Formalin, being
of formaldehyde
is
40%
?
At
38
cts. a
pound, what
formaldehyde, what per cent
there in a l-oz.-to-3-gal. mixture?
:
PERCENTAGE 27.
The average
241
net profit from spraying potatoes in
experiments carried out during 1906 was 113.89 per acre
;
the net profit from similar experiments in 1905 was
What was the What would such
120.04, in 1904 $24.06, in 1903 123.43.
average benefit for
amount
all
these years?
to on 40 A.?
Apple trees sprayed and not sprayed vention of worminess yielded as follows 28.
for the pre-
PRACTICAL ARITHMETIC
242
an
What was
acre.
the per cent of gain on the amount
invested?
Three trees affected with bitter rot yielded 21.1
32.
sound apples and 4244 diseased
bus. of apples, 188
apples.
Six similar trees, sprayed to prevent the rot, yielded 101.3 bus.,
What was
8674 sound and 989 diseased.
Spraying costs each time 3|
What was
sprayed 3 times.
was the In
A
profit
What
cts. a
bushel?
plants two fields of 10 A. each with corn.
he uses seed corn selected in the
uses seed
They were
per tree.
the cost of spraying?
with apples at 85
A man
33.
cts.
the per
In sound apples?
cent of increase in bushels by spraying?
The
selected in the barn.
and labor for each
field
produced 45 bus. and
field B,
field
cost of
was flO an
acre.
36 bus. an acre.
;
in
B
he
fertilizers
Field
A
The man
Allowing f4 an acre for rent of land, what was the profit on each field? What sold the corn at $.60 a bushel.
per cent was gained by selecting seed in the field?
Two
34.
farmers plant 5 A. each in peanuts, using
the same kind of seed.
$3.00 for commercial to the acre.
lime.
each.
Rent Mr.
Mr.
fertilizer,
B
uses the
of land
and cost
Mr.
A
made 1500
A
spends f 1.50 for lime,
and $2.00 for land
same
of labor lbs.
was $7.00 an acre
and Mr.
peanuts an acre, which they sold at 3
How much What
more did Mr.
per cent was
A
made on
plaster
as the above, except the
B
1000
cts.
lbs.
money
of
a pound.
get for his crop than Mr. the
for
B?
invested in lime?
ROOT TUBERCLES 35.
139.29
Cow-peas with tubercles upon their roots lbs.
of
nitrogen, without tubercles
yield
118.45 lbs.;
PERCENTAGE soy beans with tubercles 113.55
What
is
lbs.,
of
If
without 75.98
when
100
tubercles are present?
lbs. of
cow-pea tops contain: nitrogen 1.84
phosphoric acid .67
lbs.,
potash 1.29
cow-pea roots contain: nitrogen 1.47
acid .67 lbs.
and potash 1.43
of these foods
is
in the root
?
lbs.,
37. lbs. of
How much potash ?
—what
lbs.; lbs.,
and 100
The following amounts
lbs.
phosphoric
per cent of each
What per cent in the how much nitrogen How much phosphoric
In a harvest of 3.2 T. per acre,
moved ?
lbs.
the per cent of additional nitrogen with each of
these crops 36.
lbs.,
243
tops is
re-
acid
?
of fertilizers in each 100
dry substance were found in leguminous crops. Plant and Part
?
PRACTICAL ARITHMETIC
244
COMMERCIAL FERTILIZERS Commercial
312.
fertilizers are
used for the nitrogen,
The
phosphoric acid, and potash they contain.
nitrogen,
phosphoric acid, and potash are
POUNDS
200
ATLANTA
stances.
Some
of
sub-
these
of
all
The
these
plant
substances
used
CO
for
GA.
8 PERCENT
ACID
sub-
foods.
GUARANTEED ANALYSIS^ AVAILABLE PHOSPHORIC
different
and some
MANUFACTURED BY i.
from
stances contain one, some two,
AMMONIATED^ FERTIUZER JOHN DOE
obtained
^
supplying nitrogen, phos-
phoric acid, and potash in com-
mercial fertilizers contain
dif-
erent per cents of these plant
NITROGEN 3 POTASH 3
The
foods.
some
of
composition
these
substances
of is
quite uniform or constant, while in others the per cent of nitrogen, phosphoric acid,
and potash varies considerably.
EXERCISE 207.— WRITTEN 1-
If
ammonia
is
82.4%
nitrogen,
how many pounds
of nitrogen are there in a ton of fertilizer that has
2%
of
ammonia ? 2.
If there is 1 lb. of nitrogen in 1.214 lbs. of
how many pounds commercial 3.
3.642% 4.
2
%
fertilizer
What
ammonia,
of nitrogen will there be in a ton of
which has 6.07%
of
ammonia?
per cent of nitrogen has a fertilizer which has
ammonia?
of
What
per cent of ammonia has a fertilizer that has
of nitrogen ?
PERCENTAGE If a
5.
ton of cotton-seed contains 60
what per cent
of cotton-seed
If cotton-seed
6.
is
nitrogen
how many pounds
are there in a ton of cotton-seed meal fertilizer,
phosphoric acid at
4-| cts.,
and potash at 5
7.5%
cts.
of each
is
the ton
per pound,
cts. ?
ammonia, how
of
of nitrogen will there be in a ton of cotton-
How much will the nitrogen be worth at 18 How much, when the cotton-seed meal
seed meal? cts.
per pound?
has
8%
ammonia? there are 124
If
8.
What
?
valuing nitrogen at 19
cotton-seed meal has
If
7.
many pounds
lbs. of nitrogen,
'?
meal contains 6.2% nitrogen, 2.8%
phosphoric acid, 1.8% potash,
worth for
245
of nitrogen
lbs.
in
a
ton of
cotton-seed meal, what per cent of cotton-seed meal
is
nitrogen ? If there is
9.
15.8%
how many pounds of nitrate of soda. What
of nitrogen in nitrate of soda,
nitrogen are there in a ton of will the ton of nitrate of soda be
worth, valuing nitrogen at 18
what per cent
11.
If
of cotton-seed is phosphoric acid?
there are 14 lbs.
ammonia, and 15.8 of
per pound?
If a ton of cotton-seed contains 26 lbs. of phosphoric
10.
acid,
cts.
lbs. of
furnish 12. lbs. of
If a farmer
a 16
%
mixes a
nitrogen in 17
nitrogen in 100
how many pounds as much nitrogen as
soda,
of
of
ammonia
A
is
it
take to
fertilizer so as to contain
offered a ton of 16
800
what per cent
acid phosphate to the ton,
farmer
lbs. of nitrate
will
1 T. of nitrate of soda?
phosphoric acid will his fertilizer contain 13.
of
lbs.
of
?
%
acid phosphate
246
PRACTICAL ARITHMETIC
at 112.75 a ton,
14%
a ton of
12%
14.
%
much
is
the
cheaper, valuing phosphoric acid
pound?
Which
is
one containing 2 2
Which
acid phosphate for $11.00.
cheapest, and liow at 4 cts. a
acid phosphate at $12.00 a ton, or
cheaper, a ton of a 2-8-2 fertilizer
%
of nitrogen, 8
%
(i.e.,
of phosphoric acid, and
of potash) at $18, or a ton of a 3-8-3 fertilizer (i.e., one
containing 3
%
%
of nitrogen, 8
of phosphoric acid,
and
3
%
of potash) at $22, valuing nitrogen at 20 cts. per pound,
phosphoric acid at
4-| cts.
per pound, and potash at 5
cts.
per pound? 15.
If there are
what per cent 16.
potash in a ton of kainit,
there in kainit?
if
lbs. of potash,
What
much
potash
per cent of sulphate of potash
is
there are 48 lbs. of potash in 384 lbs. of kainit?
If there are
of potash,
1000
what per cent
If there are
36
lbs. of
potash in a ton of muriate
of muriate of potash
lbs. of
If kainit contains
potash contains 50
%
is
potash?
,
potash?
12|^% of potash, and muriate
how many pounds much potash as there is
potash,
will it take to supply as
is
potash in a ton of cotton-seed
meal, what per cent of cotton-seed meal 20.
24
Sulphate of potash contains 4 times as
potash,
19.
is
of cotton-seed is potash?
as kainit contains.
18.
lbs. of
If a ton of cotton-seed contains
what per cent 17.
250
of potash
of
of kainit in 40
lbs,
of muriate of potash? 21.
If a ton of dried blood contains
what per cent
of dried blood
is
280
nitrogen?
lbs. of nitrogen,
PERCENTAGE 22.
If a
ton of fish scrap contains 180 lbs. of nitrogen,
wliat per cent 23.
nitrogen?
is
If fish scrap contains
phosphoric acid, what ing 20
ots.
247
8.25%
of nitrogen
and
6%
of
a ton of fish scrap wortli, allow-
is
per pound for nitrogen and 4
cts.
per pound
for phosphoric acid? 24.
If a
wood ashes contains 120 lbs. of potash, wood ashes is potash? If a ton contains potash, what per cent of wood ashes is potash?
ton of
what per cent 130
lbs. of
25.
320
If there are
acid?
is
phosphoric acid?
phosphoric acid in a ton of
lbs. of
If there are
of acid phosphate
280
lbs.,
what per cent
is
phos-
is
phos-
lbs., what per cent is phosphoric what per cent is phosphoric acid?
240
If
200
If
of fish scrap
what per cent
acid phosphate,
phoric acid?
phosphoric acid in a ton of
lbs. of
what per cent
phoric acid?
27.
140
If there are
fish scrap,
26.
of
lbs.,
If there are
56
phosphoric acid in a ton of
lbs. of
cotton-seed meal, what per cent of
cotton-seed meal
is
a ton of acid phosphate analyzing 16
%
phosphoric acid? 28.
What
is
phosphoric acid worth, when phosphoric acid 4
worth
pound?
cts. a
29.
is
How much is a ton worth when 8% respectively?
it
analyzes
14%,
12%, 10%, and 30.
nitrate
there
If
of
soda,
are 329.4 lbs.
of
what per cent
nitrogen in a ton of of
nitrate
of
soda
is
nitrogen ?
The composition
of
many
fertilizing
considerably, but the following
is
materials varies
a fair average:
PRACTICAL ARITHMETIC
248
COMPOSITION OF FERTILIZING MATERIALS Per Cent of
Acid phosphate Acid phosphate Acid phosphate Giound phosphate rock Tobacco stems
.
.
.
Sulphate of potash (high grade) Muriate of potash Nitrate of potash Kainit .
Wood
ashes (unleached)
.
.
.
.
.
.
Cotton-seed meal
Cotton seed
Tankage (concentrated)
.
Dried blood (high grade) Fish scrap Nitrate of soda
Sulphate of
ammonia
....
PERCENTAGE materials
800
:
cotton-seed meal, 800 lbs. of 16
lbs. of
acid phosphate, 400 lbs. of kainit
%
?
How many
34.
potash will
pounds of nitrogen, phosphoric acid, and the ton of fertilizer mentioned in the last prob-
lem contain, and what for nitrogen, 4-| cts. a
a
249
pound
for
will
pound
be worth at 18
it
for phosphoric acid,
potash, adding
|5
pound and 5 cts.
cts.
for mixing,
a
bags, and
freight ?
FEEDS AND FEEDING If corn contains 10.3
313.
protein
digestible,
is
%
of protein
what per cent
and 76 %
of this
of digestible protein
is
there in corn? If corn contains
72.5%
of carbohydrates
and
92%
of
these are digestible, what per cent of digestible carbohy-
drates
is
there in corn?
If 5
%
of corn is fats
ible,
what per cent
314.
and 86
%
of these fats are digest-
of digestible fat
is
there in corn?
Table of digestible nutrients in certain feeds.
Feeds
Per Cent op Protein
Per Cent op Per Cent Carbohydkates OF Fats
Corn
7.8
66.7
4.3
Oats
9.22
47.3
4.2
12.2
39.2
2.7
12.8
53.0
3.4
37.2
16.9
12.2
2.8
43.4
1.4
6.8
35.8
1.7
38.6
1.1
Wheat bran Wheat middlings .
.
Cotton-seed meal
Timothy hay
.
.
Red-clover hay
Cow-pea hay Alfalfa hay Corn stover Corn silage Skim milk
.
.
10.8
.
.
.
11.10
39.6
1.2
.
.
.
1.7
32.4
0.7
.
.
.
0.9
11.3
0.7
.
.
.
90
5.2
0.3
:
PRACTICAL ARITHMETIC
250 315.
A
Ration
is
the
amount
of feed given to an animal
during 24 hrs. 316.
A
Balanced Ration
ferent nutrients in sucli
is
one which contains the
amounts
dif-
meet the needs
as best to
of the animal being fed. 317.
Scientists
have formulated balanced rations or the
nutritive requirements of the various kinds of farm ani-
mals at different stages of growth and when being fed for
different
purposes,
calculated
for
1000
lbs.
These are known as Feeding Standards, and
weight.
used as guides in
practical
feeding
in
live
are
compounding
rations. 318.
The following
table
ible nutrients in feeding lbs.
live
shows the amounts
weight
FEEDING STANDARDS
Kind of Animal
of digest-
standards, calculated for 1000
:
:
PERCENTAGE
When amount
feeds rich in protein of protein
may
251
•
high in price, the
are
be reduced 10
%
without injury
to the ration. 319.
"
How
nearly will the following ration meet the
Feeding Standard
22
"
requirements of a dairy cow giving
milk daily?
lbs. of
Ration No.
35
1.
corn silage, 8
lbs.
corn stover, 3 lbs. cotton-seed meal, 4
lbs.
To
cow-pea hay, 6
lbs.
lbs. corn.
find total protein in ration
By
on page 249
reference to table
it
is
found that corn
silage contains .9 per cent of digestible protein.
per cent of protein in corn silage, there fore, in 1 lb. of silage there is .9
of silage there
= .315 lb.
is
.009
lb.
-=-
is .9 lb.
100
= .009
of protein, in 35
lbs.
If there is .9
in 100 lbs. lb.
there
;
there-
If in 1 lb. is
35 x .009
of protein.
Ration
35
= 35 x .009 = .315 lb. protein = 8 x .108 = .864 lb. protein corn stover = 6 x .017= .102 lb. protein cotton-seed meal = 3 x .372 = 1.116 lbs. protein = 4 x .078 = .312 lb. protein corn Total = 2.709 lbs. protein
lbs. silage
8 lbs. cow-pea hay 6
lbs.
3
lbs.
4
lbs.
'
By
reference to the table of feeding standards, page 250, it found that a dairy cow giving 22 lbs. milk a day should In the ration above we have found receive 2.5 lbs. of protein. is
that she receives 2.709 lbs. .209
lb.
more protein than
is
The
ration therefore contains
required.
To
find total carbohydrates in ration
By
reference to table (page 249),
:
it is
found that corn silage
contains 11.3 per cent of digestible carbohydrates.
If there is
11.3 per cent of carboliydrates in corn silage, there are 11.3 lbs
:
252 in
PRACTICAL ARITHMETIC
•
100
lbs.
;
therefore, in 1 lb. of silage there are 11.3
.113 lb. of carbohydrates.
If in 1 lb. of silage there
of carbohydrates, in 35 lbs. of silage there are 35
100
=
.113 lb.
X .113=3.995
carbohydrates.
lbs. of
35
-f-
is
= 35 x .113 = 3.995 lbs. carbohydrates = 8 x .386 =3.088 lbs. carbohydrates corn stover = 6 X .324 = 1.914 lbs. carbohydrates cotton-seed meal = 3 x -169 = .507 lb. carbohydrates corn = 4 x .667 = 2.668 lbs, carbohydrates Total = 12.162 lbs. carbohydrates
lbs. silage
8
lbs.
6
lbs.
3
lbs.
4
lbs.
By
cow-pea hay
reference to the table of feeding standards (page 250),
found that a dairy cow giving 22 lbs. of fnilk a day needs 13 lbs. of carbohydrates. In the ration above she receives
it is
12.162
lbs.
The
ration therefore lacks
.832
of carbo-
lb.
hydrates.
To
By .7
find total fats in ration
reference to table,
per cent of digestible
corn silage, there silage there is .7
there
is
it is
is .7 lb. -f-
100
found that corn silage contains If there
fats.
=
in 100 lbs.
.007
lb.
is .7
If in 1
of fats.
.007 lb. of fats, in 35 lbs. there
per cent of fats in
therefore, in 1
;
is
35
x
lb.
.007
lb.
of
of silage
= .245 lb.
of fats.
35
lbs. silage
6 lbs.
cow-pea hay corn stover
3 4
lbs.
cotton-seed meal
lbs.
corn
8
lbs.
= 35 x = 8x = 6x = 3x = 4X
= .245 lb. fats = .088 lb. fats .007 = .042 lb. fats .122 = .366 lb. fats .007
.011
.043
Total
By
= =
^172
lb. fats
.913
lb. fats
reference to table of feeding standards,
a dairy
cow giving 22
lbs. of
In the ration above, there
is
it is
milk a day needs .913
lb.
found that
.5 lb. of fats.
of fats, or an excess of
.413 lb.
In a similar manner the amounts of protein, carbohydrates, and fats in the different feeds in any ration may be computed.
PERCENTAGE
253
TABLE SHOWING PRICES OF FEEDS
320.
Estimated
Feeds
Corn, per bu Oats, per
I 0.49
bu
0.37
^Vheat bran, per T.
Wheat
.
18.00
.
middlings, per T.
19.00
Cotton-seed meal, per T.
30.00
Timothy hay, per T.
12.00
Red-clover hay, per T.
Cow-pea hay, per T. AKalfa hay, per T. Corn stover, per T. Corn silage, per T.
Skim
Local Price
Price
milk, per cwt.
.
12.00
.
.
12.00
.
.
12.00
.
.
5.00
.
.
3.00 0.20
Pupils should ascertain local prices of such feeds as are used in their neighborhood, and complete column three.
EXERCISE 208.— "WRITTEN 1.
Wherein
will the
following ration
to the feeding standard, in
a dairy
cow giving
Ration No.
2.
16.5 lbs. milk a day
35
lbs.
fail,
according
meeting the requirements of ?
corn silage, 10
lbs.
corn stover,
5 lbs. corn, 5 lbs. wheat bran. 2.
Construct a ration from the feeds used in your
locality (if given in the table) that will better
meet the
requirements of this cow, and calculate and compare the cost of this ration with the one given. 3. fail,
Wherein and how much
will the following rations
according to the feeding standard, to meet the needs
of a horse doing
hard work?
PRACTICAL ARITHMETIC
254 Ration No
10
3.
lbs.
corn stover, 6
lbs.
cow-pea hay,
11 lbs. corn, 2 lbs. cotton-seed meal. Ration No.
4.
15
lbs.
timothy hay, 14
lbs. corn.
lbs.
timothy hay, 16
lbs. oats.
Ration No.
5.
15
Ration No.
6.
4 lbs. timothy hay, 10 lbs. alfalfa, 7
lbs.
corn, 8 lbs. oats. 4.
It is seen
No. 3
that ration
is
much
nearer the
requirements of sach a horse than ration No. is
4.
Which
cheaper? 5.
"Wherein will the following ration
to the feeding standard^ in
doing light work Ration No.
7.
according
fail,
meeting the needs
of a horse
?
7 lbs.
corn stover, 8
lbs.
alfalfa hay,
6 lbs. corn. 6. If a draught horse weighing 1500 lbs. requires 37^-% more nutrients than one weighing 1000 lbs., what will be
the weight of the different nutrients required daily by
such a horse when doing hard work?
(For nutritive
requirements for a 1000-lb. horse, see table of feeding standards, page 250.) 7.
Construct a ration that will approximate the needs
such a draught horse, and compare
composed ration 8.
Wherein
its cost
of
with a similarly
for a 1000-lb. horse.
will the following ration fail to
meet the
requirements of a fattening beef animal during the third portion of the feeding period
Ration No.
8.
35
lbs.
?
corn silage, 15
lbs.
corn stover,
4.5 lbs. cotton-seed meal, 6 lbs. corn. 9.
How
nearly will the following meet his needs dur-
ing the second part of the feeding period
?
PERCENTAGE Ration No.
15
9.
lbs.
255
corn stover, 10
lbs.
clover hay,
cotton-seed meal, 8 lbs. corn.
1 lbs.
Wherein
10.
will the following ration fail to
requirements during the Ration No. hay, lo
15
10.
lbs.
his
part of the feeding period?
corn stover, 10
timothy
lbs.
lbs. corn.
Find the weights
11.
first
meet
of the different
nutrients
that
would be required daily by a beef animal weighing 750 lbs. for each of the three fattening periods, if the same amounts of nutrients are required for eachlOO-lb. live weight as for each 100 If
12.
lbs. of a 1000-lb. aifimal.
pigs during the second part of the fattening
period require daily for 1000
will the following ration fail to
24
Ration No. 11.
25
lbs.
13.
lbs. corn,
weight,
live
lbs.
carbohydrates, and .5
protein, 24 lbs.
lb.
fats,
4 lbs.
wherein
meet their needs?
10
lbs.
wheat middlings,
skim milk.
Wherein
will 40 lbs. of corn fail to
meet their
re-
quirements? 14.
Wherein
middlings 15.
will 20 lbs. of corn,,
fail to
and 20
meet their requirements
lbs. of
wheat
?
Ascertain the rations being fed to the various kinds
of animals in
your
locality,
and compare them with the
feeding standards given in table, page 250.
Compare
cost at local prices. 16.
Ascertain local prices of feeds and construct rations
that will come near to the requirements of the feeding
standards for each of the animals for which sample rations
have been given.
Compute
cost of each.
PROFIT AND LOSS EXERCISE 1.
than
20
I paid.
What was
When 10%
3.
A
5.
is
What was
1120
is
10%
more
is
gained?
pound
that cost
|125 were sold
for $100.
cts.
a
his per cent of gain? at
the cost price and 16|-%
is
is
the gain, what
?
The per cent
321.
for
the per cent of loss?
the selling price
tion
gained, what part
Damaged goods bought If
it
the selling price?
grocer sold butter for 30
cts.
What was is
— ORAL
bought a book for $1 and sold
I
2.
4.
209.
of gain or loss in a business transac-
always reckoned on the cost or the sum invested.
A
322.
for $110.
merchant buys goods for $125 and
Does he gain or
lose
sells
them
by the transaction?
$ 125 = cost $ 110 = selling price $126- f 110= f 15 loss $15 -=-$126= 12% loss. •
EXERCISE 1.
A
crate of berries,
ping and was sold at a
on the
210.
— "WRITTEN
worth $6.40, was delayed in ship25 % What was the loss
loss of
crate. 256
.
PERCENTAGE
A
2.
profit.
man bought What did he
A man
3.
A
4.
them
What was
A
What was
and in
sell-
the per cent of loss?
did
it
cost?
A transaction nets 18| %
6.
for $472,
the per cent of gain?
quantity of dress goods sold for $67 at a loss of
What
15%.
15%
it
storekeeper bought goods for $679.50 and sold
for $665.00.
5.
at
a team for $280 and sold
gain?
bought merchandise
ing gained $67.
257
How much
profit.
must
be invested to gain $650?
A
7.
steamboat sold for $117,600,
What
cost.
did
12% more
than
it
cost?
it
EARM PROFITS With wheat
8.
a bushel, the
rent 5
%
yielding 20 bus. to the acre at 75
land, 66|
amounting
to
$6 an
9.
5
With
acre,
%
what
$40 an
cost of raising the crop is
the profit?
What
is
potatoes yielding 200 bus. to the acre at 40 12-|^
A.
at $ 50, costing
in rent
and the cost of raising amounting to what is the profit ? What is the per cent
of its value,
$ 20 an acre, of profit 10.
?
With
onions yielding 500 bus. at 50
the land 4 A. at $ 100 an acre, costing its
cts.
acre, costing in
?
a bushel, the land
cts.
at
and the
of its value,
the per cent of profit
A.
and the cost
value,
acre,
what
is
the profit
?
cts.
a bushel,
in rent 5
%
of
of raising
amounting to $100 an
What
the per cent of profit
is
?
PKACTICAL ARITHMETIC
258 11.
Suppose in problem 8 the crop weighs 4 T.
problem
40 T.
9,
in
;
problem
10,
50 T.
;
being 5 mis. from town, marketing costs
How much
will the results in each of the last three prob-
lems be changed, 12.
if
you consider
%
be the profit or loss
above that in problem
What
8.
?
10,
on land valued
a production decreased 75
14.
of
Suppose onions to be raised under the conditions
of problem
What
?
on land valued as that in problem 10, but with
8,
the yield increased 50
13.
cost of marketing
Suppose wheat be raised under the conditions
problem
Avill
in
;
and the farm 12.50 a ton.
%
will be the profit or loss
When
as that of
problem
8,
with
below that of problem
10.
?
well-sorted apples bring $2.00 a barrel and
poorly sorted apples f 1.50 a barrel, what will be the profit
on sorting 13 bbls. of apples,
of culls
in sorting, 2 bbls.
worth f 1.00 a barrel be taken out
labor of sorting at 75 cts.
upon the investment is
if
?
What
is
Estimate the
?
the per cent of profit
(Note that the expense
of sorting
the only item of expense in the investment.) 15.
Suppose there were no
are wasted.
16.
What
If a miller
buys wheat at 86
grinding obtains 72
make in
%
of flour,
cts. a
of milling
is
ifl.Sl per barrel of flour
?
profit does he if
the cost
and he gets 33|
cts.
?
At what per cent above cost must may retain ^ of it for ray own
lot so that I
and they
bushel and in
what per cent
selling flour at $ 5.85 a barrel (196 lbs.),
for the by-products 17.
sale for the culls
will then be the profit of sorting
I sell | of a city
use, free of cost
?
PERCENTAGE 18.
and
With
tools
259
a farm worth $4000, buildings 1 1000, teams
11000, and with total sales amounting to $1500,
money 5 %, depreciation in team %, depreciation and repairs on buildings 5 %,
allowing for use of the
and
tools 10
taxes and insurance f 50, labor f 200, supplies $ 200, what is
the profit
What
?
per cent
is
paid on the investment?
by $300 additional labor the total sales can be increased to $2000, what is then the net profit? What the per cent of profit? What the net profit on the $300 19.
If
additional labor ? 20.
If I sell
for the
whole
-|
What of
the per cent of profit on this ?
an article for the price which what per cent have I gained ?
I paid
article,
A
merchant marks his goods at 25 % above cost. At what per cent below the marked price must he sell to 21.
make
17^
%
?
At what price above cost must this merchant mark goods so that after he has deducted 15 % from the marked price, he will still have remaining a profit of 121 ^? 22.
his
He trades this for 23. A buys an engine for $125. another piece of machinery, and receives in addition 20 % The second piece of of the cost of the first in money. machinery
is
sold for $ 90.
Has he gained
investment, and what per cent
?
or lost on his
COMMISSION EXERCISE 1.
A
basket,
trucker
sliips
and payg 8
What
selling.
%
211.
— ORAL
100 baskets of lettuce at fS a the commission merchant for
to
does he pay for selling?
2.
What
3.
A real estate
are the net proceeds from the shipment?
agent receives 3
amount
If his collections
%
#500 in
to
for collecting rents.
a month,
what
is his
percentage ? 323.
A
person
who buys
business for another,
is
or sells goods, or transacts
Commission Merchant,
called a
Agent, or Broker. 324.
The pay
is
usually reckoned at a certain per cent
and
is
called a Commission or Brokerage.
of the price, 325.
The sum
left
after
expenses have been paid
EXERCISE 1.
What
is
the
212.
If
— "WRITTEN
will be an agent's
rents amounting to $ 675 at 2| 2.
an agent charges
commission and other
called the Net Proceeds.
commission for collecting
%
commission ?
Sj'fo for
handling supplies
for
an orphanage, and his commission amounts to f 750, what was the amount of supplies purchased? 260
PERCKNTAGE
A man
3.
He
261
has $1250.00 to invest with a land company.
pays his agent $40.75 for making the investment.
Wliat was the rate charged by the agent?
A
4.
a year all is
goods he the 5.
5
sells.
amount
An
If
he receives $1500 for
of his sales
6.
A
7.
$4.50 a
crate,
If a
is
commission 10^?
9.
how much money cts.
A
250 T. of cabbages at
who
sells
them
for
$1.25 a
should the farmer receive
8%
commission for
if
and
selling,
freight per basket?
strawberry grower ships 27 crates of straw-
berries to a commission
them
sells
On
8% ?
farmer ships 38 baskets of beans to a commis-
the merchant charges
pays 40
commis-
the commission on 20 crates of eggs at
sion merchant in Baltimore,
basket,
18%
did he receive?
$3.30 a ton, commission 8.
At
sales.
sold ?
lawyer collected a debt of $96 at
What What
sion.
?
agent receives $67.84 commission on
what was the amount
ojo
$1200 % on the year, what
clerk in a city store receives a salary of
in addition he receives a commission of 2
;
merchant
for $3.25 a crate.
in
New York
City,
who
After deducting his com-
mission, paying drayage of 3 cts. a crate,
and refrigerator
car charges of 75 cts. a crate, he remits $59.67 to the
grower. 10.
sion
A
What
per cent commission did he charge?
farmer ships 34 crates of cabbages to a commis-
merchant in Philadelphia, who
a crate.
sells
them
for
$1.50
How much should the merchant send the farmer % commission, paying drayage charges
after deducting 8|
of 5 cts. a crate
and freight charges of 50
cts.
a crate
?
PRACTICAL ARITHMETIC
262
A
11.
man
sells
27 cattle
live-stock dealer ships a car-load of
weighing 1437
them
lbs.
each to Chicago, and the commission
After paying $1.00
for $5.75 per cwt.
switching charges on the
$5.00 yardage, 600
car,
lbs.
hay
at iflO.OO a ton, 400 lbs. corn at 50 cts. a bushel (1 bu.
56 lbs.), $59.00 freight, and charging 50 selling,
what
will be the
amount
of
cts.
=
a head for
net proceeds sent
to the shipper?
What
12.
per cent of the gross receipts are the total
charges connected with selling the cattle in problem 11
?
same car-load of cattle had been shipped to Richmond, Va., and the freight charges and selling price had been the same, what would have been the net proIf this
13.
ceeds returned to the shipper,
been as follows?
hay
at
$20 per
Commission
ton,
400
if
the other charges had
for selling
4%,
600
lbs.
corn at $1 a bushel, yard-
lbs.
age $10. 14.
What
per cent on gross receipts are the charges
connected with selling the cattle in problem 13 15.
If a
grower ships 27
mission merchant
in
bbls.
of potatoes to a com-
Philadelpliia,
$2.75 a barrel, pays 50
cts. a
?
who
sells
them
for
barrel freight, 5 cts. a barrel
drayage, and remits $53.46 to the grower, what per cent
commission did the agent charge for selling? 16.
rare
A
publisher sells at auction for various customers
books which bring respectively: $125.50, $62.25,
$187.50,
$285.00,
$845.25,
$672.00, and $950.50.
what does he receive
If
$35.50,
he charges
for tlie transaction ?
$48.75,
8%
$88.00,
commission,
COMMERCIAL DISCOUNT EXERCISE merchant buys a
If a
1.
213.
and receives 10
%
— ORAL
bill of
goods marked f 500
reduction for paying cash, what does
he pay?
A
2.
school liistory costs 50
If
cts.
25
paid for the 3.
326.
will he
A
cash
history?
If a grocer allows 10
amount
is
new
allowed
is
how much
for an old text-book taken in exchange, is
%
%
deduct from a
from his
what
bill for cash,
bill of l|25?
deduction from the price or value of anything
called a Commercial Discount.
Manufacturers and dealers in merchandise often issue a Price List from which certain discounts are allowed. 327.
Prices
published in catalogues
known
as
List
Prices are often subject to discounts. 328.
Sometimes several discounts are allowed
buyer.
In cases of this kind the
first
discount
to the
is
to be
deducted, then the second computed upon the remainder
and deducted, and so on for each discount; e.g., when 5% discounts are allowed from a bill of
40%, 10%, and
40%
goods, the
is
first
remainder, and then
mainder. discounts
5%
deducted, then is
deducted from the
The amount remaining is
after
the Net Price or Net Amount. 263
10% from
the
last re-
deducting the
:
.
:
:
PRACTICAL ARITHMETIC
264
EXERCISE 214— WRITTEN
A
1.
chemist buys a
bill of
laboratory supplies from
A. H. Newsom & Co., New York. He is allowed and 10% discount from list price and 5% off for
What
is
the discount on an original bill of f 350
Mr. A's grocery
2.
his cash discount
was allowed
A
3.
the
month was $34.75; per cent of discount
for cash ?
discount of 10
%
is
ing a certain season and 5 is
offered on all purchases dur-
%
The
"
a certain gas
bill of
What
additional for cash.
the discount on a bill of .$249.60? 4.
?
What
for
bill
was 12.78.
50% cash.
On
$ 678.00
?
company reads
The following discount will be allowed if this bill is paid company on or before the fifteenth instant
at the office of the
100 to 2000 cubic feet, monthly,
$
1.26 per 1000 feet.
Over 2000 to 6000 cubic
feet,
monthly, $ 1.25 per 1000 feet
less
5%. Over 5000 to 10,000 cubic feet, monthly, $ 1.25 per 1000 feet less
10%. Over 10,000 to 15,000 cubic feet less 15
Over 15,000 to 20,000 cubic feet less
feet,
monthly, $1.26 per 1000
feet,
monthly, |1.25 per 1000
%
20%.
20,000 cubic feet or over, monthly, light and fuel,
1000 feet
What
less is
1990 cu.
6100
per
f 1.25
25%."
the net cost of the following amounts of gas ft. ?
cu. ft.?
2100 cu.
9000 cu.
ft. ?
ft.?
3500 cu.
4900
cu.
ft. ?
9900 cu. ft.? 10,000 cu.
ft.?
ft. ?
INSURANCE EXERCISE
What
1.
$6000
its
for
its
|-
value at I
3.
What
— OBAL
will be the cost of insuring a building
value at 40
A merchant
2.
215,
cts.
on a hundred dollars?
insures his store valued at
What
1%.
does
worth
pay i96 annually for a the rate per thousand?
for |
him?
cost
it
$5000
life
insurance of $4000.
is
329.
Insurance
and property 330.
Insurance
tornado, etc. 331.
is
The
the promise of indemnity for personal
losses.
;
two kinds
of
is
Personal
:
life,
fire,
hail,
written contract between the insurance com-
pany and the person insured 332.
— Property:
accident, health.
The Premium
is
the
EXERCISE
called the Policy.
is
sum paid
216.
for the insurance.
— WRITTEN
LIFE INSURANCE 1.
What
is
premium on
the
a 14000 policy at
$28 per
$1000? 2.
If a
$1000 policy
of life insurance costs the insured
$32.16 each year, what will be the policy for 20 yrs.
?
265
total cost of a
$4000
PRACTICAL ARITHMETIC
266
The are
rates per $ 1000
at 20 yrs. of age, 114.96; at 30, $19.06;
:
$26.07
$38.92
at 50,
;
What would
3. if
on a policy in a certain companyat 40,
at 60, $63.42.
;
be the cost of a $4000 policy per year
What
taken at 20 yrs. of age?
taken at each of the
if
other years given?
what would be the total cost if What would it be if taken at each of
taken at 20
If
4.
carried 20 yrs.
?
yrs.,
the other ages and carried for 20 yrs.
What
5.
is
the difference in premiums, per thousand,
between a policy
man
A
for a
man
of 20 yrs.
and a policy
for a
Of 60?
40?
of
6.
?
participating
endowment
20-yr.
policy
is
one
which pays the insured the face of the policy at the end of 20 yrs., and in addition thereto profits or dividends.
If this
policy costs $48.10 each j'ear and the profit at the end of
the 20 yrs. is this
is
$316.00, what per cent of the total premiums
profit ?
PROPERTY INSURANCE on
Insurance
7.
water supply and for one year, of
a
fire
what
is
shingle-roofed
dwelling with a
protection costing 50 cts. on $100
the cost of insurance to the amount
$4500? If
8.
costs
it
3 yrs. as
it
much
twice as
does to carry
it
per year in the last problem period of 3 yrs.
7
if
what
will be the cost
the owner insures for a
?
of 5 yrs. as for 1 yr.,
lem
if
If it costs three times as
9.
to carry the insurance
1 yr.,
what
is
taken for a term of 5
much
to insure for a term
the rate per year in probyrs.
?
PERCENTAGE Each dwelling within 30
10.
to
problem
ft.
What
cost of insurance.
tlie
267
adds 15 the
will
will
be
it
and another 30
there
if
to the
ft.
a dwelling 30
ft.
How much
f 100.
left?
to the right
Suppose the dwelling of problem 7 were
11.
The
less
rate then
would
slate in-
might be 40
cts.
per
the insurance be?
Suppose the dwelling instead of being in a city
12.
well protected from tion, the rate
conditions of
fire
were
in a city
with no
fire
protec-
might then be 75 cts. per $100 under the problem 7. What would be the cost per
?
The
13.
on certain
rates
What would
What per
14.
15.
the
yearly.
?
cent of the face of the policy
problem 7
in
%
be the premium for 1 yr. on a $3500 saw-
mill insured for | value
premium
classes of unprotected property
Saw-mills sometimes cost 14
are very high.
is
is
to the left?
ft.
stead of shingle roof.
year
per f 100
insurance in
7 cost if there is a building 29 ft. 6 ins. to the
right of this dwelling and another 32
What
cts.
is
the yearly
?
The insurance rate in the country being 1 %, what premium on the insurance of a barn with contents
valued at $2700,
if
the property
is
insured for | of
its
value? 16.
at
What
$6400
is
at the
the
premium on
same
rate, if the
a country dwelling valued
property
is
insured for J
of its value? 17.
The
rate being
|%,
or 75 cts., on the hundred,
the buildings are metal roofed, what in
problem 16
?
is
if
then the premium
TAXES EXEBCISB 1.
If a
man pays
217.
— ORAL
annually for public purposes
the value of his property, which
does he pay 2.
Mr.
estate,
3.
If
2%
of
f 7000, what amount
?
A
2% on his real on money in bank, which is
pays for public purposes
valued at $-4000,
$1000.
is
2J% What amount does he pay for public purposes? a man pays annually $200 upon real estate for
public purposes, which
is
2%
of its value,
what
the
is
value of his property? 333.
Taxes are required from individuals for the sup-
port of the government and for other public purposes. 334.
Land, buildings, and
other
fixed
property
is
called Real Estate. 335.
^lovable property, as household goods, clothing,
jewelry, mortgages,
live-stock,
machinery,
etc., is
Per-
sonal Property.
The valuation of property Taxes Assessors, or Tax Listers. 336.
rate or per cent 337.
He
for taxation
is
an
made by
are levied at a certain
on the assessed valuation
A Tax Collector
is
officer
who
of the property.
collects the taxes.
usually receives a percentage of the taxes collected. 268
PERCENTAGE EXERCISE 1.
A
2.
The
The
city
tax rate being .7%, what
boundary
The
half of this farm. is
— WRITTEN
farm valued at $6750 near a city
value.
its
218.
269
is
assessed at | are the taxes? is
extended so as to include one-
city tax rate being
2.49%, what
the increase in taxes? 3.
A man
owning $4200 worth of personal property, the city, pays what taxes at the above rate?
living in 4.
With
the same property
what
are his taxes
if
out-
side the city limits? 5.
An
#1000 of a
income tax of collected in
is
man
%
on
is it if
his salary
$ 250 additional by extra labor 6.
The
all
annual incomes over
What is
states.
the income tax
receiving a salary of $1200?
What
$3500?
1
some
rate being .6
Of $2400? Of be $2400 and he earns
?
%, what are the taxes on 160 A. of At $16.88? At
timber land assessed at $9.38 per acre?
At $31.88?
$24.38? 7.
If a
taxes at
|,
man owns $8700 worth and the
and county taxes is 1.05 %, 1.25%, poll tax is $2.00, and he $2700, on which he pays an income tax rate for state
the city or local rate
has an income of of 1 8.
%
on
If
all
of property valued for
is
over $1000, what will be his taxes?
a school
district
having an assessed property
valuation of $200,000, maintains a public school 7 mos. at a cost of $720,
an additional cost the taxes of a
and could maintain it 2 mos. more of $180, what will be the increase
man owning
at
in
property valued for taxation
-
PRACTICAL ARITHMETIC
270 at $2600,
a special tax
if
voted for maintaining the
is
school 2 additional months?
A
9.
The
man owns
property in the city worth $9750.
valuation for taxation
is
|
and the
rate
2.15%.
He
$776 rent for this property. He also owns farm property of the same value, which is The rent valued the same for taxes, but the rate is .9%. On which does he obtained for this property is $682.50. receive the larger net profit, and how much more ?
receives
If a state
10.
982 increases
having an assessed valuation of $393,571,
its
appropriation for the support of
its
Agri-
cultural College from $100,000 to $150,000 per year, what will be the increase in taxes of a
man who owns
property
valued for taxes at $3500? 11. is
If the assessed valuation of the
what is the tax on the dollar?
to $185,554.55,
and
as mills
12. is
property in a county
$14,844,364 and the total state and county taxes amount rate, stated in
per cent
If the assessed valuation of the property in a county
$15,452,776 and the total state and county taxes
col-
lected amount to $245,931.64, what is the rate of taxation if there be 7552 polls on which there is a tax of $1.87
each?
DUTIES OR CUSTOMS 338.
A
charge
is
fixed by the
imported from other countries.
government upon goods
Such charges
are called
Duties. 339.
When
of the goods,
the duty
it is
is
called an
a certain per cent of the cost
Ad Valorem Duty.
:
PERCENTAGE
When
340.
the duty
value of the goods,
it is
271
fixed without
is
regard to the
called a Specific Duty.
This table gives the customs duties according to
341.
Act
the Tariff
1897 on several
of
articles
imported into
the United States
Apples, 25
per bu.
cts.
Coffee, free.
Barley, 30 cts. per bu.
Diamonds, 60
Beef, 2 cts. per lb.
Eggs, 5
Bottled beer, 40
60%
Bonnets,
Books, 25
Books
%
cts.
ad
ad
per gal.
Cigars,
cts.
per
2.
%
lb.
ad val.
cts.
per bu.
Wool, 11
cts.
Woolen
clothing
and
per
lb.
per
lb.
40
and 60% ad
cts.
val.
val.
EXERCISE 1.
per doz.
cts.
Jewelry, 60
lb.
$4.50 per
25% ad
val.
Horses, f 30 per head.
val.
val.
free.
Cheese, 6
ad
Hay, $i per ton.
public libraries. Potatoes, 25
for
%
What What
219.
— WRITTEN
is
the dutj' on 360 lbs. of cheese
is
the duty on 400 lbs. of cheese costing 8
is
the duty on 12000 worth of diamonds?
?
cts.
per pound? 3. 4.
What What
is
the duty on a consignment of 3 head of
horses valued at $350 each? 5.
What
is
the duty on a car-load of 9 T. of hay worth
18 a ton? 6.
a
What
|4
is
the duty on 4 lbs. of cigars valued at
is
the duty on 4 lbs. of cigars valued at |8 a
pound? 7.
What
pound?
PRACTICAL ARITHMETIC 8.
Pupils should
make ten
similar problems concerning
the articles given in the table that are used in their homes. 342.
Foods
COMPOSITION OF FOODS
PERCENTAGE
273
TABLE OF DIGESTIBILITY OF FOODS
343.
Meats and fish Eggs Dairy products
Protein
Fats
Carbohydrates
Per Cent
Ptr Cent
Per Cent
.
.
.
97
95
97
95
.
.
.
97
95
85
90
78
90
97
83
90
95
90
90
Cereals
98
Sugars
Dried peas and beans Vegetables .
.
.
.
Fruits
EXERCISE
The human body
1.
is
220.
— WRITTEN
composed of: ash 6%, protein
18 %, fats 15 %, carbohydrates about 1 %. The remainder is water. man weighing 150 lbs. has how many
A
pounds
A man weighing
2.
The
fat?
A
3.
protein?
5.
fat equals
body tissues? 150
lbs.
has
what per cent
how many pounds
of
of the water?
man weighing 150 lbs. has how many pounds The fat equals what per cent of the protein?
The carbohydrates equal what per cent
4.
tein
of water in his
of
of the pro-
?
Since
digestible,
97
%
of
the
protein
of
meat and
fish
is
how many ounces
are digestible in 2 lbs. of
95%
meat and
beef flank? 6.
Since
of the fats of
how many ounces 7.
Since 98
digestible,
%
fish is digestible,
are digestible in 1 lb. of fish?
of the carbohydrates of
how many ounces
meat and
fish is
are digestible in 3 lbs. of veal?
:
PRACTICAL ARITHMETIC
274
Find the number of ounces of water, refuse, and digestible protein, fats, and carbohydrates in the following 1 lb. of bread.
8.
milk.
1 lb. of corn bread.
11.
13.
1 lb. of cabbage.
16.
1 lb. of rice.
14.
17.
at
of four
1
lb.
of potatoes.
15.
lib. of ham.
12.
grown
Food Materials
Rice
.
Eggs Milk
.
Tea
.
.
DINNER
.
Sweet potatoes Bread
Bread
12
.
drates, 20.
4
.
4
.
.
6
.
.
3
12
.
.
Butter
.
3
.
12
.
8
Bananas Cake
12
.
....
19.
.
.
SL'PPER
Roast beef (flank) .
.
Sugar
2
.
Potatoes
.
Rice pudding
.
.
PoUN'lS Ounces
DINNER
Butter
Veal cutlet Bread Butter Coffee
two men and two
persons,
Pounds
.
.
1 lb. of cheese.
materials were consumed in one
BREAKFAST
.
18.
moderately hard work:
Food Materials
Oatmeal Milk Sugar
1 lb. of
lo.
1 lb. of turnips.
1 lb. of apples.
The following food day by a family
women,
1 lb. of chicken.
9.
.
Find the amount of digestible protein, carbohy-
and
fats
per person in the three meals.
Estimating 453.6 grams to a pound, compare with
food standards, as follows
:
man
grams, carbohydrates 400 grams,
requiring protein 100 fats-
60 grams
;
woman
requiring protein 90 grams, carbohydrates 350 grams,
40 grams. deficient
?
Wherein
is
the ration excessive
?
fats
Wherein
INTEKEST What What
per cent of 100 per cent of f 1
6
is
is
?
6 cts.
?
$6 is charged for the use of f 100, what per cent the sum loaned is the sum charged? If
The money charged
344.
for the use of
money
is
of
called
Interest.
is
345.
The money loaned
346.
The per cent which
is
called the Principal.
the interest
is
of the princii^al
the Rate of Interest.
The
347.
principal
plus
the
interest
is
the
called
Amount.
Many
348. interest,
states
This fixed rate 349.
have established
an excess of which is
Usury
known
is
a
fixed
rate
of
unlawful to accept.
as the Legal Rate of interest.
interest
is
it
charged
in
excess
of
that
allowed by law, or the legal rate. 350.
Interest
is
usually calculated by taking a certain
rate per cent of the principal for one year. 351.
The time
for
which interest
is
to be reckoned is
and days. When over a are used, and when under a
calculated in years
year, both
years and daj^s
year, days
275
:
PRACTICAL ARITHMETIC
276
In both cases the exact number of days
only. if
exact interest 352.
less
is
counted,
desired.
is
In practice, however,
than a year interest
of 30 days to the
when money
is
loaned for
usually reckoned on a basis
is
month, and 12 months, or 360 days,
when exact
to the year, instead of 365 days as
interest
is
computed. If
1500
is
May
loaned from
Aug.
1906, to
1,
1,
1907,
the exact time is 1 year and 92 days, but in business, interest is usually reckoned for 1 year and 3 months, or 1^ years, instead of for l/g^ years. The United States
government and some banks, however, use the exact method, and in the above example would reckon interest ior 1^6^^ years. 353.
When money
is
loaned for a certain number
months, or when interest
is
of
payable monthly, calendar
months are meant.
EXERCISE
221.
— ORAL
Find the interest on the following sums for the times
and
rates specified
4% at 3 % at 4 %
5% at 6 % at 6 %
1.
$5
2.
125
for 1 year
3.
150
for 1 year
4.
$300
for 2 years at 4
5.
$600
for 1 year
and 6 months
6.
1800
for 1 year
and 3 months
7.
$400
for 2 years at 6
for 1 year at
3 'months at 8
%
;
at
;
at 10
%.
;
;
%
;
%
at
;
at 7
;
at
6%.
;
at 8
%.
;
at 7
%.
%
;
at 9
%.
4% at 6 %. at 6 % at 8 %. 8 % for 2 years at
;
;
;
and
INTEREST
6
8. 11200 months at
354.
The 22.515
9
%
;
for 3
months
for 3 years at
at 5
6%
interest for 1 year is
7%;
for
%.
Find the interest on $375.25
at
6%
for 2 years.
of 375.25, or, 375.26
X
.06
=
= $22,515.
For 2 years the interest
Find the
$22,515 x 2
is
= $46.03.
on $450 for 3 years, 4 months, and
interest
8%
15 days at
The The The The
8%;
for 1 year at
277
per year?
= 36.00 = $36.00 = $ 108.00 interest for 4 months is j\, or |, of $ 36 = 12.00 interest for 15 days is ^f, or i) of J^ = ^^ of $ 36 = 1.50 interest for 1 year
450
is
interest for 3 years is
'
355.
x
.08
$36 x 3
Therefore, the total interest
To
find
the interest
interest for 1 year
for a
$ 121.50
is
given time, find the
and multiply by the number
of years
or fraction of a year.
EXERCISE
Find the
interest
222.
— WRITTEN
and amount
:
1.
1 275.25 for 1 yr. 3 mos. 20 days at 8 %.
2.
$345
3.
1 435 for 3 yrs. 11 mos. at 5 %.
4.
$ 850 for 1 yr. 8 mos. 15 days at
5.
I 340 from June
6.
$ 450 from Sept.
7.
I 815.27 from Jan. 10, 1905, to Oct.
8.
$427.25 from Nov.
9.
$ 650 from April 10, 1908, to Oct. 10, 1908, at 4 %.
10.
for 2 yrs. 6 mos. 15 days at 6
1,
5-|
%.
1906, to Sept. 15, 1908, at 6 %.
10, 1905, to
1 347.50 from Feb.
%.
5,
5,
Dec. 25, 1907, at 8 %. 1,
1908, at 10 %.
1906, to Jan. 20, 1908, at 6 %.
1908, to Sept. 10, 1908, at 6 %.
PRACTICAL ARITHMETIC
1^78
BXEECISB Find the exact
223.
interest on
—WRITTEN
:
1,
1905, to
Aug.
1450 from July
3,
1907, to
May
3.
$775 from Dec.
9,
1905, to Feb. 17, 1908, at 6 %.
4.
1 2550 from
5.
% 90 from Aug. 10, 1906, to Nov. 10, 1906, at 7 %.
6.
11750 from Jan.
7.
1335 from July
8.
1 3750.50 from Jan.
1.
1200 from July
2.
May
21, 1907, to
24, 1906, to 1,
time, the following table
others
:
1907, at
6%. %.
Dec. 13, 1907, at 4J %.
Feb. 16, 1907, at 5 %.
1900, to June 19, 1903, at 6 %.
For convenience
356.
7,
31, 1908, at 8
29, 1899, to Feb. 29, 1908, at 6
/o.
in finding the correct or exact is
frequently used by bankers and
INTEREST
279
may be added or subtracted as the case may from July 10, to Dec. 10 is 163 days. Erom July 10 to Dec. 23 is 153 + 13 = 166 days. From July 31 to Dec. 20 is 153 - 11 days = 142 days. the difference require,
e.g.,
On many
357.
calendars used in business offices the
days of the years are
numbered consecutively through the
months, and in calculating interest for periods year, business
men
frequently take the
on which interest begins and subtract of the
day when
day from June 18
it is
of the year, to
due
;
e.g.,
June
What
For one day
is
it
less
than a
of the
day
from the number
18, 1908, is the
170th
and Nov. 12 is the 317tli day, therefore Nov. 12 is 317-170 = 147 days.
METHOD
SIX PER CENT 358.
number
the interest on
$1
at 6
%
for 1
month?
?
If the interest on
$
1 for 12 mos. is
=
for 1 mo. is j\ of $ .06 $ .005, 1 da. is of $ .005 $ .000^.
^
$
.06,
the interest on $ 1
and the interest on $
1 for
=
Thus:
The The The
% = f .06. % = f .005. % = f .OOOf on $360.40 at 6% for 2
on f 1 for 1 yr. at 6 interest on $1 for 1 mo. at 6 interest on $1 for 1 da. at 6 interest
What
is
the interest
yrs. 8
mos.
18 days?
The The The The The
interest
on f 1 for 2
interest on
$1
yrs. is
for 8 mos.
is
|
.06
x 2
= f .12
$.005x8=
.04
$ 1 for 18 days is $ .000^ x 18 = .003 = $ .163 interest on $ 1 for 2 yrs. 8 mos. 18 days interest on $ 360.40 for 2 yrs. 8 mos. 18 days = $ 360.40 X .163 = $58.7452, or f 58.75. interest on
:
:
PRACTICAL ARITHMETIC
280
To
359.
number number
on any sum at 6 % and days, multiply 6
find the interest
of years, months,
for a given
by the by the number of months and of a mill by the number of days. Find the sum of these and multiply this sum by the principal. of years
;
.
cts.
5 cts.
;
1^
EXERCISE Find the
by the
- "WRITTEN
six per cent
method on:
6%.
1.
$475.40 for 1
2.
1820 from June
3.
$528.60 for 3 yrs. 8 mos. 18 days at 6 %.
4.
1360.50 for 3
5.
$750 from May
360. 8,
interest
224.
or
mos. 6 days, at
yr. 2 1,
1904, to Oct. 12, 1905, at
yrs. 9
mos. 24 days at 6 %.
12, 1901, to
April 18, 1903, at 6%.
Short-time loans are frequently
made
for
3, 4, 6,
more months
% is sum at 6%
Since the interest on $1 for 1 mo. at 6
^
6%.
ct.,
to find the interest
on any
$.005, or for
time
expressed in months, move the decimal point two places to the left in the principal and multiply by one -half the
number of months. The interest on $320.50
for 6 mos.
is
3.205 x 3
= 9.615
= $9,615. 361.
made
Loans made for three months or for 30, 60, or 90 days
Since the interest on $1 for 1 da. at 6 find the interest
move
less are usually
%
is
^ of a mill, to
on any sum for time expressed in days,
the decimal point three places to the left in the
principal
and multiply by | the number of days.
:
:
INTEREST
The
281
interest on 1160.75 for 30 days
= .16075
X 5
= .80375 = $.80375, EXERCISE
Find the
interest at
225.
6%
is
.16075 x } of 30
or 80 cts.
— WRITTEN
on
1.
1325
for 8 mos.
6.
1 945 for 30 days.
2.
$785
for 6 mos.
7.
11500
3.
$957
for 9 mos.
8.
$525
4.
$2450
for 7 mos.
9.
1 343 for 30 days.
5.
$375
for 11 mos.
10.
The
362.
six per cent
$250
for 60 days.
for 90 days.
for 90 days.
method may be used
the interest at other rates, as follows
for finding
:
% is f, or |, of 6 %, therefore, take ^ of the interest at 6 %. % is f, or of 6 %, therefore, take of the interest at 6 %. 4 % is ^, or f, of 6 %, therefore, take | of the interest at 6 %. 2
3
-^j
4i-%
is
—
2^,
-J
or J of 6
%,
therefore, take f of the interest at
6 %, or subtract I of the interest at 6 %. is f of 6 %, therefore, take f of the interest at 6 %, or 5 subtract ^ of the interest at 6 %.
%
7
%
is
I of 6
%,
therefore, take ^ of the interest at 6
%,
or
add ^ of the interest at 6 %. 71
Ji
6%,
is
cf„
or
363.
~^! or I of 6 %, therefore, take
add J of the interest
The
six per cent
at 6
-J
of the interest at
%.
method being based on 12 months,
or 360 days, to tlie year, of course, does not find
tlie
interest.
EXERCISE 226.— WRITTEN Find the 1.
interest
$ 250 for
by the
1 yr. 3
six per cent
mos. at 2 %.
method on
exact
PRACTICAL ARITHMETIC
282 2.
1335 from July
3.
1 945 for 2 yrs. 4 mos. 20 days at 4 %.
4.
11350 from Dec.
5.
1725
6.
$ 2450 from Aug. 15, 1905, to Nov.
7.
$ 183 for 2 yrs. 5 mos. 23 days at 7J
8.
1420 from July
364.
20, 1898, to
or principal
:
3%.
20, 1905, at
12, 1905, to Feb. 1, 1907, at
It is seen that in
Any one
June
41%.
5%.
for 1 yr. 7 mos. 13 days at
factors involved est,
10, 1903, to
June
20, 1908, at 7
5,
%.
%. 1901, at 8 %.
computing interest there are four
time, rate per cent, principal and inter-
and amount, or interest and amount.
of these factors can be
found
if
the other' three
be given, but in business the principal, rate per cent, and time are usually given and the interest, or interest and
amount, are required to be found. It may be necessary to find the principal, when only two of these and the interest,
365.
time
rate, or
or the
amount, are given. 366.
To
interest or
What
find the
amount
principal
6 mos. at 6
principal,
are given Avill
when
the rate, time, and
:
produce fl5 interest in 2
yrs.
%?
Interest on Interest on
f $
% = $.06. 6 % = f .06 X = —— = $ 100.
1 for 1 yr. at 6 1 for 2^ yrs.
.at
Hence, principal required
2i
=
f
.15
.15
What amount
A
principal at 6 9^ interest for 2 yrs. 6 mos. will to f 115
principal of
?
f1
at 6
%
for 1 yr.
=
$
.06 interest.
:
INTEREST
A
principal of
283^
=
$
1 at 6
%
for 2| yrs.
$
1 at 6
%
interest for 2i yrs.
$
.06
X 2^ = $
.15
interest.
A
principal of
principal
1
1
Hence, principal
amounts to
= $ 1.15. $115 = required = ~ f 100.
+ interest
$
.15
$1.15
EXERCISE Find the principal that
at
— WRITTEN
227.
will bring
1.
1450
2.
172.74 interest
3.
111.33 interest from July
interest in 3 yrs. at 6
%. mos. at 2^%.
in 3 yrs. 9
5,
1904, to Feb.
9,
1905,
4%. 118.72 interest
4.
in 5 mos. 27 days at
EXERCISE
1.
11283.33 at 5
2.
1 1303.41 at 6
3.
1 25.76 at
4.
$ 94.31 at
367. pal,
To
% 6 %
% %
— WRITTEN
228.
Find the principal that
5^%.
will
amount
to
:
interest for 3 yrs. 4 mos. interest for 60 days.
interest for 33 days.
interest for 1 yr. 7 mos. 21 days.
find the rate per cent,
when
the time, princi-
and the interest or the amount are given:
At what
rate per cent will
interest in 3 yrs.
The The The
6 mos.
f 1 for 1 yr. at 1 % = f .01. f 1 for 3^ yrs. at 1 % = f .035. on 1 100 for 31 yrs. at 1 % = $ 3.50.
interest on
interest on
interest
$100.00 produce 124.50
?
Hence, the rate
is
f2450 ^ ^ ^^ 3.50
:
PRACTICAL ARITHMETIC
284
EXERCISE
229.
— WRITTEN
Find the rate per cent
2.
When When
3.
When 16130
1.
amounts 4.
the interest on 1 2300 for 1 yr.
at interest
368.
is
$118.28.
from June 6 to Nov. 24
to $6237.28.
When $1050
March
1138.
is
the interest on f 675.88 for 5 yrs.
at
interest
from Sept.
21,
1904, to
1905, amounts to $1069.15.
5,
To
find the time,
interest or the
amount
when the
rate, principal,
and the
are given:
In what time will $100, at 6%, bring $21 interest?
The interest on $ 1 at 6 % for 1 yr. = | on $ 1 for the unknown time = $ 21 ^ 100 Hence, the unknown time
=
$.21 '^^
The
.06.
=
$
interest
.21.
= 3|- yrs.
.06
EXERCISE 230.— WRITTEN Find the time in which
:
1.
The
interest on
$1500
will be
$180
2.
The
interest on
$8520
will be
$1746.60 at 6%.
3.
The
interest on $17,040 will be
4.
$238.74 at
369.
will
amount
4%.
$3493.20
at
6%.
to $308.20.
In the foregoing solutions the unit in finding the
principal was $1
and
4i%
at
;
the unit in finding the time was 1 year,
in finding the rate the unit
was
to find the principal, time, or rate,
1 per cent.
when
are given, divide the given interest
Hence,
the other factors
by the
interest ob-
tained by using the unit as the required factor.
STOCKS AND BONDS When two
370.
more persons form an organization
or
under the laws of the state to conduct business as one body, the organization
is
called a
Company, Stock Company,
or Corporation.
The money contributed for the purpose of carrying on the business of a company is known as its Capital, 371.
Capital Stock, or Stock. Tlie stock of a
372.
of equal parts
is
374.
company
known
is
divided into a
number
as Shares, or Shares of Stock.
A person holding
373.
stock
known
or
owning one or more shares of
as a Stockholder.
The document or certificate issued to each stocknumber of shares he owns, is called a
holder showing the Certificate of Stock.
375.
A
Bond
is
a written promise or obligation of a cor-
poration, or a government, to pay a specified
money
intervals 376. its
and
of
The
at a certain rate.
original, certificate, or face value of a stock is
The
Par Value.
Value.
sum
at a certain time, with interest at regular stated
When
price for which
the market value
value, the stock
is
is
it sells is its
greater than
said to be at a premium, 285
Market its
par
and when
it
:
;
PRACnCAL ARITHMETIC
286 sells for less
than the face or par value,
it is
at a Discount
or Below Par. 377.
The
profits of a
company which
are divided
among
the stockholders according to the stock which they hold are
known
378.
as the Dividends.
The
capital stock of a corporation
divided into two kinds
dend
is
:
Preferred and
common
A
divi-
is
paid on the
stock.
Persons
who buy and
sell
called Stock Brokers, or Brokers,
called
sometimes
usually guaranteed on the preferred stock, and in
such case must be paid before any dividend
379.
is
Common.
Brokerage.
Brokerage
stocks and bonds are
and
is
their commission
is
computed on the par
value of the stock. 380.
Small certificates of interest, called Coupons, are
usually attached to bonds. to
pay interest
this interest
is
These coupons are promises
at a certain time at a specified rate.
not paid
when
If
due, the interest itself draws
interest at the legal rate. 381.
Large numbers of different stocks and bonds
regularly on the market, and sively.
The following
are
are
are bought arid sold exten-
a few with the
quotations
given in a daily newspaper June 27, 1908
The figures indicate the price in dollars per share or bond. The par value is usually f 100, but in some cases it may be $50, or some other value. In the following problems f 100 is the par value of the stocks or bonds in question, unless otherwise stated
PRACTICAL ARITHMETIC
•288
Find the cost
2.
at 34|, brokerage
Find the amount realized from the
3.
of B.
&
S.
O. R.R. stock at 86, brokerage
sale of 32 shares
^%.
Find the amount realized from the
4.
U.
of 27 shares of stock (par value $ 50)
^%.
bonds, at 113|, brokerage
How many
5.
^%.
of
$67.50, can be bought for
|%?
How many U.
6.
S.
money
raise sufficient
§500
shares of stock having a par value of
$50 and a market value $4869, brokerage
sale of 9
$100 bonds must I sell at 107| to pay a debt of $3432.80, broker-
to
|%? How much income will paying 36 % dividend, yield ? age
$3600 Standard Oil
7.
8.
stock,
What is the profit in buying 26 shares of Chicago W. R.R. stock at 150 and selling for 159, broker-
and N.
age on each transaction ^ % 9.
What
is
value $50) at transaction 10.
-j
?
the gain in buying 37 shares of stock (par
49-|-
and
selling at 62^, brokerage on each
%?
What sum must be invested in U. S. 4's at 118|, ^%, to yield an income of $160? What sum must be invested in P. R.R. stock at
brokerage 11.
92|
of par value,
come 12.
of
What income
$5287.50
brokerage | 13.
paying 3|
of $ 630, brokerage
A
%
half yearly, to give an in-
^%?
will be obtained
in stock at 105J,
from the investment
paying
3%
semiannually,
%?
man bought
Illinois
Central R.R. stock at 137|
INTEREST
.
and sold
it
for 1421,
making a
289
profit of $512.50.
How
many shares did lie buy, brokerage ^ % in each transaction? 14. A man buys 200 shares of Colorado Midland R.R. stock, paying 4%, at 63 and holds it 2 years, receiving 2 dividends, and sells it at 78. Money being worth 6 % per annum and brokerage -^^ on each transaction, how much did he gain? 15.
Which
is
the best investment
:
7
%
stock at 127^,
bonds at 82J, or money loaned at 6 % ? 16. If a man buys U. S. 4 % bonds at 116|, what per cent does he receive on his investment ? 5
(Jo
17.
Which pays better, a 5 % stock at 90 or a How much better? A man has 13800 to invest. Which wilt
7
%
bond
at 130? 18.
larger income,
How much
5%
larger
stock at 95, or
5J%
yield the
bonds at par?
?
NEGOTIABLE PAPERS 385. A written order to a bank to pay money, from one having money deposited in such bank, is called a Check.
J^ewYorh,...Ci'wc}. 6, ..,190 8
Ji'o.--337-
The Corn Exchange Bank FIFTH
Pay
to
^.
AVENUE BRANCH
(S,
or order
B'uyuyyi&
(Z.
A Bank Check
/"f.
M-aAJMi^
V
&0-
PRACTICAL ARITHMETIC
290
A
386.
Payee or
to
may
check
which case
Bearer, in
to
A
check
may
name may make
it is
be " indorsed in blank,"
person to whose order
it
is
across the back of
his
to
;
be indorsed by the person to whose order able.
Payee or
may be collected by auy one or made payable to "order," it must
If
order.
made payable
be it
made payable
made paywhen the
writes only
the check as in
A
;
or he
a special indorsement, as in B.
S'au to tk&
o-vcIea, o-l
/'ftn-vu j.akni'Cyn, ^eA>\a£, l/O-Lttia.yyh^
Indorsed in Blank
A.
B.
387.
a
A
Certified
Check
bank has written,
is
one upon which the cashier
in red ink, the
word
and
his
name
the bank responsible for
its
payment.
date,
name
of bank,
Special Indorsement of
" Certified," with
This makes
as cashier.
DRAFTS 388.
sum
of
A
written order to one person- to pay a specified
money
to another person at a certain time
a Draft, or Bill of
389.
Drawer paid
is
Exchange.
The person who makes of the draft
the Drawee
;
;
the person
and the person
the Payee.
is called*
to
the order
who
is
whom
is
called the
ordered to pay
the
money
is to
is
be
INTEREST
A
390.
draft which
the drawee
A
391.
whenever presented
draft payable after date or at a certain time
Time
Draft.
Atlanta, Ga.,..Mel. f,-..190 8
JVo. __f/.,
Pay
to the
order of
^ovn ^cK^kanaSt
ffa,nA,
ol c^e^w-
$260
Z/o-ik
Dollars.
c^^^vc^•^^>^^^c^•^i«> /i-wncll&ct c/t/^i^^^i-^T^^^^^^^-^^r^
To
to
called a Sight Draft.
is
after sight is a
3'k&
paj'able
is
291
Sands,
T. T.
Jfeiv York.
A Draft 392.
person
A
time draft must be presented to the drawee or
who
ing across
is
its
to pay,
who must
face the
accept the draft
by writ-
" Accepted," together with
word
the date and his signature. 393.
A
a deposit
draft is
a
by one bank upon another
Bank
in
which
it
has
Draft.
PROMISSORY NOTES 394.
A
written promise to pay a certain
at a specified time after date
395.
The person who
to
pay
to
whom
is
the
Maker
signs a note
of the note.
the promise to pay
is
sum
of
money
called a Promissory Note.
is
and thereby promises
The Payee
made.
is
the person
PRACTICAL ARITHMETIC
292 396.
A
note signed by one person only
is
called an
Individual Note. 397.
A
note signed by two or more persons
is
a Joint
Note. 398.
A
payment
note
is
usually written so as to include the
of interest at a specified rate for the time of the
note.
3'kvt^ •yyuyyCth^-- -after date.. -o^^.. promise to jiay to tlze
order
^to-n&
/%5a^ra-.
of.
a/yicl
/'f&vvi&k
at the Xational City Bank, of Jfew York, with interest at six per cent.
Value received. Jfo.. .¥-/-.
I>ue...fa,rv.
A 399.
When
no rate
/,
/f^f_._
Promissory Note is
mentioned, a note bears interest
at the legal rate of the state in 400.
A
note
may be made
which
it is
payable.
payable to the payee or
bearer, to the payee only, or to the order of the payee.
Notes are indorsed in blank or to special persons, as with
The indorser of checks. payment unless the words his signature.
a note "
is
I'esponsible
Without Recourse
for
its
" precede
INTEREST 401. it
The Day
of
Maturity of a note
becomes due or the
last
day
the day on which
is
of the time for
which
it is
In some states after the note becomes due, three
drawn.
days are allowed for
known
293
as
Days
its
These three days are
payment.
of Grace.
BANK DISCOUNT 402.
and others make
Bankers
from a note or draft for paying deduction or charge
is
it
it
Bank
due.
is
This
the simple interest on the face of
the note or draft from the date on which
date of maturity.
deduction
certain
a
before
paid to the
it is
This charge or deduction
is
known
as
amount
of
Discount.
403.
The
Proceeds of a note or draft
is
the
the note or draft less the discount and exchange.
The paying or transferring of money by means of money orders is called Exchange. The charge made by banks and other institutions for issuing or cashing these checks, drafts, or money orders is also The rate of exchange varies from ^ to called Exchange. different 1^ of 1%, or may be a certain fixed amount for 404.
cheeks, drafts, or
sums.
EXERCISE 1.
on a
A
draft for 1 320
New York
is
232.
sold
— WRITTEN
by
bank, rate ^fo.
a
bank
What
in Raleigh,- N.C.,
is
the exchange
A draft for $125 is sold by a bank in on a bank in Chicago, 111., rate |%. exchange ? 2.
La.,
3.
A
?
New Orleans, What is the
United States postal money order for $76 costs
PKACTICAL ARITHMETIC
29i 30
and one
ets.,
What 4.
for
Which
S.
same
at the
price.
?
cheaper, a draft on a
is
f 40 at ^ %, or a U. a cost of 15 cts. ? 5.
$100 can be bought
the rate per cent on each
is
money order
New York
for the
bank for same amount at
bank in Chicago, 111., charges 15 cts. for f 100 on a New York bank, what is the rate
a
If
draft for
a of
exchange charged?
A
405.
note for |100 at
6%
1905, due 9 months after date, 15, 1905, for discount.
interest
drawn July
15,
presented to a bank Oct.
is
Find the discount and the
pro-
at 6
%
from
The
note
ceeds.
The discount Oct. 15, the
drawn July
The The
it
the simple interest on is
months, and
interest
1905, at
months.
and payable
of
|6
=
proceeds. 233.
— WRITTEN
in 90 days,
if
for
f 480 dated
Sept.
discounted Sept.
30,
5%.
Find the proceeds of a note for 1375, dated May
1907, payable Aug. 20, 1908, by a bank July 15, 1907.
Jan.
=6
$ 100 at 6 % for 1 year = f 6. on $100 at 6% for 6 months = ^
Find the discount on a note
15, 1905,
3.
is
therefore, due April
Oct. 15, 1905, to April 15, 1906
BXEECISB
2.
is,
interest on
f 3 = the discount. $ 100 - $3 = $ 97 = the
1.
$ 100
discounted, to maturity.
15, 1905, for 9
From
15, 1906.
is
day
at 6
%
interest,
if
5,
discounted
Find the discount on a note for 12250, drawn 1,
1905, for 4 months at
Jan. 15, 1905.
8%
interest,
discounted
:
INTEREST
295
Find the discount and the proceeds on the following Raleigh, N.C, Jan.
1342.00.
4.
Seven mouths of
after date I promise to
pay
Samuel Wolfe three hundred forty -two
25, 1907.
to the order
dollars,
with
interest at. six per cent, for value received.
James Baird. Discounted Feb.
10, 1907.
Atlanta, Ga., July
1785.00.
5.
Ninety
daj's after date I
or order, seven
promise to
paj'
hundred eighty-five
1905.
1,
John Williams,
dollars,
for
value
received.
William Jones. Discounted July I
6.
10, 1905, at
wish to pay for a car-load of
but must give obtain this
my
amount
if
it
I sell fifty acres of
is
which
cost 1860,
I
draw the note
to
discounted at 10 per cent
?
land for f 62.50 an acre, on a
cash basis, but the purchaser
and
cattle
note to the bank for 90 days to obtain
For how much must
the money.
7.
7%.
is
not able to pay the money,
offers instead his note for 6
months
at 8
For how much must the note be drawn that
I
%
interest.
may
receive
the cash price after discounting the note at the bank? 8.
I sell a car-load of cattle,
issory note for 60 days.
taking in payment a prom-
After discounting the note at
the bank at 5 per cent, I have 11487.50. did I
sell
For how much
the cattle?
Write a promissory note for 90 days, with yourself payee. Properly indorse it and find the bank discount
9.
as
and proceeds on the day
it
at the legal rate of interest in is
drawn.
your state
PAETIAL PAYMENTS A payment
made on
which
is
principal and the interest then due
is
406. tlie
a note
not equal to
known
as a
Partial Payment. 407.
When such partial payments
are made, the amount
paid and the date, with the signature of the person receiving the payment, are indorsed on the back of the note. Received on the within note
$S20, March
:
1904
1,
jo-kn j. fcm&i,
$1SB, April
15,
1905 jo-hn
$85, June
f.
jo-n&O'
1906
20,
UNITED STATES RULE 408.
The
rule adopted
by the United States Supreme
Court for finding the amounts due on notes when
payments have been made, has been adopted method hy most states, and is as follows
partial
as the legal
:
Find the amount
of the principal to the time
payment or the sum the interest due or the
new
sum
of
principal,
;
of the
when
the
payments equals or exceeds
from this amount subtract the payment
the payments; treat the remainder as a
and proceed
as before.
296
INTEEEST
A
409.
297
note for 1 935, drawn Jan.
from date, at 6 per cent dorsements on
135; June
it:
March
1,
1903, due one year
interest, has the following in1,
1904, 1320; April 15, 1905,
20, 1906, 1 85.
What was
the balance due Sept.
1,
1906
?
Solution by United States Eule Principal Jan.
1,
Amount March
1,
= = = = = =
1903
Interest from Jan.
1,
1903, to
March
1,
1904
1904
payment March 1, 1904 March 1, 1904 Interest from March 1, 1904, to April
16,
(Since the interest due April 15, 1905,
is
First
New
principal
1905
$ 935.00 65.45
$ 1000.45 320.00
$ 680.45 45.93
greater
than the payment made, no new principal
is
calculated.)
Interest from
March
Amount June
20,
1, 1904, to June 20, 1906 1906 Payments deducted June 20, 1906 ($ 35 + $ 85) New principal June 20, 1906 Interest from June 20, 1906, to Sept. 1, 1906 Amount due Sept. 1, 1906
= = = = = =
94.13
$ 774.58 120.00
| 654.58 7.64
f
662.22
MERCHANTS' RULE For calculating the amount due on accounts and
410.
notes bearing interest, on which partial payments have
been made, merchants often use what Merchants' States
Rule.
method and
year or
less, it
It is
is
is
known
as the
not as accurate as the United
not legal, but for short periods, one
gives nearly the same results, and
is easier.
Find the amount due on the original 2. Find principal to the time final settlement is made. the amount of each payment from the date it was made It is as follows:
1.
:
PRACTICAL ARITHMETIC
298
to date of final settlement.
amounts
of the
sum
Subtract the
3.
payments from the amount
of the
of the original
principal at the time of final settlement. If
used for periods greater than one year, find the
balance due at the end of each year by the rule above stated,
and take
this balance as a
new
principal.
Find the correct settlement on Feb.
411.
note for |100 dated March the following indorsements
1,
:
May
1,
15, 1908, on a
%
1907, at 6
interest, with'
1907, $ 20
;
July
15,
1907,150; Jan. 1,1907,120. Solution by the Merchants' Rule
Amount Amount Amount Amount
of principal for 11^ mo.
$ 20 f 60 $ 20
of of of
for 91 mos. for 7 mos. for 1| mos.
= = =
Correct settlement 412.
=
$ 105.75
= =
$ 92.85 $ 12.90
$ 20.95 $ 51.76 $ 20.16
In a few states other rules are used.
In such states
the teacher should furnish the pupils with the special rule in use,
and have the following problems solved by
special rule as well as
by the
EXERCISE
this
rules indicated.
234.
— WRITTEN
Find the balance due on date
of
settlement by the
United States Rule 1.
A
note for ;$300 at
6%
is
dated March
has the following indorsements: July 1,
1905, 130;
June
1,
1906
?
Jan.
1,
1906, $100.
1,
1,
1905,
-f
1905, and
50; Sept.
How much
is
due
:
INTEREST 2.
A
299
note for fSOO dated i\[ay
1901, at
1,
has f 50 partial payments indorsed on
from date to Nov.
ment Feb.
it
A
is
the correct settle-
note
is
settled 4 years after date.
it
draws
and
1 year
much 4.
is
A
8
8%
interest.
months before
final
Its face value
has $150 paid on
It
How
settlement.
required to settle the note? note for $800 dated April 10, 1901, has the follow-
ing indorsements:
$50; Dec.
June
1901, $20;
1,
How much
1902, $100. interest
interest,
1906?
1,
$400, and
3. is
What
1905.
1,
6%
every 6 months
it
20, 1901,
May
$30; July
25, 1902,
was due Jan.
10, 1901,
$25; Sept.
20, 1903, at
10,
7%
?
Find the amounts necessary to settle the following notes, by both the United States and the Merchants' Rules,
and compare 5. is
A
results
%
note for $320 dated July 15, 1906, at 6
indorsed as follows: Sept. 25, 1906, $80; Dec.
$40; Jan.
1,
1907, $50; June
1,
1907, $10.
interest, 1,
1906,
How much
was due July 1,1908? 6.
at
A
6%
note for $150 dated
interest, has indorsed
three months.
How much
ance of note on the date 7.
An
May on
it
10, 1906, for one year,
payments
of
$25 every
will be required to settle bal-
it falls
due ?
account amounting to $375, due Jan.
1,
1904,
is
The following amounts had been settled May 15, 1905. paid on it: March 1, 1904, $75; Jiine 15, 1904, $30; Sept. How much was re10, 1904, $80; Jan. 15, 1905, $100. quired to pay the balance, with interest at
6%?
PRACTICAL ARITHMETIC
300
On Jan. 1, 1904, A owes B 1650, on which he agrees pay 6 % interest and make a payment of f 75 every three months and the balance Jan. 1, 1905. When the balance 8.
to
is
due,
A
is
unable to pay
est until paid.
July 10, 1905,
If
A
it,
and
B
charges him 8
pays 185 Feb.
1,
%
inter-
1905, and f 135 on
how much money must he
raise to
pay the
balance Sept. 20, 1905?
COMPOtWD INTEREST 413.
When
the interest as it falls due is added to the and the amount forms a new principal on which is paid, the owner receives Compound Interest.
principal,
interest
414.
Compound
interest on notes
is
not
now
generally
allowed by law, but savings-banks allow compound interest
on balances remaining on deposit for a certain
interest term.
Interest
may
semi-annually, or quarterly. is
usually 415.
definite
be compounded annually, Unless otherwise stated,
it
compounded annually.
What %?
is
the
compound
interest
on f 100 for
3
years at 6
$ 100 == first principal. f 100 X .06 = $ 6 = first interest. $ 100 $ 6 = f 106 = second principal at end of 1 year. f 106 X .06 = $ 6.36 = second interest. $ 106 -|- $ 6.36 = $ 112.36 = third principal at end of 2 years. f 112.36 X .06 = $ 6.7416 = third interest. $ 112.36 -I- I 6.7416 = f 119.10 = amount at end of 3 years. Therefore $119.10 - .f 100 = $19.10 = compound interest on f 100 for 3 years at 6%. -I-
•
:
:
INTEREST
EXERCISE
235.
301
— WRITTEN
Find the compound interest and compound amount on the following
4%.
1.
$375
for 4 yrs. at
2.
$125
for 3 yrs. 6 mos. at 5
3.
$650
for 5 yrs, at 6
4.
$2300
for 3 yrs. at
6%.
5.
$1875
for 4 yrs. at
8%.
6.
$3250
for 6 yrs. at
6%.
7.
$4325
for 3 yrs. at
5%.
8.
$7575
for 7 yrs. at 5
Find the amount and on the following
$500
9.
%.
%.
%.
interest
compounded semi-annually
:
for 2 yrs. 6 mos. at 6
%.
10.
$ 250 for 2 yrs. 6 mos. at 7 %.
11.
$ 1750 for 1 yr. 9 mos. at 8 %.
12.
$2225
13.
$ 3575 for 3
for 3 yrs. 6 mos. at 5
man
yrs. 9
%.
mos. at 6 %.
$2500 in a savings-bank, which pays 4% semiannually, and leaves it for 2 yrs. 6 mos., will he have more or less money than if he had loaned it at simple interest for the same time at 4^ % ? If a
14.
How much money
15.
1908,
if
ing 4
%
July
1,
$150
deposits
;
I
made
did
I
have to
my
credit Jan.
1,
deposits as follows in a savings-bank, pay-
and compounding it Jan. 1 and July 1 1906, 1200; Aug. 1, 1906, $75; Dec. 1, 1906, May 10, 1907, $100; and July 1, 1907, $ 185. interest
:
:
EATIO 416.
How many weeks
part of one
month
is
417.
may The
This relation
What
one week?
one week to one month
It
are there in one
relation of
the relation of
is
expressed in fractional form,
is
two numbers is
What
?
also be expressed thus, 1: 4,
pressed by division
month?
of
^.
which is read 1 to 4. the same kind as ex-
called the Ratio of the first to the
second. 418.
The two numbers
of a ratio are called its Terms.
EXERCISE Express the following
236.
— ORAL
common
fractions in the form of
ratios 1.
i?•
4. •*•
2.
f
5.
3.
i.
6.
4. 3
f.
i.
7.
I.
8.
1.
9.
1.
1
Express the following ratios as fractions 10.
3:10.
12.
8:9.
14.
1:15.
11.
10:3.
13.
12:11.
15.
15:1.
419. The first term of tlie ratio is The second term is the Consequent. 302
called the Antecedent.
:
RATIO
Two
420.
terms of a
may
terms 421.
6
by
303
quantities of different kinds cannot form the
A
ratio.
ratio is
always abstract, and the
be written as abstract numbers.
Multiply, also divide, both terms of the ratio 4
:
2.
we have
Multiplying,
8
:
12; dividing,
we have 2:3.
express as a fraction the value of each ratio so obtained,
If
we
we
see
that multiplying or dividing has not changed the value of the ratio.
Multiplying or dividing both terms of a ratio by the
same number does not change 422. is
In order to compare readily two or more
ratios, it
convenient to reduce the ratios to such forms that the
terms of the ratios to be compared shall be the same,
first
usually 423.
1.
Reduce
7
:
28 to a ratio having
Dividing both terms by ratio
the
with one for
first
term
1 as the first
;
its first
term of
Reduce each first
term
7,
we have
1 for its first
1
:
4.
To
term
:
obtain a
term, divide the second term by
take the quotient as the second term and this
EXBRCISB
1.
its value.
new 237.
ratio.
— WRITTEN
of the following to a ratio
having
1 for its
:
PRACTICAL ARITHMETIC
304
The following numbers express
the density of popula-
Compare
tion per square mile in various countries.
the
population of the Uuited States with that of other countries in the
form of
ratios,
using the number represent-
ing the population of the United States as the
Reduce
in every case.
all
the ratios so that the
first
term
first
term
shall be 1.
United States 188,
Germany
208,
Canada
25,
Great Britain and Ireland 344, France
Belgium 609, Switzerland
288, Italy 293,
1.
THE NUTRITIVE RATIO
What is the ratio
424. first
of 2.5 lbs. to 16.25
lbs.,
with the
term reduced to 1 ?
What
is
the ratio between 1.5 lbs. protein and 10.5
carbohydrates and fats its first
425.
Reduce
?
term.
Find the nutritive
ration for a dairy
cow
:
ratio of the following standard
2.5 lbs. of digestible protein, 13
of digestible carbohydrates,
The
lbs.
to a ratio having 1 for
and
.5 lb.
fats in a ration are 2.4 times
carbohydrates.
To reduce
lbs.
of digestible fats
more valuable than
the
the fats in this ration to the value
number expressing the amount of fats, must be multiplied by 2.4. .5 x 2.4 = 1.2. Adding this to the number expressing carbohydrates, we have 1.2 + 13 = 14.2, the value of the carbohydrates and fats taken together. The of carbohydrates, the .5,
nutritive ratio of this standard dairy ration 2.5 is to 14.2, or, reducing the first term to 1,
The
nutritive ratio
426.
The
is
therefore 1
:
is,
therefore, as
we have 1
:
5.68.
5.68.
Nutritive Ratio of a ration
is
the weight of the digestible protein to the
the ratio
sum
of
of the
RATIO
305
weights of the carbohydrates plus 2.4 times the the weights of the fats. Digestible protein
A
427. tive
it
A
438.
(2.4
Balanced Ration
is
x
fats)
+
of
carbohydrates.
one having the correct nutri-
is
the particular animal and purposes for
ratio for
which
:
sum
being fed.
Narrow Ration
one in which the proportion
is
of protein to carbohydrates
and
fats is greater
than the
standard requirements.
A
429.
Wide Ration
is
one in which the proportion of
protein to the carbohydrates
and
fats
is
less
than the
standard requirements.
EXERCISE 1.
A
— WRITTEN
ration consisting of 10 lbs. of corn and 20 lbs. of
timothy hay contains 1.35 lbs.
238.
of carbohydrates,
lbs. of digestible protein,
and
.71 lb. of fats.
What
15.35 is
the
nutritive ratio? 2.
A
alfalfa lbs. of
ration consisting of 10 lbs. of corn and 20 lbs. of
hay contains 2.99 lbs. of digestible carbohydrates, and .67 lb. of fats.
nutritive ratio 3.
A
protein, 14.57
What
is
the
?
ration consisting of 8 lbs. of corn, 1 lb. of cotton-
seed meal, 12 lbs. of alfalfa hay, and 20 lbs. of corn silage
contains 2.50 lbs. of digestible protein, 12.52 ible
carbohydrates,
and .75
lb.
of
fats.
lbs. of digest-
What
is
the
Compare these three rations with the feeding standard for a cow giving 22 lbs. of milk a day. (See page 250.) Which is too narrow? Which is too nutritive
ratio ?
PRACTICAL ARITHMETIC
306
Which most
wide?
nearly meets the requirements of the
standard? 4.
If a ration consisting of 10 lbs. of corn
and 20
red-clover hay contains 2.15 lbs. of digestible
13.83 lbs. of digestible carbohydrates, and .77
what
ible fats, 5.
is
the nutritive ratio
lb. of digest-
?
If a ration for dairy cows, consisting of
corn and cob meal, 1.5
lbs. of
Ihs. of
protein,
7 lbs. of
cotton-seed meal, 10
lbs. of
clover hay, and 40 lbs. of corn silage contains 2.14 of protein, 13.02 lbs. of carbohydrates,
what 6.
A ration consisting of
othy hay, and 5
lbs.
20
lbs. of corn, 5 lbs. of tim-
of corn stover contains 1.8 lbs. of
protein, 17.13 lbs. of carbohydrates, is
the nutritive ratio?
Is
and .96
this
Determine the nutritive
lb. of fats.
too wide or too
narrow a ration for a fattening beef animal period? -(See page 250.) 7.
lb. of fats,
the nutritive ratio?
is
What
and .93
lbs.
for the third
ratio of the feeding stand-
ards in the table on page 250. 8-18. Find the nutritive ratio of rations Nos. 1 to on pages 251 to 255.
Find the nutritive 19.
12
11,
ratio of the following rations:
Red-clover hay, 12
lbs.,
corn stover, 15
lbs., corn,
lbs.
20.
Corn
40
silage,
lbs.,
red-clover
hay, 5
lbs.,
corn
stover, 5 lbs., corn, 6 lbs., cotton-seed meal, 3 lbs.
SPECIFIC GRAVITY 430. its
The
Specific
Gravity of a substance
is
the ratio of
weight to the weight of an equal volume of water.
:
:
RATIO 431.
To
307
find the specific gravity of a substance, state
the ratio of its weight to that of an equal
volume
of water,
reducing this ratio so that the second term shall be
1.
EXERCISE 239 — WRITTEN Find the
specific gravity of
weight of which 1.
Water,
2.
Cast iron,
is
each of these substances,
tlie
given per cubic foot
62.42
lbs.
6.
Cork,
449.86
lbs.
7.
Maple wood, 46.815 lbs.
3.
Cast copper, 548.55
lbs.
8.
Ebony,
83.0186
lbs.
4.
Cast lead,
708.59
lbs.
9.
Butter,
58.6748
lbs.
58.04
lbs.
10.
Clay,
74.904
Ice,
14.9808
lbs.
lbs.
Find the weight per cubic foot of the following subwhich are given
stances, the specific gravities of 11.
:
PROPORTION When
432.
two
a Proportion,
ratios are equal, the four terms form
2:4::8:16
e.g.^
are
in
proportion, since
Jg. f equal
A proportion, therefore, is
433.
between two ratios and
ity
is
written by placing the sign
of equality or the double colon
The proportion 4 as 8
4
:
:
:
8 16, or :
between the two
2:4=8:16,
is
ratios.
read, 2
is
to
to 16.
is
The
434.
2
an expression of equal-
first
and
last
terms of a proportion are called
the Extremes, and the two middle terms are the Means.
When four numbers
435.
are in proportion, the product
of the extremes equals the product of the means.
This
constitutes the test of the proportion.
EXERCISE
240.
— ORAL
Complete the following statements of proportions
?
5.
6:?:: 5: 10.
6.
2.8
12:?
7.
9:24::?:
5: 15:: 6:?
8.
1.2
2: 4::
2.
?:4::4:8.
3.
6: 9::
4.
:
:
5.6
?
: :
:: ?
2
:
4.8.
8. :
4.
Find the missing term in the following propor-
436.
tion
3:?
1.
:
•
8
1
•
•
1
9,^- ^
'^^^ product of the extremes equalling
the product of the means, 8.1 SOS
X
1.25
=5
PROPORTION the
times
unknown number. X 1.25
8.1
—
therefore
^—
309
.
The unknown number
is
Solving this example by cancellation,
.
o
.25
we have
8.1
x
l-?^
The completed
_2qk
proportion, therefore,
EXERCISE
241.
is
2.05 8.1
:
:
1.25 5.
:
:
— WRITTEN
Find the missing terms in the following proportions 1.
?: 136:: 84: 336.
5.
17.4
2.
12: 144::?: 1728.
6.
?: 6.25
::
3.
15:?:: 6: 82.
7.
?: 18::
45: 32.
4.
22: 5:: 35:?
8.
18.2 :?:: 7.3
437.
:
191.1
::
.75
11.5:
:
:
:
?
8.36.
9.1.
10 bus. of apples cost 17.60, what will 15 bus.
If
of apples cost
?
This problem may be stated and solved as a proportion we have two ratios, one between the number of bushels
since
of apples in the first instance
and the number of bushels
in the
second instance, 10 15 the other between the amount paid in the first instance and the amount paid in the second instance ;
:
$ 7.50 and f two
?.
The
price of apples remaining the same, these
Therefore,
ratios are equal.
we have
10 bus. :15 bus.:: $7.50:$? Since unlike quantities cannot be multiplied, we may substinumbers instead of the first two terms, which will
tute abstract
not affect the value of the ratio.
10 15 :
:
:
f 7.50 $ :
?
Solving,
We
then have
we have $12.25,
the cost of
the 15 bus. of apples.
Arrange the three known quantities and the unknown
PRACTICAL ARITHMETIC
310
quantity of the problem in the form of two ratios which Solve as a proportion.
shall be equal.
BXEBCISB If
1.
cost
25
of sugar cost $1.50,
lbs.
If a railroad ticket
3.
what
costs
same
rate
will 75 lbs.
14.01
cts. to
is
for 80 miles costs $1.80, ?
64 miles at 2|
cts. a
mile
spray 3 acres 3 times, how
ft.
?
from spraying 6 acres of potatoes
the profit from spraying 33 acres
moment how long is
If at a certain
ft.
long,
a post 32 the
ft.
?
high
shadow of a
casts a
tree which
high?
At
moment how
the same
a shadow 32
ft.
long
tall is
a tree that casts
?
Measure the height of a post in your neighborhood
and the length
of
its
shadow;
also, at
shadow
any
the same time,
measure the length
of the
by means
measurements calculate the height
the
of
of these
of
tall object,
and of
tall object.
The height of a tall object is also often measured, is shown in the accompanying figure, using a triangle which UD = DC. The sides of the triangle are in the
10.
as
?
will a ticket for 17 miles cost at the
If the net profit
shadow 48
9.
will 36 tons cost
will it cost to spray 21 acres 3 times
$ 138, what
8.
what
?
If it costs
5.
much
48
good
If a railroad ticket for
$1.76, what
7.
72,
good for 60 miles cost
will a ticket
4.
6.
hay cost $
If 6 tons of
what
is
— WRITTEN
?
2.
is
242.
;
PROPORTION proportion
AB :GD:: BE
of the triangle
64
ft.?
H.
If
in
Exclusive of the height
I)E.
from the ground, what
15
is
the height of the
EB
tree, if the distance is
:
311
of
lbs.
oats there are 13.35 lbs. of dry matter, 1.395 lbs. of protein, 7.125 lbs. of
carbohydrates, and .54
lb.
how many pounds
of fats,
of each of these are there in
2000 12.
lbs. of oats ?
If in 5 lbs. of
cow-
pea vine hay there are 4.4 lbs. of dry matter, .465 lb. of protein, 1.92 lbs. of
carbohydrates, and .06
each are there in 2000 13. tein,
If in alfalfa
how much
lb. of fats,
lbs. of
hay there
protein
is
how many pounds
of
cow-pea vine hay? is
10.6%
of digestible pro-
there in 2500 lbs. of alfalfa
hay?
LEVERS 438.
In
considering
vers, three things
recognized
:
(1) the Power
applied to do the
overcome
le-
must be
the
work
or
resistance
(2) the Weight or the resistance
to
and (3) the
be overcome
;
immovable
point on which the lever turns, called the Fulcrum.
:
PRACTICAL ARITHMETIC
312
In the figure on page 311 where is
the power
A
439.
What
?
is
is
Where
the weight ?
the fulcrum?
lever can always be divided into
two parts
(1) the distance from the weight to the fulcrum, called
Arm
the Weight
(2) the distance from the power to the
;
fulcrum, called the Power Arm.
In the figure is
the weight
The
440.
how
long
the power
is
arm?
How
long
arm ? factors of a lever are always in proportion,
thus:
Power arm Weight arm :
:
:
Weight Power, :
or, abbreviating.
Pa :Wa EXERCISE
90
:
W:
243.
man
exert to
lift
P
— ORAL
In the figure on page 311
1.
the
:
the stone
how many pounds must if
weighs 30
it
lbs. ?
lbs. ?
If the
2.
man
stone can he lift? If the
3.
what
If
he exerts 9
power arm
is
9
ft.
will be the answers to
In this figure where
4.
power
exerts a
is
of 3 lbs., lbs. ?
100
how heavy lbs. ?
3^
and the weight arm
a
lbs. ?
1
To No. 2? power? Where the
ft.,
No. 1? the
crum? weight
Where
ful-
the
(resistance)?
Will a wire be cut more ^ '"""'
base
?
arm
?
~
Why ? What
easily near the tip of the
shear blades, or near the
'
is
the power
arm ?
The weight
PROPORTION In this figure what
5.
weight arm
a pressure of 80
can be overcome
man who
how much
weight arm
How much
is
ft.
rear
reduced to 9
ins.,
how
is
fall
short of raising a stone
of 1 ft.?
needed to
end
long
with a lever having a power arm of
lbs.
a wagon-jack of the dimensions indicated,
much power the
lbs. of
with a weight
arm be to enable power to do the
does the weight of a 156-lb. man, on
and a weight arm
With
3.
resistance
?
the end of the power arm,
weighing 1200
lbs.
the power
can exert only 200
If the
need the power arm be 2.
Of
244. — WRITTEN
how long must
1 ft. long,
work?
4
lbs.,
In raising a stone weighing 1400
1.
arm
arm?
?
EXERCISE
a
the length of power
?
With
6.
is
313
of
a
how
lift
loaded
wagon, the rear end, loaded, weighing 1600
With
4.
lbs.?
steelyards as in
the figure on page 314, with a weight (a) of 8 ozs., far
how
from the fulcrum must
lbs. ?
25
lbs. ?
16
lbs. ?
this
weight be to balance 18
PRACTICAL ARITHMETIC
314 5.
In fishing John
lield the large
The
tionary in the left hand.
right
farther
was 12 right
end of the pole
sta-
hand was 2 ft. 9 ins. up the pole, which ft.
long.
hand
it
With
his
took a force
of 8 ozs. to sustain the
What did it weigh ? Draw a diagram to
fish.
aid in
stea solving this problem. 6.
How much
11 ins. it
requires
95
is
lbs.
is
exerted upon the nail
if
is
of pull
to
it ?
A
lbs. is
the distance from
2 ins., from fulcrum to hands
direct pull
upon the hammer handle extract 7.
hammer
In drawing a nail with a
the fulcrum to the nail
boy weighing 96
swinging on a gate,
having 2 hinges, 12 the hinges.
It is 3
ft. ft.
from 4
ins.
from one hinge to the other.
How
,much pull does the upon the upper hinge ? How much does it push upon the lower hinge ? Draw a diagram before attempting to solve. Compare with the last boy's weight exert
problem. 8.
Two men
carry a weight of 195 lbs. suspended on
a pole between them.
man and each carry
9 ?
ft.
If the
is
6
ft.
from one
how many pounds does may carry ^ of the weight weight be hung? from the
other,
In order that one
where must the
weight
:
PROPORTION
31c
COMPOUND PROPORTION 441.
50
ft.
men working hrs. per day can dig a canal how many men working 10 hrs. per
18
If
(j
long in 25 days,
day can dig a canal 80
ft.
long in 8 days
?
This problem can be separated into simple proportions
and solved as follows If 18
men
:
can dig a canal in 25 days,
how many men
quired to dig the same canal in 8 days ? proportion.
(1)
18
ok
ziN a
)y^
80
10 6 •
„
•
9
•
90^
"
y ..y X no X 10 ^
^,
of 50
m X90 X
^r
=:
™^^
ifi
18
^^^
*^^^
^
^
lo'ia; ill
.
men
?
how-
is,
^°"S instead
If...
long.
ft.
„,
8 davs,
°^^^^^
^^
^*'
how many
A ^to dig Aare required a
^
days :
^^-
are re-
expressed in
^^^ ^^° ^
80 ft. long in 8 This is expressed
canal
18
is
Tlie canal ^"^
®^''^'^''
'
—
8
get ^j^ men.
--
'
50
we
Solving,
This
men.
in
?
(2)
Solv-
get 90 men.
The
proportion.
ing,
we
assumption that previous statements have been made under of 10 hrs. If 90 men were to worlt 6 hrs. per day instead the men can dig a canal 80 ft. long in 8 days, working 6 hrs. per day, how many men will be required to dig a canal 80 ft. long tlie
working 10
in 8 days,
(3) Solving,
portion.
hrs. per
This method of procedure
in 4.
new
We
see
may
is
stated in pro-
is tlie final
answer.
IMultiplying the
1, 2,
proportion, which, expressed as a ratio,
may now
and solved,
This
be shortened.
portions cancel, leaving the second ratio
?
and 3 together, term by term, we is shown that the answers obtained from the first two pro-
completed proportions, obtain a
day
we get 54 men, which
member
a simple ratio.
be expressed as a proportion, as
as follows
3
10
23X80X0X18 :
8
X
50
X
10
54 men.
is
shown
The in 5,
PRACTICAL ARITHMETIC
316
The
two answers cancel shows that
fact that the first
unnecessary to obtain them to arrive at the
Rule
unknown quantity
Place the
1.
final
it
was
answer.
as the fourth
term of the proportion. 2.
Place as the third term of the proportion the quan-
tity
given in the problem expressing the same kind of
unknown
thing as the 3.
Take each
quantity.
of the other ratios separately,
and arrange
according to their relation to the ratio already stated. 4.
The product
of all the
means divided by the product
of all the extremes, except the
unknown
one, will give the
answer.
The product Compound Ratio. 442.
A
443.
of
two or more simple
is
a
If 17
22 days,
245,
— WRITTEN
men working 7 hrs. a day can build a how many men working 10 hrs. a day
take to build the bridge in 4 days 2.
men 3.
If 3
men
will
it
?
can milk 35 cows in 1.5 hrs.,
how many
milk 65 cows in J hr. ? 3 teams working 5 hrs. a day can haul
If
7 hrs. a
men can
excavate
it,
how many
day are required to haul
can excavate 4.
bridge
will it take to
fast as 5
days,
a
Compound Proportion. EXERCISE
in
is
proportion in which either or both ratios are
compound
1.
ratios
dirt as
teams working
dirt as fast as 15
men
it ?
men can draw and house 32 tons of hay in 2 how many men are needed to draw and house 14
If 6
tons in 6 hrs.
?
PROPORTION 5.
If 2
men cut 8 men to
will it take 12
cords of
317
wood
cut 36 cords
in 4 days,
how long
?
men with a one-horse plow break 28 acres in how many days will it take 3 men with two-horse plows (a man with a two-horse plow doing twice as much work as a man with a one-horse plow) to break 6.
If 4
7 days,
42 acres 7.
?
If the
eggs laid by 28 hens in 16 weeks are worth
132.50, what will be the value of the eggs laid by 50 hens in 12 8.
weeks
?
If it requires
35 cows giving 77 qts. of milk each,
how many cows
per week, to supply 425 customers,
giv-
ing 270 qts. per month will be required to supply 125
customers ? 9.
If
30 cows give 462
many cows 10.
much 11.
If
4320
12.
of silage last 30
cows 48 days, how
lbs.,
what
tank of water 2 x 4 x 10
will the contents of a tank 7
ft.
x 12
weigh?
6" X 4J" X
13.
how
make 40 posts take to make 678
If it takes 2 cu. yds. of concrete to
posts 4"
is
lbs.
If the contents of a
ft.
milk in 21 days,
needed for 15 cows for 60 days?
silage is
weighs 4994
X 19
lbs. of
are required to give 1200 lbs. in 7 days?
7',
how many
X 4" X
If the
yards will
it
5'?
weight of a volume of water 1 x IJ X 9 ft. fill blank), what is the weight of a piece
(pupil
ebony | x | x 3 ft., ebony weighing 1.33 times as much as water of equal volume? of
POWEES In the figure
how many tlie
units are there on each side of
square?
How many
in the whole
There are 9 square units
square ?
in a
square of 3 units on a side, therefore, 9 said to be the Square of
is
larl}-,
3.
Simi-
a square witli 4 units on each
side has a total of 16 square units.
The Square of a number
is
the product of a
number with
itself.
444.
In the figure
How many
edge?
how many
units are there on each
y y // y'/
27 cubic units in a cube with 3 units
on an edge, 27
is
There being
cubic units in the cube?
said to be the Cube
of 3.
The Cube uct of
/
number is the prodthe number taken 3 times as of a
/
/
/
a factor. 445.
As
Squares and cubes are called Powers of a number.
the square and the cube are the second and third
powers of numbers, so taking the number 4 times factor gives the fourth power, 6 times the 446.
by
The power
of a
number
a small figure written above 318
to
fifth, etc.
be taken
and
as a
is
indicated
to the right of the
:
:
:
POWERS means the square means the ninth power of
number, of 4, 6^
e.g., 3^
The
447.
319 3, 4^
of
means the cube
6, etc.
figure used to indicate the
power taken
is
called the Exponent.
EXERCISE Find the value
246.
— ORAL
of the following
1.
62.
4.
13.
7.
19.
10.
122.
2.
92.
5.
82.
8.
102.
11.
252.
3.
202.
6.
112.
9.
34_
12.
303.
EXERCISE Find the value
247.
—WRITTEN
of
1.
843.
3.
1.253.
5.
2.
123.
4.
.752.
6.
448.
We
(^|V)2.
7_
(7)3.
8.
(-ll^)3.
12.53.
have seen that the square of a number
number multiplied by itself, 24 X 24. We may write this 2 tens 2 tens
e.g..,
is
the square of
is
multiplication thus
4
units^, result of
multiplying
by 4 4 units X 2 tens,
+ 2(4 units X 2 tens) H- 4
units.
result of multiplying
by 2 2 tens^
the
+ 4 units + 4 units
4 units X 2 tens 2 tens'
24
units',
sum
tens.
of partial products.
number greater than 10 may be regarded as comsum of two numbers, the square of the sum of any two numbers is equal to the square of the first number + 2 X the square of the last. (the product of the first x the second) The same formula may be arrived at by considering the Since any
posed of the
-(-
square of 24 as representing an area 24 units on each edge, as accompanying figure, and cutting the lines of the sides
in the
:
PRACTICAL ARITHMETIC
320
and 4 units to represent 2 tens and 4 units. It is then seen that the whole square of 24 consists of the large square a, which is 20^ and two times into 20 units
;
the rectangle 6, which is 2 x (20 x and the small square c, which is 4^
4),
Represent the square of the same
number,
in a diagram, similar
24,
to that just used, but cutting the
and 6 units instead
lines into 18
We may represent figure
;
then we have
+
(n
By 63
this
= 6 tens
X
20 and
Does
this
change
affect the result?
the lines by letters n and :
s)2
=
w2
+
2(w,
X
and 3
(6 tens
=
s)
+
s2.
x 3
3 units squared
units.
GO
x
units)
60
=
= 3x3
2
x 60 X
3
of
Solve as above.
4.
formula determine the square of 63
6 tens squared
2
into
= 3600 = 360 9 = 3969
s,
as in the
:
EOOTS 449.
"What number multiplied by
itself will
give 25
?
What number used three times as a factor 8? 27? 125? 1000? What number squared equals What number cubed equals 8? 27?
16? 4? 100? gives
25?
450.
number 5
is
is
number which when squared equals
is
;
4
is
the square root of 16.
A number which when cubed equals a certain num-
said to be the Cube Root of that number, e.g., 2
cube root of 8 452.
known
The
453.
root of a
number
How many root of a
root, etc.
is
the square of 1?
figures does
number
5 or 6 figures?
Of 10?
Of 100?
Of
If a
take to express the square
it
of 1 or 2 figures?
How many
figure in the square root
Of
3 or 4 figures?
figures in the
Of
power equal
1
?
whole number be divided into groups of 2
figures each, beginning
at
units' place, the
groups will equal the number 455.
indicated by the sign, V~,
Of 10,000 ?
?
454.
is
V~indicates the cube root,
as the Radical Sign.
What
the
is
3 is the cube root of 27.
;
V~, the fourth
1000
a certain
said to be the Square Root of that number, e.g.,
the square root of 25
451.
ber
A
Find the square root of 529 321
number
of figures in the root.
of
:
:
:
PRACTICAL ARITHMETIC
322
Separating into periods, ods, the root consists of
of the root
we
two
see that since there are
must be contained
greatest square in 5
is 4,
The square
figures.
two
in the second period, 6.
the root of which
is
peri-
of the tens
2,
The
which
is
therefore the tens' figure of the root desired.
Subtracting the square of 2 tens or 400
5'29^23
from 529, we have 129.
^QQ
—
contain, 2
A.^y[9Q
x
(tens
X
This remainder must
units)
+ units^ (see para-
graph 448). Two times the 2 tens = 4 tens. — 4 is contained in 12, 3 times. We therefore take 3 as the next figure of the root. To find whether the remainder exactly contains 2 x (tens x units) + units ^, or what is equivalent (twice the tens + the units) x units, add the units to twice the tens and multiply by the units, thus 23 is therefore the square root (3 + 40) X 3, securing 129. 19C)'
—
of 529.
To prove
square root, multiply the square root by
itself,
Find the square root of 15,713,296
456.
) 15,713,296 )3964
9_
69)671 Proceed as in the preceding pro'bIn each step consider the part
nn-i
_—— .
lem.
786)5082 4716
Qf ^j^g
j.jjjj^
already found as tens with
relation to the next figure.
7924)31696 31696
Find the square root
457.
of 94,864
94864)308 Since the divisor 6
g fin8"vd8RJ. ^
4864
^^
is
not contained in
4,
placed in the root as well as in the divisor,
and the next group ^
is
brought down.
ROOTS 458.
Rule for the extraction
number
Separate the
1.
323
of square root.
into
groups of two figures
each, beginning at the decimal point.
Find the greatest square
2.
root
is
3.
first
in the left
this
root
Its
from
tlie
first
and bring down the next period.
Divide the remainder by twice the part of the root,
already found, considered as tens, as a
ing the next figure of 5.
period.
figure of the required root.
Subtract the square of
period, 4.
the
To
the trial divisor add the
then multiply by the
trial divisor, secur-
tlie root.
new
figure of the root,
last figure found,
and subtract the
product from the last remainder. 6.
Bring down the next period, and continue as above.
459. to the
number is not a perfect square, add ciphers number and continue the division, expressing the If the
result as a decimal.
What is How many more 460.
the square of
.25?
Of .75? Of 1.25?
decimal places are there in the square of
a decimal than in the decimal?
How many decimal
places
are there in the square root of a decimal?
The square
root of a decimal has half as
places as the decimal
many decimal
itself.
must contain two
figures.
What is the square of J? Off? Off? What is the square root of ^6? Of |? Of^? To obtain the root of a fraction, extract the
root of
Each group
Annex
of the decimal
a cipher,
if
need
be.
461.
both numerator and denominator separately.
324
PRACTICAL ARITHMETIC
ROOTS 6. 7.
How 8.
What
the diagonal of a rectangle 80 x 40 rds.
The base
of a 32
ft.
high on the wall can
ladder
is
7
how much walking
?
from the house.
ft.
touch?
it
In cutting across the diagonal of a
5 days, 203'
is
325
saved
is
if
lot twice dailj^ for
the lot measures
X 98"?
In carpenter necessary to
work and other building
know
frequently
it is
the hypotenuse of a right triangle.
It
may be found with sufficient accuracy for many such by use square and rule. purposes
9. is
What
the
of
length of brace
needed from an upright
post to a horizontal beam,
iil'ill'ii|iiir'iH'ii|M;|'Mji|
/
two ends of the brace ft. and 4 ft. from the right angle ? Place the rule on the square at 4 and 5 ins., as shown in the figure. Read the length of the hypotenuse in inches. Let each inch on the square and rule stand for a foot in the problem. Solve the same problem by square root, and compaire i,i°'i.i^,i?i,Ki,i^i,m,!':i,i':hRi,r,F-a
the
to be 5
answers.
CUBE ROOT Since the extraction of the cube root easily understood
since
it is
after
customary to defer
not be discussed here.
cube root
is
given in the
who may have
may
algebra has its
much more
study until then,
The method Appendix for
occasion for
be
been studied, and
its use.
it
will
of extracting the
the benefit of any
PRACTICAL ARITHMETIC
326
EXERCISE
251
MiscELLAXEous Review Problems
What
is the cost of spraj'ing 6| A. of cucumbers with Bordeaux mixture, applying 100 gals, per 6 times 1.
acre each time, using 3 lbs. of bluestoue at 1^
pound, 6
lbs. of
of mixture
lime at 1
Allow 33
?
cts.
per pound in each 50
ct.
cts. for
labor of
per
gals,
making each
100
Tower 984
ft.,
gals. 2.
Some
structures are: the Eiffel
tall
Monument 555
the Washington dral 521
Cheops Pj-ramid 486
ft.,
the Eiffel
named?
Monument than each Tower ? 3.
Alcohol
as heavy.
1 cu. 4.
ft.
is
.83 as
Strasburg Cathe-
is
others, except the
the
heavy
as water.
heavier
1 cu.
if
ft.
is
Copper
is 8.8
times
1 cu. ft. of lead than
of water weighs 62.42 lbs.
3 chisels at $.42; 1 gauge, 52
claw hatchet, $.80; 1 ratchet brace, $1.08; 5
$-19, $.28, $33, $.41, and $.49; 1 level,
Eiffel
?
the cost of: 1 smoothing plane, $2.40; 1
spoke shave, 1.90; 1
of
How much
of alcohol,
What
ft.,
ft. How much Tower than each of the other strucHow much higher is the Washington
ft..
tures
the Cologne Cathe-
Bunker Hill Monument 221
dral 474
higher
is
ft.,
$2.00; 1 square, $1.50
;
cts.;
bits, at
1 screw-driver, $.16;
1 rip saw, $1.65; 1
hand
saw, $1.65? 5.
two
From pieces,
a roll of carpet 21|^ yds. long there are cut
one 1\ yds.,
one
17f yds.
How much
remains ? 6.
Allowing ^
in.
per foot for shrinkage,
how much
MISCELLANEOUS REVIEW PROBLEMS larger
and wider than the desired
tern for a cast-iron support 7.
must be the pat2' 1.3" wide?
how long when finished,
for lead,
for a casting, to be,
4" X 5"? 8.
Allowing
-j^g"
per foot for shrinkage in brass cast-
what would be the answer
ings, 9.
at
article
11" long x
Allowing the same shrinkage
must be the mould 2'
9'
327
the examination at
8-4 made mark on examination?
term grade of
tion
two problems?
In an arithmetic class where term grade was valued
75% and
10.
in the last
On
a final
25%, one student with a mark of 77. What was his
an examination paper of 16 questions one ques-
was three-fourths
correct, three
were one-half
right,
four were one-third correct, one was eight-ninths correct.
What was
the grade?
same errors had occurred on an examination paper of 12 questions, what would have been the grade? If on a paper of 9 If on a paper of 10 questions? 11.
If the
questions ? 12.
If in feeding pigs, 1 bu. of corn
of gain,
what
price per bushel
pigs sell for 5.75 cts. per 13.
1596 is
If .92 lbs. of
is
produces 10.9
obtained for corn
pound?
A. of rape furnish feed for pigs equal to lbs. of wheat middlings, what
corn and 796
the feeding value of an acre of rape,
worth 45
cts.
lbs.
when
when corn
is
a bushel and wheat middlings 1^18 a ton?
Five pigs at 10 months of age average 243 lbs. in weight and sell for 5J cts. per pound. If they consumed 14.
98
lbs. of
wheat bran
at
$ 18 a
ton,
1862
lbs. of
corn at
:
PRACTICAL ARITHMETIC
328 50
cts.
a bushel, and grazed .25 A. of clover, .25 A. of sor-
ghum, and
.60
A.
of peanuts,
what was the combined
value per acre of these grazing crops for pig feeding ? 15.
If
duce 1426
1 A. of peanuts lbs. of
pound, what
worth 47 16.
cts.
is
and 37.8 bus.
gain in hogs and they
sell for 5 cts.
the value of an acre of peanuts
if
per
corn
is
per bushel?
The population
of the
United States
It is estimated that the
76,059,000.
corn pro-
of
number
in
1900 was
number
of births
every 10 yrs.
by 15.2 per 1000 of population Based on these estimates, what may the popu-
lation of the
United States be expected to be in 1910?
exceeds the
17.
The
of deaths
increase in
population of the United States
through immigration in 1903 and 1904 was 800,000 annually.
In 1905 and 1906 the increase was 1,000,000 annually.
Taking the average
of these four years as the probable
increase through immigration for the next ten years,
gether with the results of the last problem, what
is
to-
your
estimate of the population of the United States in 1910? 18.
Estimated in a similar way, basing each time upon
the estimated population of the preceding decade, what will be the population in
19.
Add
1920? 1930? 1940
?
1950?
each line without writing in columns a.
79, 46, 87, 93, 84, 72, 16.
I.
857, 965, 847, 964, 876.
c.
965, 864, 791, 862, 764, 968.
d.
6482, 9683, 7981, 8472, 6897, 9861.
e.
64,875, 89,672, 978,459, 679,821.
>
MISCELLANEOUS REVIEW PROBLEMS
329
Estimate the average speed per mile of the trains as given in the time-table on page 145. 20.
21.
It requires
to develop into
151 days for the eggs
honey bees that are
to
honey bee become queens:
of the
^j of this period is required for the eggs to hatch; || of this period is required to mature the larvae and pupse.
How many
How many
days are spent in the egg state?
in the larval
and pupal
states ?
^
more days for the eggs to develop become worker bees than to become queen bees -f of this period is required for the eggs to hatch ^ to mature the larvae and pupee. How many days are spent in the egg state? How many in the larval and pupal states? It requires
22.
to
:
;
The
23.
in one
plant louse often produces in 12 generations
season, 10,000,000,000,000,000,000,000
These are each about live,
how many
ranged single sion reach
-^-^
of an inch long.
miles long
file?
How
ofCspring.
If all should
would such a procession be, armany times would this proces-
around the earth, considering the circumference
of the earth as 25,000 miles? 24.
If
on an average
1 cattle tick
produces 1000 young
and there are four generations in one year, how many ticks may be produced in the fourth generation ? If onehalf these ticks are females, ^ inch in length, and one-half
males, ^ of an inch long, arranged single
file,
times would this procession encircle the earth
A
family of two persons has an income of f 520.
expenses are as follows
Eent Food
how many ?
Their
:
$120 Clothing 210 Fuel
$60 30
330
PRACTICAL ARITHMETIC Charity
.
.
.
:
MISCELLANEOUS REVIEW PROBLEMS
much does
the
exceed that of
the two latter together
population of
New York?
Five sugar-producing districts are
32.
862,000
lbs.,
520,138,232
Louisiana 695,101,878 Philippine
lbs.,
Porto Rico 122,000,000
Islands
The
Cuba
1,664,-
435,000,000
How much
lbs.
:
Hawaiian Islands
lbs.,
of the other four together exceed that of 33.
331
lbs.,
does the produce
Cuba?
leading states in wheat production are
five
Minnesota 142,345,672, Kansas $32,469,706, North Dakota 128,383,767, Ohio 127,788,094,
What
398.
.states is
grown
The
34.
Indiana 124,208,-
per cent of the wheat produced by these five in each state?
iron manufactured in five states was
:
Pennsyl-
vania $264,571,624, Ohio $65,206,828, Illinois $39,011,-
New York
051,
$15,849,531,
New
Jersey $11,018,575.
Find the total amount. The production what per cent of the total?
The
35.
manufactures of
textile
of each state is
five
leading states
Massachusetts $184,938,074, Pennsylvania $132,-
were:
New York $86,171,293, Rhode Island $67,005,New Jersey $52,831,023. The production of each
367,499, 615,
state is 36.
what per cent
The number
of the total of the five states?
of miles of railroad for every 100 sq.
mis. of area in five groups of states tic
States
New
15.8,
England
Southern 5.31, Western 2.09. mileage per 100 sq. mis. for each section
The following
is
?
:
Middle AtlanCentral
What was
10.63,
the average
The mileage per 100
what per cent
table
was
11.72,
sq. mis.
of the total?
shows the value of raw cotton and
:
PRACTICAL ARITHMETIC
332 its
manufactured product for 6 years, with the number engaged
of wage-earners
Materials
MISCELLANEOUS KEVIEW PROBLEMS weigh
1
lb.,
and 22,260
Find the number
yds.
of
filling
yards of warp and
of
333
weigh
1
lb.
used in
filling
the sheet.
A
44.
gingham
stripe
The
per inch.
colors
form a pattern
:
cloth
made 28"
is
wide, 56 ends
arranged in the following order
28 ends white, 16 ends blue, 8 ends
How many
black, 4 ends red.
peated in the cloth, and
times
is
how many ends
the pattern re-
of each color are
there ?
A
45.
loom weaves 50
How many
of cotton-seed
of corn for cattle feeding,
meal
what
is
cotton-seed meal for cattle feeding
50
cts.
a bushel? If for cattle
47.
1 bu.
what
ton for cattle feeding
Ten
if it
hrs.
56
is
is
equal to 1.75
lbs.
sell for
when corn
is
worth
lbs.
lbs. of
cotton-seed are equal
the value of cotton-seed per
when corn
is
worth 45
cts. a
bushel?
pigs weighing 56 lbs. each bought for f 50,
$5,625 a hundred.
If it costs 4.07 cts.
to
each.
lbs.
What was
cost 4.25 cts. in feed to produce a
49.
?
the value of a ton of
feeding for 120 days weigh 224
after
then
=
feeding 3
to 3.48 lbs. of corn,
48.
10-|-
yards will be woven in 60 hrs.
If 1 lb.
46.
yds. of calico cloth in
They
the net profit
pound
of gain?
produce a pound of gain
with hogs fed corn and wheat middlings, and 3.25
cts. to
produce a pound of gain with hogs fed corn and green clover, how much less will it cost to grow 12 hogs from 50
lbs.
up
to a weight of 243 lbs. each on corn
than on corn and wheat middlings, for the clover pasture
?
if
and clover
no charge be made
PRACTICAL ARITHMETIC
334
A
50.
3.875
beef animal weighing 986 lbs.
cts.
a
pound and
a ton, 10 lbs.
of
corn worth 41
cts.
is
clovei-
fed 30
is
bought
lbs. of silage
hay worth
!^8
for
worth |3
a ton, 8 lbs. of
a bushel, and 3 lbs. of cotton-seed meal
worth $32 a ton, per day for 180 days. What is the on the feeding if the animal gains 1.95 lbs. a day and sells for $5.37^ per hundredweight? If the animal profit
gains 2.1
weight 51.
lbs.
a day and sells for $5.42 per hundred-
?
How much
equal area,
a, h, c,
will
it
cost to fence each of the lots of
as chicken lots, if the figures
showing
MISCELLANEOUS REVIEW PROBLEMS and setting posts
6 cts. each
;
fence to be 5 boards high
for each board 16
at 11.2 cts.
335
in length.
ft.
Estimate
exclusive of cost of nails and labor of construction. 53.
of
If tlie figures indicate rods,
what
will
be the cost
fencing each with barbed wire: posts 16
cost of posts
each;
;
1480
of
and labor
ft.
apart;
ft.
cost of setting posts
fence 4 wires high costing
pounds
54.
cach
cts.
Irt
1|-
cts.
$2.75 per hundred
Estimate exclusive of cost of staples
of construction.
Procure at home the prices of the materials used problems and the cost of construction in
in the last three
your community, and using such facts solve each of these problems.
In plowing, a furrow one foot wide
55.
turned.
is
How many times must the field a be crossed to plow all of it ? How many turns must be made ? (Figures indicate rods.)
each turn consumes 30
If
56;
turning in field
field
a
In
field 5,
from east
plowing
c,
?
to
sees. ,
what time
is lost
plowing lengthwise west?
(Figures
?
in
In
indicate
rods.) 57.
What
is
plowing each
the value of the time lost
field
at % 3.50 per
day
turning in
in
of 10 hrs.
(Figures
?
indicate rods.) 58.
In raking the same fields with an eight-foot raks,
how many each 59.
turns are
field ?
With
of turns
made ?
time
is
lost in
(Figures indicate rods.) a twelve-foot rake,
and the time
cate rods.)
How much
lost in
what
each
will be the
field ?
number
(Figures indi-
PRACTICAL ARITHMETIC
336
Two wagon
60.
circumference,
How
one 22
tii-es,
upon
lie
A
window
of tJie third story of a
How
from the ground.
At
62.
i 18 a thousand
a piece of timber 18
How many
63.
in diameter,
and 20
ft.
ft.
what
feet,
To
is
24
and 8
ft.
deep in the
if
If I
silage will a silo 10
deep.
ft.
within 5
ft.
gold
the temperature
how much
(1
?
70.
if
a
lbs. ?
ft.
gold
for
will a pile
high cost
karat =
it is
its
lbs.
diameter to
each a day for
37.5° Centigrade, what
is
thermometer indicate
If a ring is
cent of
in
in diame-
of the top,
ft.
AVhat must be
pay f 3.50 a cord
wide, and 3 J 69.
ft.
a cubic foot of silage weighs 37 lbs.?
When
sawing,
ft.
and 1
insure the silage keeping well, a silo should not
will a Fahrenheit 68.
silo
?
?
hold enough silage to feed 25 cows 40
67.
?
ins. thick
water will a tank 8
barrels of
high hold
ft.
Iiigh hold, filled
be less than 30
185 days,
ft.
will be the value of
cubic foot of silage from such a silo weighs 30 66.
32
from the building
long, 10 ins. wide,
How many tons of
65.
is
lbs. ?
How many
64.
house
tons of silage are there in a silo 16
weighs 33^
ft.
ft.
the silage
if
diameter and 8
ter
in
ft.
long must a ladder be to reach
with the foot of the ladder 10
cu.
the other 17
contact at one point.
far apart are their centres ?
61.
it,
ft.
a floor in
me
18 karats ^^.)
?
wood and $.95 a cord for of wood 29 ft. long, 8 ft.
?
what per cent of it is 14 karats fine, what per
fine,
If it is
?
A haberdasher buys hats
at
$ 18 a dozen and
sells
MISCELLANEOUS REVIEW rROBLEMS them is
is
the gain?
"What
the selling price ?
A
71. is
What
33^%.
at a profit of
33T
his
man
invests
$1250
so as to gain 12]
income from his investment
A
73.
%
To
?
man
gain 16f
%
What
it
be sold
?
If flour costs f 6 a barrel, at
72.
to gain 8^
%.
what mnst
?
purchases a hogshead of 12 gross of glass
$45; 5% was broken in shipping. At what price per dozen must the remainder be sold to gain 20 % on the whole? articles for
buy a
I
74>
30-gal. barrel of vinegar at 25 cts. a gallon.
Upon examination
How
leaked out.
36%
it
is
found that 4
gals.
2 qts.
must the remainder be sold
have
to gain
on the whole?
75.
A
and
B
are engaged in different lines of business
The first year A gains and B loses 20 % of the investment. The second year A loses and B gains 20 % on the capital each has then. Which
with a capital of $4000 each.
is
now 76.
the better off?
A
%
of his tobacco crop by hail company in which the crop 75 % of its value, the sum of $450, coverFor what amount was the entire crop
farmer losing 20
received from the insurance
was insured for ing the
loss.
insured ? 77.
10%
of
5%
of a
number
is
|2.88.
What
is
the
number? CROP ROTATION Systems of crop rotation prove to be more profitable under most conditions tlian the continuous growing of
PRACTICAL ARITHMETIC
338
The
one crop.
conditions in one section of the South are
page by the record of
illustrated on the opposite
a 90-acre
farm continuously cropped and that of a similar farm divided into three 30-acre
The
cost
fields
and the crops
and produce per acre for each
rotated.
field for a series
of years are given. 78.
Find the
and the 79.
profit
on each 30-acre
profit each year
Find the
field for
each year
on the whole farm under
profit of the
rotation.
whole farm each year under
continuous cropping. 80.
Which
How much
the more profitable for the
is
more
profitable than the other
first
year?
method?
Which is the more profitable for the last year? How much more profitable than the other method? 82. How much does the profit of the last 3 years under 81.
rotation exceed the profit of the last 3 years under con-
tinuous cropping?
83. tilizer
A
farmer has land that, with $1.86 worth of
fer-
per acre and $6.85 per acre for labor and other
expenses, including taxes, will produce 56 bus. of corn
With corn
per acre. ing
5%
84.
at 50 cts. a bushel the land
is
draw-
on what capital?
L'nd
that,
with
il.46 worth of
fertilizer
and
$12.50 for other expenses, will produce f of a bale of cotton, worth for the seed f5, for the lint 333 lbs. at 11 cts. per pound, 85.
is
Land
drawing 4 that
will
%
on what capital
produce
worth 50
cts. a
penses,
paying interest at 4
is
260 bus.
bushel, with an outlay of
%
?
of
potatoes,
$96 for all on what amount ?
ex-
MISCELLANEOUS REVIEW PROBLEMS
<
339
PRACTICAL ARITHMETIC
340
Land near a
86.
certain city produces
1300 worth
of
garden truck per acre at a total expense of f 120 per acre. Land of similar quality, but so located as to have no ma,rket for truck, can raise of
60 bus. per acre at 50
cts.
its
most profitable
crop, corn,
per bu. at a cost of $8.50.
Disregarding taxes, estimate the capital or value of each
farm at
4%
interest.
What
87.
is
the increased value of the
first
farm, due
to its location?
A field produces
88.
816
tobacco averaging 8
lbs. of
The
per pound at a total cost of $47 per acre.
%?
drawing interest on what capital at 4
cts.
land
is
Suppose the
tobacco wilt to take possession of the field and render
to-
bacco raising impossible and that the next most valuable crop
is
corn, 23 bus. per acre, valued at 65 cts. per bushel,
costing to raise $9.20 an acre.
What
capital at the
same
rate will the land then represent? If the
89.
yam sweet
how many pounds
of starch,
of starch
yellow
potato contains 16.64%
are required to contain 2 tons
?
90. The Red Bermuda contains much sugar is there in 3 cwts. ?
%
2.59
of sugar,
How many
how
tons are
required to contain 2.9 T. of sugar?
The average starch content of corn 58%, rice 75%, Irish potatoes 18%, sweet 91.
21
%
.
What
is
potato starch 3.57
92.
cts.
65 %, wheat
potatoes about
the value of the starch in a ton of each of
these crops at the following prices
4.78
is
cts., rice
:
corn starch 1.93
starch 6.53
cts.,
cts.,
wheat starch
per pound?
If there is
28%
sweet potato and 9.79
of starch in
%
Red Bermuda Nansmond, how
the
in the Early
MISCELLANEOUS REVIEW PROBLEMS
much more
starch
341
there in 2 T. 3 cwts. of the
is
variety than in 3 T. 7 cwts. of the second? starch present can be separated,
how
If
58
%
first
of the
mucli can be had in
each case?
At 13.50
93.
for 3 wks. 4
a
At 19.00
94.
what
day
7 hrs.
work?
How many loads
less are
In 6 weeks?
roads?
a
hauled in a week because of poor
Counting 4 loads
man
the loss in this time to one
On
97.
daj''
How much
lost
time
is
occasioned by the poor road in
market (1 bu. at #3.50 a day?
is
the loss
If 3 forty-quart cans of
to
quart cans of 4
Grafting
100.
bus.
%
milk
wax
tallow 3 ozs. If
is
=
milk containing 3
ter fat bring 6| cts. a quart, for
ozs.,
Allowing four loads
on a good road and two loads a day on a poor
drawing 1600 bus. of potatoes
99.
what
poor roads a teamster can draw | of a ton at
how much
98.
to the day,
with team ?
each load, on a good road 1| T. to each
prices.
good road a farmer can haul on a poor road only two loads daily.
four loads daily,
5
due
liarvester,
two problems, using these
last
Drawing produce on
96.
road,
is
Ascertain the local price of such labor in your com-
95.
munity, and solve the
is
team, wliat
a day for a man, team, and
due for 3 days
is
man and
for a
days 3 hrs. work?
what should
60 lbs.)?
%
of but-
6 sixty-five-
sell ?
made
of:
resin 5 ozs.,
beeswax
State the composition in per cents.
12 % of the stalks of a corn-field -producing 63
per acre are barren,
through barren stalks?
how many
bushels are lost
PRACTICAL ARITHMETIC
34i
What
101.
is
the weight of a 40 bu. wheat crop on au
the grain weighs 2400 lbs. and the straw weighs
acre
if
3600
lbs. ?
What
per cent of the total crop
The following amounts
102.
grain?
is
water expressed
of
as
inches in depth are required to mature wheat crops of the following yields ins.
;
:
15 bus. to the acre require 4.498
20 bus. require 5.998 ins.; 25 bus., 7.497 ins.; 30
bus., 8.997 ins.
35 bus., 10.495
;
ins.
;
40 bus., 12
15-bu. crop?
An
How many
acre of water 1 in. deep weighs 226,584 lbs.
more pounds are -required
ins.
to raise a 35-bu. crop than a
A 20-bu. crop than
crop than a 15-bu. crop?
a 15-bu. crop?
Make
A
40-bu.
other similar problems
from the data given.
A
Week's Food foe Two Persons
Meats 2
lbs. flank of
Cost
lb. salt
pork
lb.
3
lbs. veal cutlet
1
lb.
bacon
.
fresh fish
lbs.
sugar
06^ seasoning 08^ 3 lbs. bananas 24^ 5 lbs. apples 18^ .
.
.
and Milk
.
.
.
.
Cost
16/ 05/ 10/ 15/ 10/
.
baking powder
1 lb. pickled tongue
\ \
Groceries
2
beef
.
.
.
Vegetables Cfroceries
2
qts.
milk
lbs.
butter
1 doz. eggs
.... ....
|-
lb.
of coffee
lb.
tea
6
lbs. flour
lbs.
potatoes 1 pk. (15 lbs.)
cabbage 2
^
lbs.
and Milk
.
,
.
....
corn meal and 2
oatmeal
.
.
lbs.
40/ lettuce ^ lb 20/ peas 1 lb 08/ string beans 1 08/ turnips 5 lbs 23/ squash 5 lbs
.
.
.
lb.
.
.
.
15/ 08/ 05/ 16/ 05/ 05/
2
lbs.
dried beans
20/ 2
lbs.
canned tomatoes
.
.
.
08/ 10/
.
12/
MISCELLANEOUS REVIEW PROBL-EMS 103.
Find the
104.
At
348
total cost of supplies for a week.
the same rate what will the food cost for the
year ? .
105.
If
the food costs ^ of the income, what
the
is
income ?
Find the amount of digestible protein in the meat consumed. (For data consult tables on pages 272 and 273.) 106.
and
fish
107.
Find
vegetables.
the amount of digestible protein in the Find the amount of digestible protein in the
groceries and milk. 108.
Digestible fats in meat and
109.
Digestible carbohydrates and fats in groceries.
110.
Digestible carbohydrates and fats in vegetables.
111.
If in
60 grams of
one day a fats,
man
requires 100 grams of protein,
and 400 grams
woman requires 90 grams week exceed
or
fall
of carbohydrates,
of protein, 40
350 grams of carbohydrates, a
fish.
grams
how much
short
of
this
and a and
of fats,
does the diet for
standard
?
(See
preceding page.) 112.
The
cost of spraying cantaloupes being |4.47 an
acre per season,
what
is
the cost for 12 A.
?
The net profit from spraying one acre of cucumbers on Long Island being 1163.50, what would be the profit 113.
at the 114.
same rate from spraying 14 acres?
The net
profit
from spraying an average-sized tree
from 12 to 20 years old throughout one season at a total When apples are worth cost of 50 cts. is from 13 to 17.
11 per bushel, what are the highest and the lowest per cents realized upon the investment?
:
PRACTICAL ARITHMETIC
344 115.
shown
Sprayed and iinsprayed apple trees yielding in
tlie
table below,
what
sprayed and the 3 unsprayed
is
as is
the total yield of the 6
trees, in bushels, in
sound
apples and in diseased apples?
Sound Apples
Diseased Apples
15.76
1278
Number 144
2
18.26
1.563
3
18.76
1526
163
4
10.26
749
103
5
1-3.76
6
24.50
1394 2164
309
Date of Spraying and Tree Numher Trees sprayed July 10 and 26 and Aug, 9
No. No. No. No. No. No.
:
1
Biixli els
253
17
Trees not sprayed
A
5.875
B
9.35
C
5.875
116. cities
The population for
two decades
What was the per cent
of several is
shown
3
1276
135
1670
50
1298
American and
foreign
in the following table.
of increase in each city
?
Was
the
average increase greater abroad or in the United States
?
:
MISCELLANEOUS REVIEW PROBLEMS
The population
117.
3;928,037
;
of the
in 1800, 5,308,937
;
345
United States in 1790 was in 1810, 7,239,814
;
in 1820,
9,638,191; in 1830, 12,860,702; in 1840, 17,017,788; in 1850, 23,151,876
in 1860, 31,335,120
;
;
in 1870, 38,784,597;
in 1880, 50,152,866; in 1890, 62,622,260
000.
What was
given?
;
in 1900, 76,059,-
the increase in popuhition the
The second?
The
third?
first
decade
For each succeeding
decade?
What was
118.
mach
was the 119.
the increase from 1800 to 1900?
How
greater was the increase during the last decade than total population of
1790?
Than
of 1820?
According to the twelfth census the working popu-
lation of the
United States was engaged as follows
Pursuit
PRACTICAL ARITHMETIC
346
member
of the average Pennsylvania farmer's family re-
What
ceives 1198.26 yearly.
per cent above the average
income do these farmers receive? 122.
In 1820, of the people engaged in commerce, manu-
and agriculture, | were engaged in agriculture. What fraction |- were engaged in agriculture.
facturing,
In 1900, less
was there
123.
iia
agriculture in 1900 than in 1820?
In 1870 for every 1000 persons engaged in agri-
culture there were 1112 engaged in other pursuits
in
:
1900 for every 1000 in agriculture there were 1806
Show
other pursuits. in.
by
lines, letting
in |
represent 100 people.
124.
in
these relations
The average value
1900 was:
of farms in the
United States
total value 13574, buildings 1620, imple-
ments and machinery $133,
live stock
cent of the value of the land
is
$536.
What
per
each of the three other
items given? 125.
For each $1000 of
total investment,
how many dol-
lars are invested in each of the other three items
126.
given?
For each f 1000 invested in land, how much
is in-
vested in each of the other three items? 127.
If
1200 cu.
ins. of air is
rendered unfit for breath-
ing by one person in one minute, what volume of
air will
be required to last 100 persons an hour? 128.
When
the air
is
taken into the lungs (inspired),
it
20.81% oxygen, 79.15% nitrogen, .04% carbon when it comes out of the lungs (expired), it has 16.035% oxygen, 79.557% nitrogen, and the balance is What per cent of the oxygen is retained carbon dioxide. contains
dioxide
;
MISCELLANEOUS REVIEW PROBLEMS in the body,
and what per cent
347
of carbon dioxide has been
added ? 129.
If
the following be the pulse rate and rate of
breathing per minute, what per cent
is
the rate of breath-
ing of the pulse rate for each animal? Kespiration
Man
16
.
Horse
12
Cow
15
.
Sheep
14
Dog
16
.
130.
Compare the number
of heart-beats of a
131. ute,
by
Cow
with sheep.
for
Compare horse
one day with that of a horse and a cow.
with cow.
man
Sheep with dog. 38 per min-
If the pulse (heart-beat) of a horse is
and that of a mule 46, and both are increased 50 what will then be the pulse rate of each ?
%
disease,
132.
lows,
If the
what
is
body temperatures
of five horses are as fol-
the average body temperature 7 a.m.
(1)
98.9°
(2)
99.6°
(3)
99.4°
(4)
98.8° 1°
?
12 m.
99.3°
(5) 100. 133.
If the
as follows,
body temperatures
of five
cows were taken
what was the average temperature 8 a.m.
(1) 100.5°
12 m.
100.8°
?
6 p.m.
100.9°
PEACTICAL AKITHMETIC
318 (2)
99.8°
MISCELLANEOUS REVIEW PROBLEMS
when meal
is
worth $28 a
him
ton, to justify
349
in
exchang-
ing seed for meal ? 140.
If
the fare of 4 people, 96 mis.,
be the fare of 12 people, 48 mis.?
Q
of 8 people, with 4 chiklren 141.
If a pay-roll for 9
how much 142.
make
If it takes 8 boys,
a tennis court,
If
18.64, what will
What
will be the fare
going 72 mis.?
fare),
employees for 6 days
is
the pay roll for 15 employees for 9 days
is
ing 2 hrs. daily 143.
is
working 8
how
long will
hrs. a day, 12 it
172, ?
days to
take 50 boys work-
?
men can do a certain piece of work in 7 days how many men will be required to accom-
20
of 8 hrs. each, plish the 144.
wheat, 145.
same work
If a
grain bin
how many
A
in 12 days of 7 hrs. each? 4-|-
x 9 x4
ft.
holds 1262 bus. of
bushels will a bin 4^ x 15 x 6
hold?
truck grower ships 18 baskets of beans and 27
The
crates of strawberries.
freight
is
40
cts.
on the beans and the refrigerator charges 75
on the
ft.
berries.
The beans
sell for
a basket
cts.
a crate
$1.35 a basket and
How much will the grower a commission of 8| % is charged
the berries for f 2.87-^- a crate. receive for his shipment
if
for selling? 146.
If at the
Chicago stock-yards the usual charge
for selling beef cattle
is
50
cts.
a head,
what
is
the per
cent of commission on 25 head of cattle weighing 1325 lbs.
at
each and selling for 5.75
147.
What
148.
A
cts. a
pound
?
two cattle weighing 1225 i 5| per hundredweight ? will
lbs.
each bring
farmer makes the following exchange with his
PRACTICAL ARITHMETIC
350
he gives 27^
grocer:
butter at 221 cts
lbs.
a pound,
a dozen, and 3J bus. potatoes at 45 cts. a bushel, and receives 20 lbs. sugar at 5J cts. a
15| doz. eggs at pound, 3
17-| cts.
cheese at 13-|
lbs.
How much
in cash.
cts.
a pound, and the balance
cash does he receive
?
149. If 10 lbs. of corn and 2 lbs. of cotton-seed meal a day for each horse may be substituted for 14 lbs. of corn, what will be the saving in a year on a farm where 15 horses are being fed, if corn is worth 50 cts. a bushel and cotton-seed meal 1 28 a ton ?
can be cut, shocked, and
If a 10-acre field of corn
150.
shredded for $4 an acre and" yields 2960 per acre, what
is
harvesting the corn,
hay valued
of grass 151.
a ton of stover
if
at
of stover
is
worth 1200
items represent the cost of pro-
of potatoes,
what
will be the profit per
acre on a yield of 235 bus. worth 47 cts.
per bushel
Cost of seed $3,939, plowing $1,607, dragging 92 planting
60
cts.,
lbs.
$10 a ton?
If the following
ducing an acre
lbs.
the value of the stover over the cost of
cultivating
$1.709,. hoeing
?
cts.,
$2,865,
spraying $3.60, digging $4.35, wear of machinery $21.24,
and rent 152.
of land $5.00.
In Minnesota
acre of corn
seed 2.3 22.5
cts.,
cts.,
ing 52.6
it
costs as follows to cultivate an
manuring 57,6
:
cts.,
seed 21.3
plowing $1,205, dragging 48
cultivating $1,619, cutting cts.,
twine 46.7
cts.,
cts., shelling
cts.,
66.5
planting
cts.,
shock-
picking up ears 24.9
cts.,
shredding $3,794, wear of machinery $1,202, rent of land $3.50.
What
per acre at 42
is
the profit on 40 acres yielding 53 bus.
cts.
a bushel, and 2964 lbs. of shredded
MISCELLANEOUS REVIEW PROBLEMS stover at 13.00
What
per ton?
the
is
351
profit
on one
acre? 153.
If
an acre of clay
soil 1 ft.
deep contains 6.38
tons of potash and grows a crop of 40 bus. of wheat hav-
ing a ratio of weight between grain and straw of 2
how many such
crops would
potash as there
is
6.3 lbs. of potash
in the soil
and 1000
it if
lbs.
1000
lbs. of
:
3,
much
take to contain as
wheat contain
wheat straw 5.2
lbs. ?
154. The average number of marketable potatoes from each " seed " piece of several varieties was variety No. :
1,
3.14 potatoes, No.
No.
2,
3.03 potatoes, No.
3.29 potatoes, No.
4,
tatoes,
No.
5,
1.7 potatoes.
7,
3.28 potatoes.
3.48 potatoes. No.
What was
ber of potatoes per seed piece of
By what
3,
num-
all of
these varieties ?
?
By
?
In Virginia the Burbank potato yielded 230 bus.
of marketable potatoes per acre, the
What would
Crown Jewel 197
bus.
be the difference in value of yield on 40
acres of each of these 156.
1.91 po-
per cent did the best exceed the poorest
what per cent did the best exceed the average 155.
6,
the average
Of 67 hens
two
varieties at 55 cts. per bushel
tested for egg laying ability for
?
two
more eggs the second year than the first and 57 laid fewer eggs the second year. What per cent laid more the second year ? What per cent laid fewer years, 10 laid year,
the second year 157.
bus.
A
?
10-acre field continuously in corn yielded 357
When
crimson clover was used in a rotation, the
yield the year following the clover
was the per cent per bushel ?
was 551 bus.
What
of increase in value with corn at 48 cts.
What was the per
cent of increase in bushels ?
PRACTICAL ARITHMETIC
352 158. is
buy a bill of hardware on which the list price The discounts are 25%, 10%, and 5%. How
I
$134.
much do
have to pay?
I
If I bu}- a bill of
159.
groceries on which there
15% and 5%
discount of
for cash,
is
a
how much must
I
pay?
am
$390 with disand off for cash. A 5 second firm offers % % me the tile at the same price with a discount of 15 % and 10% off for cash. From which firm shall I buy? Why? 160.
I
offered a quantity of tile for
counts of 20
A farmer
161.
He
time.
sold a team of horses for
and how much, by
lose,
worth 162.
6%? A feed
§28
cts.
corn
money
118
or
being
cts. a
a ton, 35 bus. of
a bushel, and 700 lbs. of cotton-seed meal at
make
by weight
Did he gain
merchant mixed 62 bus. of oats at 34
How much
a ton.
order to
350 on 1 year's
selling on time,
bushel, 1200 lbs. of wheat bran at
corn at 43
i|
refused an offer of §325 cash.
must he charge per 100
a profit of 20
%
for grinding the oats
lbs. in
after giving a toll of 6
and 5
%
%
for grinding the
?
163.
If
when corn
dry matter
loss in
11 %, what
is
is
is
cut and cured in the shock the
31%, and when put
into the
silo
the total gain in dry matter by putting
the corn from 10 A., weighing 12 T. per acre, into a
when ready for cutting, corn contains 73.2% of How much is the dry matter saved worth if silage containing 79.1 % water has a feeding value of $3 per ton? silo,
if,
water?
164.
at 6
%
If I
buy corn
interest,
at 42 cts. a bushel on 3 months' time
and the shrinkage
in the
weight of the corn
MISCELLANEOUS REVIEW PROBLEMS is
to
353
10 %, at what price must I sell at the end of 3 months make 20 % on the transaction ? 165.
The
one year
interest
collected
is
on a mortgage for 1320 at by an agent who receives 10
What
mission for collecting.
per cent 166.
his
is
A
8% for % comWhat
does he receive?
commission of the principal?
farmer has 1350 bus. of corn for which he
offered 37 cts. a bushel on
December
He
1.
keeps
it
is
until
March 1 and sells it for 43^ cts. a bushel. Did he make or by holding the corn if it lost 8 % in weight, and money was worth 8 % interest ?
lose
If the
167.
farmer makes
% 10 %
12^%
profit
on his wheat, the
and the
miller charges 20
for grinding
grocer receives
for selling a barrel of the flour for
$5.65, what did
make
required to
A man
168.
it
it
into flour,
cost the farmer to produce the
wheat
a barrel of flour?
\
What
pays 197 taxes on $9682.
is
the
rate ?
What
169.
are the taxes on $19,862, the rate being
.00971? 170.
A
town
raises
$6859 on property assessed
$684,936, there being 428 polls at $1.67 each. will be the rate 171.
A
A
What
?
town having 248
polls,
$868,730, raises $6482.94 taxes. 172.
at
property
What
note for $1575 dated April
is
9,
valuation
the rate?
1903 was
in-
dorsed as follows: Oct. 15, 1909, $115; July 27, 1904,
$135; April
Jan. 9,
21,
1906 at
1905,
6%
$325.
interest?
What amount was due
PRACTICAL ARITHMETIC
354
What must
173.
I
pay, Sept. 17, 1907, to take up
note for |268 given Jan. 25, 1905, at
A
174.
gage,
not procured until Oct.
%
interest,
first
are the taxes on
A
man
takes out
should be the
money?
17682
of personal property valued at f, rate 176.
is
half-yearly interest be-
cause of the delay in delivering the
What
but the money
What
1907.
9,
amount deducted from the
175.
my
interest?
note dated Aug. 24, 1907, secured by a mort-
given for 1400 at 8
is
8%
of real
.9%
and 12986
?
insurance for 13500 at 30
life
years of age for f 19.06 a year per thousand, and pays for
20 years.
If
he lives to 76 years of age and money
is
worth 6%, what has his protection cost over and above the $3500 which his estate receives? 177.
farmer living 15 miles from market makes a
If a
$2.50 in time, to deliver 50
trip costing
25
cts. a
in cost of 178.
If
butter at
lbs. of
pound, what per cent of his receipts
is
consumed
marketing ? he delivers 650
lbs.
instead, at a cost of
$3
what per cent of the receipts is the cost of marketing? By what per cent is the cost of marketing refor time,
duced in the second instance ? 179.
If
it
costs
a
strawberry grower living 5 miles
from market 12 in time to deliver a 32-qt. berries at 11^ cts. per quart,
of the crate 180.
If
is
If
in
what
of
marketing?
he markets 20 crates at a cost of |3 in time,
what per cent 181.
consumed
crate
per cent of the value
it
is
so
costs
consumed ? the
Vermont farmer $1.93
to haul
MISCELLANEOUS REVIEW PROBLEMS 2321
lbs. of
potatoes 7.1 miles, and the Connecticut farmer
$2.80 to haul 2500
more
355
potatoes 6.7 miles,
lbs. of
how much
will it cost the Connecticut farmer to haul the crop
on 9 A. yielding 268 bus. per acre 5 mis. to market than
would the Vermont farmer to haul a similar crop the same distance? How much more per acre? it
182.
If it costs
$2.11 to haul 3020
in Pennsylvania
and $2.76
mis. in Georgia,
how much more
lbs. of
corn 6.6 miles
to haul 1553 lbs. of corn 11.8 will it cost the
Georgia
farmer to haul the corn from 25 A., averaging 32 bus. per acre, 9 miles to market, than
it
will a Pennsylvania
farmer to haul a similar crop the same distance ? 183.
If
it
costs 6 cts. to haul 100 lbs. of corn 6 miles to
market
in Ohio, and 30 cts. to haul 150 lbs. of corn 13 miles market in Arkansas, the difference being due to better roads and larger horses in Ohio, what is the gain per acre,
to
from good roads and large horses, to the Ohio farmer living If this 7 mis. from market on a crop of 42 bus. per acre ? gain
is
taken to represent interest at 6
value of the land, what
is
%
on the increased
the increase in the value of
the land per acre? 184.
A
dairyman has 2000
lbs. of
of butter fat.
From 1000
by the gravity
settling method,
milk 20
%
of all the butter fat.
does recover in this
He
way
milk containing 4
lbs. of this
%
he skims the cream
which loses in the skim
The butter
fat that
he
he sells for 20 cts. per pound.
separates the cream from the other 1000 lbs. of milk
with the centrifugal cream separator, which loses in the skim milk 2 % of all the butter fat. The butter fat he obtains in this way, on account of the superior quality.
PRACTICAL ARITHMETIC
356 he
25
sells at
per pound.
cts.
on the 1000
profit
than on the 1000
taining 186.
3.5%
milk skimmed by the separator skimmed by the gravity system?
milk containing 5
%
of butter fat are
the value of 100 gallons of milk con-
is
of butter fat?
milk containing 5 9^ of butter fat
If
quart,
cts. a
greater was his
lbs. of lbs.
If 70 gals, of
185.
worth $28, what
How much
what
is
is
worth 10
milk containing 3.5% of butter
fat
worth ? 187. fat.
I
have 1000
How much
add to bring have no cream I
no butter of 4
it
%
fat
it
up
to a 4
%
%
%
of butter
of butter fat must
butter fat standard?
If I
how much skim milk containing remove to bring it up to the standard
to add,
must
I
have 1000
I
to a
4%
can I take out of I
% milk and wish to reduce How much skim milk must I add? milk to add, how much 25 % cream
lbs. of 4.5
standard.
have no skim
189.
milk containing 3.5
butter fat?
188.
If I
lbs. of
cream containing 25
it ?
wish to mix cream containing 35
%
of butter fat
and milk containing 5 % of butter fat, so as to produce 140 lbs. of cream containing 25 % of butter fat. How many pounds of each must I use in the mixture?.
190.
I wish to obtain 200 lbs. of milk containing
of butter fat from
two
lots of milk,
butter fat and the other
pounds of each must 191. cts.
If
I
4.9%
of butter fat.
per gallon, what ?
is
How
maily
use?
cream containing 20 % of butter
of butter fat
4%
one testing 3.8% of
fat
is
worth 60
cream worth which contains 25
%
MISCELLANEOUS REVIEW PROBLEMS
What
357
pound of butter fat if cream containing 20 % of butter fat and weiy:liing 8.3 lbs. sells for 50 cts. a gallon ? At 32 cts. per pound of butter fat, what would be the price per gallon of cream containing 27 % of butter fat ? Of cream containing 25 % of butter 192.
%
20
fat?
is
the price per
of butter fat?
milk containing 3.5% of butter fat
If 5 qts. of
193.
%
15
of butter fat?
have an energy value as food of 3066
calories,
and
1
pound
rpund beefsteak has an energy value of 841 calories, what should round steak sell for per pound Avhen milk
of
worth 8
is
cts.
a quart?
5 cts. per quart?
10
cts.
per
quart?
A
194.
dairyman has 1000
of butter fat.
he
skim milk 25
sells at
lbs. of
15
cts.
lbs. of
lbs. of this
and obtains
process, in the
500
a 20
%
%
milk containing 5
cream.
He, however, loses
of the butter fat.
per 100
lbs.
"Jo
he skims with the gravity
From
This skim milk
the remaining 500
milk he separates the cream with the centrifugal
making
separator,
a 50
%
cream and losing but
butter fat in the skim milk.
On
account of
1
%
of the
its
being
fresh and pure from the separator he sells this skim milk
How much
more did the dairyman receive from his separator skim milk than from the skim milk left from the gravity skimming process? for
25
195.
cts.
per 100
lbs.
The maximum amounts
various forms of farm produce table.
Placing nitrogen at 18
acid at 6 cts.,
of these table.
of fertilizer is
shown
cts.
removed by
in the following
a pound, phosphoric
and potash at 5 cts., find the value of each removed in each crop given in the
fertilizers
.
PRACTICAL ARITHMETIC
358
Pounds op
Produce
Nitrogen
Kind
Corn, grain
.
.
.
Corn stover
.
.
.
Oats, grain
.
.
.
Oat straw
AVheat, grain
Wheat, straw Timothy hay
.
.
.
.
17
19
48
6
52
100 bus.
66
11
16
2^T.
31
5
52
50 bus.
71
12
13
2iT.
25
4
35
72
9
71
7 160
2
3
20
120
.
.
3T.
.
.
.
4 bus.
Clover hay
.
.
.
Cow-pea hay Alfalfa hay
.
.
.
.
.
.
4T. 8T. 8T.
Apples .
Potatoes
.
196.
5
57
59
7
47
2
5
63
13
90
100
18
157
lbs.
25
7
1
lbs.
18
3
1
10,000 lbs.
300 bus.
.
.
.
.
.
.
.
1000
.
.
.
.
1000
lint
.
.
20 T.
.
Of 4402 samples
in Indiana
from 1902
98
192
47
.
Butter
Cotton
14 36
4T. ^tree
.
Milk
130
400
600 bus.
.
.
Sugar beets
Fat cattle Fat hogs
.
Potash
100
Clover seed
Apple leaves Apple wood growth
Acid
3 T.
100 bus.
....
Phosphoric
57
7
12
500
lbs.
1
0.2
0.1
500
lbs.
1.7
.5
2.3
of commercial fertilizer analyzed
to 1907,
3158 were equal in value
that guaranteed, 323 were not within 10
and 835 were with one or more below the guaranteed value. to the guaranteed value ?
%
of the ingredients 20
What
to
of such value,
%
per cent was equal
MISCELLANEOUS REVIEW PROBLEMS
What
197.
What
per cent
per cent was not within fell
in the last class
10%
named
TABLE OF ANALYSIS OF FERTILIZERS Class
1.
2.
....
particular
7.
Number with one
8.
Number with one
5.
1904 1905
.
.
.
20% below guarantee
592 679 674 648 734 879 793
469 564 492 451 528 642 481 85 93 139 148 158 176 210 38 22 43 44 48 61 102 103 112 138 132 148 136 177
ingredient or
more
30% below guarantee
in class 2
per cent of
lbs.
What
?
21
21
25 29
In class 4
?
In class 5
?
fell
In class 6
?
6 ins. of soil weighs per acre 1,370,000
of moisture;
if
may
contain
poorly cultivated, only 8.02%.
amount of Avater in the soil under Under good cultivation? Obtain the
will be the total
poor cultivation? last
64 75
samples analyzed in each year
If the surface is cultivated thoroughly, it
14.21%
77
?
The upper
198.
all
In class 3
?
In class 7
65
ingredient or more
50% below guarantee
What
190T
281 335 286 248 812 374 265
6.
4.
IN INDIANA
in every
Number equal to guarantee in value Number within 10% of guarantee Number not within 10% of guarantee Number with one ingredient or more
3.
value?
of
?
1901
Number of samples collected Number equal to guarantee
359
answer by two different processes.
199.
In Minnesota
it
was found that during 10
yrs.
of exclusive grain farming the per cent of nitrogen in a soil
had decreased from .601
%
to
.523%.
If the soil to
a depth of 8 ins. per acre weighs 1282 T.,
nitrogen was lost from the
soil ?
how much
PRACTICAL ARITHMETIC
360 200.
How much
nitrogen will 30 bus. of wheat per acre
annually take from the takes .625 201. soil of
soil in
10
yrs., if 1 bu. of
wheat
nitrogen from the soil?
lb.
What
per cent of the total nitrogen lost from the
problem 199
10 yrs. would be taken out by
in the
wheat as in the preceding problem? 202.
After 10 yrs. under a system of mixed farming,
including rotation of crops, the growing of legumes, and live-stock husbandry, in another field, the nitrogen in the soil
had decreased only from .31% to .309%. If the soil weighs 58.9 lbs. per square foot of sur-
to a depth of 8 ins.
how many pounds less What was after 10 yrs. ? face,
nitrogen did this
contain
field
the difference in the loss of
nitrogen per acre from this field and that of problem 199 in the 10 yrs. 203.
?
If it costs
to 40 yrs. of age,
what
is
204.
$29.52 to raise an acre of white pine
and
it
yields on the
stump $4 per
the profit on 40 cords of box-board timber
?
In 1871 a strip of forest land 40 mis. wide and 180
mis. long
was devastated by
fire.
The
loss is estimated at
4,000,000,000 board feet worth 110,000,000.
the loss per square mile in board feet ? 205.
cord,
If
What was
In dollars
?
one toad destroys in 30 days 720 cutworms,
600 thousand-legged Avorms, 720 sow-bugs, 1080 ants, 120 weevils, 120
ground
beetles,
would 19 toads destroy?
months ?
Many
cutworms
at the rate of a
toads earn in a 206.
Two
how
;-^any of each of these
How many
in a
week?
In 3
gardeners pay their children for killing
month
penny
each.
at this rate ?
boys were known to
What would
19
In 3 months ? kill
19 toads.
What
MISCELLANEOUS REVIEW PROBLEMS
361
was the loss in 3 mos., even if it required 19 toads to do what it was shown one could do in the last problem?
Corn
growth contains dry matter (useful) and water as follows, expressed in tons: 207.
at different stages of
Watbr
Corn ACKR
I'KR
Fully tasselled
I'
9
Fully silked
Kit
ACKK
Dry Matteu PER Acre
8.2
12.9
11.3
Kernels watery to full milk
16.3
14
Kernels glazed
16.1
12.5
Ripe
14.2
10.2
Complete column of dry matter. What per cent of water and what per cent of dry matter are there at these different periods? 208.
If a
good clay
soil
contains 12,760 lbs. of potash
per acre one foot deep, and a 40-bu. crop of wheat uses 35.1 lbs. of potash,
how many
crops will
it
take to use
potash equal to that in the clay soil? 209.
If,
with the same
field conditions,
one variety of
corn yields 7 bus. per acre more than another variety,
what
will be the gain in planting the better variety
96 acres,
if
the poor seed costs 60
cts.
per bushel and the
Allow 1 bu. every eight acres planted and value the
seed of the better variety $2.50 per bushel of seed corn to
on
corn of the crop at 49
cts.
?
per bushel.
Eight bushels of clover seed containing 3 bus. of dead seed were bought at I 3.50 per bushel. What was 210.
the price paid for the live seed? 211.
Fifteen bushels of clover seed containing 1 bu. of
PRACTICAL ARITHMETIC
362
What
dead seed were bought at 15.50 a bushel. the price paid for the live seed
was
?
A variety of flax, improved by seed selection, on an average, 2.2 bus. per acre better than the What is the best common varieties, which yield 15 bus. per cent increase due to seed selection ? 212.
yields,
If it takes 6|- hrs. to test 9 bus. of seed corn for
213.
germinating power,
enough
A
214.
pound
No. 40 sewing
many yards
A
215.
number
many
will
of cotton can be
thi-ead,
number
into 168 spools of
finer thread
spun
can be made, of which the
How
-f^.
made from
a
pound
?
still
finer thread
of yards in
of cotton
217.
How
?
can be made, of which the
problem 214 equals only
miles of this quality of thread can be
pound
?
200 yards to the spool.
of thread can be
much
spun
A.
of j^ards in the last problem equals
A
216.
take to test seed
it
miles of this fine thread can be
of cotton
many
how long
for 600 A., allowing 1 bu. to each 5
^-J
How
j.
made from
a
?
From one pound
of cotton can be
of bleached muslin worth 8 cts. a yard.
made 4
yards
What amount
lawn can be made from the same amount of cotton if, for every yard of bleached muslin, 2\ yards of lawn may of
be
made
?
The value
218.
of the bleached muslin
What
value of the lawn.
Four yards
is
of sheeting can be
of the
is -^^
the value of the lawn
made from
?
a pound
of cotton with a value equal to | the value of the bleached
muslin.
What
is
the value of the sheeting
?
MISCELLANEOUS REVIEW PROBLEMS
The number
219.
from a pound
is
-J
per yard
What
of the ^f-
If the
of yards of
^| of the price of the sheeting, how yards of calico can be made ? What is the value
price of the calico
many
is
made.
number
of the
made number of yards of number of yards of calico bleached muslin and the
of handkerchiefs that can be
of cotton
calico that can be
363
is
How many
?
handkerchiefs
the value of each,
is
the value of a yard of lawn
if
can
be
made ?
one handkerchief equals |
?
220. The value of the denim that can be made from a pound of cotton bears the same ratio to the value of gingham as the number of yards of lawn to the number of handkerchiefs. \ as many yards of denim as gingham can be made. With gingham worth 7| cts. a yard, what is
the
denim worth per yard?
221.
pound
Arrange
in
tabulated
form
products
the
of
a
cotton from the smallest quantity of material
of
at lowest price
to
the
most valuable product here con-
sidered, 222.
An
about 14
untreated loblolly pine fence post, It lasts about 2 yrs.
cts.
interest at 5 per cent,
post?
what
is
set,
costs
Compounding the
the annual cost of such a
If a preservative treatment,
which
costs 10 cts., in-
creases the length of use of the post to 18 yrs., what is
then the total cost of a post, set?
amount
to annually,
compounded
Assuming that there a mile of fence, what is the saving each This is the interest on what amount at
saving due to treatment per year ? are 200 posts to
year for a mile 5 per cent?
?
What does this What is the ?
as above
PRACTICAL ARITHMETIC
364 223.
The accompanying
table
shows the production in
thousand feet of the leading kinds of lumber for 3
What was
the total production for each year ?
yrs.
What was
the per cent of increase or decrease of each kind from
1899 to 1906?
What
the total per cent of increase or
decrease ?
1906
Mfeet
Mfeet
Mfeet
9,658,923
11,533,070
11,661,077
1,736,507
2,928,409
4,969,843
7,742,391.
5,332,704
4,583,727
3,420,673
3,268,787
3,537,329
Oak
4,438,027
2,902,855
2,820,393
Spruce
1,448,091
1,303,886
1,644,987
944,185
1,279,237
1,386,777
633,466
587,558
882,878
495,836
749,592
839,276
1,115,242
853,554
683,132
Redwood Red gum
360,167
519,267
659,678
285,417
523,990
453,678
Yellow pine Douglas fir White and Norway pine
Hemlock
Western pine Maple
....
Cypress
Poplar
Chestnut
206,688
243,537
407,379
Basswood
308,069
228.041
376,838
Birch
132,601
224,009
370,432
Cedar Beech Cottonwood
232,978
223,035
357,845 275,661
....
415,124
321,574
Elm
456,731
258,330
224,795
Ash
269,120
169,178
214,460
All others
486,848
684,526
936,555
224.
A
tree
cent carbon. the tree?
weighing 10,000
How many
lbs.
pounds
when dry
263,996
is
50 per
of carbon are there in
MISCELLANEOUS KEVIEW PROBLEMS
365
Carbon dioxide being ^\ carbon, and all the carbon of the tree being derived from carbon dioxide, how many pounds of carbon dioxide are required to furnish the 225.
carbon in the tree of the 226.
of
air
dioxide
%
are required
to furnish this
?
how many pounds amount of carbon
?
cubic yards
amount
problem
carbon dioxide,
Air weighing 31.074
227.
many
last
Air being .03^
of
per 100 cu.
grs.
of carbon used in the
ins.,
how
required to furnish the
are
air
growth
of the tree
men-
tioned above ?
There are
228.
in the
atmosphere of the earth about
6,000 billion pounds of carbon dioxide.
does
contain?
it
lem 224 would
An
229.
carbon. lion,
For how many
to the
carbon
trees like that of prob-
this suffice ?
adult exhales daily into the air about 245 g. of
Estimating the earth's population at 1400 mil-
how much carbon
230.
How much
is
thus restored daily to the air
?
Wood, coal, etc., in burning restore their carbon One manufacturing works thus restores from air.
the coal burned about 5,100,000 lbs. of carbon.
A
forest consisting of
how many
trees like the
one men-
tioned in problem 224 would be raised from this carbon?
One square meter of pumpkin or sunflower leaf in a summer day of 15 hrs. makes 25 g. of starch which is How many cubic meters of air are required 1^ carbon. 231.
to furnish the requisite carbon ?
How
long a room 3 m.
wide and 3 m. high would be required to contain 232.
Convert
all
it ?
the measurements of the last problem
into English measure,
and
solve.
PRACTICAL ARITHMETIC
366 233.
If Alfalfa
hay contains 10.44 per cent digestible and 1.2 per cent fats,
protein, 39.6 per cent carbohydrates,
and red-clover hay contains 6.8 per cent protein, 35.8 per what is the cent carbohydrates, and 1.7 per cent fats,
—
difference in the feeding value of a ton of Alfalfa and a
ton of red clover, estimating digestible protein at 3 a pound, carbohydrates at 1 a
pound 234.
ct. a
pound, and fats at 21
cts.
cts.
?
On
land worth $65 an acre Alfalfa
maintained for 4 yrs. at an expense of 130. harvesting the hay
is
$1.25 a ton
;
is
sowed and
The
the crops are
:
cost of
1st year
2.78 tons, 2d 3.15 tons, 3d 4.60 tons, 4th 4.28 tons.
What
is
the profit on 9 acres, allowing 10 per cent inter-
on the value of the land, $12 a ton for hay, and $3 a ton for cost of baling and marketing ? est
APPENDIX SURFACES OF SOLIDS
The surface of a solid except its base or bases is called the Lateral Surface. The Entire Surface includes its bases. solid, the base of which is a polygon and the sides of which are triangles meeting at a point or vertex, is called a
A
Pyramid.
The distance from the vertex to the side of the base is called the Slant Height. If the sides and angles of the pyramid are respectively equal and the apex is directly over the centre of the base, the pyramid is said to be regular. The surface of a pyramid, as may be seen, is composed of a number of triangles with an altitude equal to the slant height of the pyramid and the bases forming the perimeter of the solid. solid, the base of which is a circle, and the surface of which tapers to a point or vertex, is called a Cone. The lateral surface of a cone may be assumed to be made up of a number of infinitely small triangles. Hence, to find the lateral surface of a pyramid or cone, multiply the perimeter of the base by ^ the slant height. The portion remaining after a part of the top has been cut from a pyramid or cone is called a Frustum of a pyramid or of a cone. The lateral surface of a frustum of a pyramid may be regarded as composed of a number of trapezoids, the sum of the parallel sides of which forms the perimeter of the
A
367
PRACTICAL ARITHMETIC
368
bases and the- slant height of which equals the altitude of the frustum. The lateral surface of a frustum of a cone may be considered as made of a number of infinitely
narrow trapezoids.
To
find the lateral surface of the frustum of a pyramid or of 'a cone, multiply half the sum of the perimeters of the two bases by
the slant height.
A
having equal polygons parallel to each other two ends and parallelograms for its sides is a
solid
for its
Prism.
From the form of their bases, prisms are triangular, quadrangular, etc. The lateral surface of a prism may be regarded as a series of parallelograms, with their combined bases equal to the perimeter of the two bases of the prism and a height equal to the altitude of the prism. To find the lateral surface of a prism, multiply the perimeter of the base by the altitude.
VOLUMES OF SOLIDS The volume contains. To find the
of a solid is the
volume
number
of solid units
it
of a prism, multiply the area of the base by the altitude. square prism has three times the solid contents of a pyramid. In like manner, the cylinder has three times the solid contents of the cone. To find the volume of a pyramid or cone, multiply the area of the base by one-third the altitude. The frustum of a pyramid or cone is equal to three pyramids or cones, the common altitude of which is the altitude of the frustum and the bases of which are the
A
APPENDIX
369
upper base, the lower base, and a mean proportional between them. Hence, to find the volume of a frustum of a pyramid ar cone, add to the sum of the areas of the two ends, the square root of the product of these areas, and multiply the result by one-third of the altitude.
A
solid, bounded by a curved surface, every point of which is equally distant from the point within, called the centre, is a
Sphere.
The Diameter of a sphere passes through the centre and terminates at the circumference. The circumferOne-half the diameter is the Radius. ence of the circle, the radius of which is the radius of the sphere, is the Circumference of the sphere. The surface of a sphere is equal to the square of the diameter of the sphere multiplied by 3.1416. sphere may be regarded as composed of pyramids, the bases of which form the surface of the sphere and the altitudes of which equal the radius of the sphere. Hence, to find the volume of a sphere, multiply the surface by one-third the radius, or multiply the cube of the diameter by .5236.
A
THE EXTRACTION OF THE CUBE ROOT Rule. 1. Beginning at units, separate the of three figures each.
number
into groups
2. Find the greatest cube contained in the left-hand Write its cube root as the first figure of the regroup. quired root. 3. Subtract this cube from the first period, and bring down the next period. 4. Divide the number so found by three times the
:
:
PRACTICAL ARITHMETIC
370
square of the root already found, considered as tens, as a trial divisor, to find the next figure of the root. 5. To this trial divisor add three times the product of the two parts of the root plus the square of the second part of the root, to make the complete divisor. 6. Multiply the complete divisor by the second figure of the root subtract and bring down the next period. 7. Continue in a similar way until all periods have ;
been used. For example, to find the cube root of 242,970,624, ceed according to the rule as follows
pro-
242'970'624(624 required root 1st trial divisor X (60 X 2)
3
2^
1st complete divisor 2d ti-ial divisor 3 X (620 X 4) 42
2d complete divisor
216 cube of 1st figure of root 10800 26970 360 22328 product of 2d figure 4 of root with 1st com11164 plete divisor. 1153200 4642624 7440 4642624 product of 3d figure 16 of root with 2d complete divisor. 1160656
Separate into periods. find by inspection or trial that the cube of 6 is the 6 is put down largest cube contained in the first period, 242. as the first figure of the root. 3. Subtracting the cube of 6, 216, from the first period, 242, we have 26 bringing down the next period, we have 26,970. The 4. The root already found considered as tens is 60. square of this is 3600; three times this is 10,800, the trial This trial divisor, 10,800, is contained in the dividend, divisor. 2 is, therefore, set down as the next figure 26,970, two times. of the root. 5. The two parts of the root already found are 60 and 2. The product of 60 x 2 is 120; three times this is 360. The square of the last figure found is 4. Adding 360 plus 4 to the trial divisor, we have the complete divisor 11,164. 6. Multiplying the complete divisor by the second figure of the required root and subtracting, we have 4642. Bring down the next group, 624, giving 4,642,624 for the next dividend. 7. Proceeding as before 1. 2.
We
;
APPENDIX
371
The root already found is 62 or, considered as tens, is 620. The square of this is 384,400. This multiplied by 3 is 1,163,200, the trial divisor. This trial divisor is contained 4 times in the dividend. 4 is, therefore, set down as the next figure of the root.
The two parts of the root already found are 620 and 4. Their product is 2480; three time^ this is 7440. Adding thi.s together with the square of the last number of the root, whicih is 16, to the trial divisor, we have the complete divisor 1,160,656. Multiplying this complete divisor by the last figure found, we have 4,64/!,624, completing the problem. The cube root of 242,970,624 is 624. If the number of vt^hich the cube root is to be extracted has decimal places, divide the figures at both sides of the decimal point into periods of three figures each, annexing ciphers to the last period of the decimal, if need be, to give three figures. There are as many decimal places in the cube root of a decimal as there are periods of three figures each in the decimal. If the number is not a perfect cube, annex ciphers and continue the process to as many decimal places as may be desired. The cube root of a fraction is found by taking the cube root of its numerator and of its denominator, or by reducing the fraction to a decimal and then extracting the root.
PROOF OF THE FUNDAMENTAL PROCESSES BY CASTING OUT NINES Addition.
Add:
71287 67328 79816 42983 54631 316045
7 8
4 8
Add.
1 1
To test accuracy of the addition, cast out the nines from each row and from the sum, setting down the remainders. 1, set down 7; second Thus in the first row drop 7 + 2,
8+
:
;
PRACTICAL ARITHMETIC
372
row drop 6 + 3 and 7 + 2, set down 8 third row drop 9 and 8 + 1, add 7 + 6 = 13, "drop 9 from 13, leaving 4, set down 4 ;
+ +
2 fourth line drop 4 fifth line drop 3, drop 9, set down 8 Prom sum drop 6 3, 5 4, set 6 4 and 6 3, set down 1. down 1. Add the iiumbers set down from the first five numbers, cast out 8 8 7 19, cast out 2x9, leav1, add 4 ing 1. The number remaining being 1 in both cases, the work
+
+
presumably
+
+ + =
+
is
;
+
correct.
Subtraction.
3726813 2619832
Subtract:
1106981
3l
41 Subtract. sj
^
-
Cast out the nines from both minuend and subtrahend subnumber remaining from the subtrahend from that remaining from the minuend, restoring one of the nines cast out, if need be, in order to subtract. If the work is correct, the number so found should equal the number left after casting nines from the remainder. ;
tract the
Multiplication.
Multiply
643 249
4
6787 2572 1286 160107
24
6
Multiply. I
6
Cast nines from multiplier and multiplicand. Find the product of the numbers remaining, and cast nines from it. The number then remaining should equal the number left a,fter casting nines from the product.
ARITHMETICAL PROGRESSION
An Arithmetical Progression is a. series of numbers which increase or decrease by a common and constant difference, e.g., 4, 8, 12, 16, 20, 24, etc., the common difference here being
4.
The numbers
of the series are called its Terms.
;
.
APPENDIX To
any term
find
373
of an arithmetical progression, multi-
ply the common difference by a number one less than the required term; add this product to the first term if the series is increasing; subtract this product from the first term if the series is decreasing. Find the 17th term of the series 7, 14, 21 .
112+7 =
16x7 = 112. Find the 12th term
119.
of the series 217, 213, 209
.
217-44 = 173.
11x4 = 44.
find the sum of the terms of an arithmetical progresmultiply the number of terms by the sum of the first and last terms and divide by two. What is the sum of the first 10 terms of the series
To
sion,
2,4,6
?
9 (2
X
2
=
+ 20)
18.
X 10
18 + 20 = last term. = 110 = sum of the terms.
2
GEOMETRICAL PROGRESSION
A Geometrical Progression is a series of numbers in which any term is equal to the product of the preceding term and a constant factor, e.g., 2, 4, 8, 16, 32, 64 To find any term of a geometrical progression, raise the constant factor to a power one less than the number of the required term, and multiply by the first term. Find the 6th term, of the series 1, 2, 4, 8
——
.
The constant
factor 2 to the fifth power 32. Ans. 32 X 1
= 32.
=
To find the sum of the terms of a geometrical progression, multiply the last term by the constant factor subtract the
first
minus 1. Find the sum
term and divide by the constant of the series
1, 2, 4,
to
8
factor,
and
in-
cluding the 6th term.
The 32
X
last
2
term
= 64.
= 32. 64
The constant
-
1
=
Go.
factor
= 2. =
63 -h 1
63.
Ans.
PRACTICAL AKITHMETIC
374 If the
from the
progression term.
is
decreasing, subtract the product
first
TABLES OF MEASURES LENGTH inches (ins.)= 1 foot (ft.) = 1 yard (yd.) feet or feet, 16J = 1 rod (rd.) 1 5J yards 1 mile (mi.) 820 rods
12 3
=
yds.
rds.
1
= 320 = 1760 = 5280 = 63,360 =i6i =198 1 = 51' =36 1 = 3 =12
1
= 1 inch, used by shoemakers. = 1 common cubit. = 1 sacred cubit. = 1 hand, used to measure
3 barleycorns 18 inches 21.888 inches 4 inches
the
height of horses. 9 inches 6 feet
=1 =1
span.
3 feet
~
P
fathom, used to measure depths at sea.
^
5J paces 8 furlongs 1.15 statute miles
=1 =1 =
3 geographical miles
60 geographical miles 69.16 statute miles
1
,
used in pacing distances.
mile.
geographical nautical mile or
knot. 1 league. of latitude on a meridian, or of longitude
|
I
The length garded
on the equator.
of a degree of latitude is as 69.16 miles, and is that adopted
States Coast Survey.
commonly
re-
by the United
APPENDIX
375
ANGULAR MEASURE 60 seconds (") 60 minutes 360 degrees
= = =
minute
1
(')
degree (°) 1 circumference
1
SURFACE OR SQUARE MEASURE 144 square inches
= 1 square foot (sq. ft.) = 1 square yard (sq. yd.) = 1 square rod (sq. rd.) = 1 acre (A.) = 1 square mile (sq. mi.) = 1 section = 1 township
(sq. ins.)
9 square feet
30| square yards 160 sqiiare rods 640 acres 1 square mile 36 square miles sq. mis.
1
=
A.
1
sq. yds.
sq. rds.
640
= =
= = = =
102,400
1600 1
100 square feet
8,097,600
4840 30J
sq.
= = =
ft.
27,878,400 43,560
272J
1 square (in roofs, floors, etc.)
SOLID OR CUBIC MEASURE
1728 cubic inches (cu. 27 cubic feet cu. yd.
1
=1 =1
ins.)
cu.
=
cu. ins.
ft.
=
27
cubic foot (cu. ft.) cubic yard (cu. yd.)
46,656
WOOD MEASURE 16 cubic feet 128 cubic feet]
8cordfeetl
=
1
cord foot (cd. ft.) a ^ a \
^
= l''°^''i(°^-)
CAPACITY Liquid Measure
4
gills (gi.)
2 pints 4 quarts
= = =
1 pint (pt.) 1 1
quart (qt.) gallon (gal.)
376
PRACTICAL ARITHMETIC
1
pts.
qts.
gal.
=
4 1
1 gallon
g-is.
= 8 = 32 = 2= 8 = 231 cu. ins.
DRY MEASURE 2 pints 8 quarts
4 pecks 2.5 bushels bbl.
= = = =
1
quart
1
peck (pk.)
1
bushel (bu.)
1 barrel (bbl.)
,;
:
APPENDIX
377
WEIGHTS OF PRODUCE The following are minimum weights per bushel
of certain articles of produce according to the laws of various States
Wheat Coru
in the ear
60 70
lbs.
except in Miss., 72 lbs.; 68 lbs.; in Ind. after Dec. 1, and in Ky. after May 1, following the time of husking, it is 68 lbs. 56 lbs., except in Cal., 52 lbs. 56 lbs., except in Cal., 54 lbs.; in La., 32 lbs. 48 lbs., except in Cal., 40 lbs.; lbs.,
in Ohio,
Corn shelled
Rye Buckwheat
1bs.; Ida., N.D., Okl., S.D., Tex., Wash., 42 lbs.; Kan., Minn., N.C., N.J.
Ky.,56 Ore.,
Barley
Oats
Peas
White beans White potatoes Sweet potatoes Onions Turnips Dried peaches Dried apples Clover seed Flax seed Millet seed
Hungarian grass seed Timothy seed
Ohio, Tenn., 50 lbs. lbs., except in Ore., 46 lbs.; Ala., Ga., Ky., Pa., 47 lbs.; Cal., 50 lbs.; La., 32 lbs. 32 lbs. except in Ida., and Ore., 36 lbs.; in Md., 26 lbs.; in N.J. and Va., 30 lbs. 60 lbs. 60 lbs. 60 lbs., except in Md., Pa., Va., 56 lbs. 65 lbs. 57 lbs. 55 lbs. 33 lbs. 26 lbs. 60 lbs., except in N.J., 64 lbs. 56 lbs. 50 lbs. 50 lbs. 45 lbs., except in Ark., 60 lbs. N.D., 42 lbs.
48
.
PRACTICAL ARITHMETIC
378
44 44 50
Blue grass seed
Hemp
seed
Corn meal
lbs. lbs.
48
Bran
20
except in Ala., Ark., Miss., N.C., Tenn.,
lbs.,
Ga.,
111.,
lbs.
lbs.
TROY WEIGHT For Precious Metals, Jewels, 24 grains 20 pennyweights 12 ounces
iS7^ 7000 480 5760
etc.
= 1 pennyweight = 1 ounce = 1 pound
grains grains grains grains
=1 =1 =1 =1
ounce
I
pound
J
ounce
1
(pwt.)
»
rp
pound]
•'
APOTHECARIES' WEIGHT
=1 =1 =1
20 grains 3 scruples 8 drams
12 ounces! 5760 grains 1
=
scruple (sc. or 3) dram (dr. or 3) ounce (oz. or 5 ) ,
-,
.,1
,»
1 P°^"^'l<^l^-°'^^)
APOTHECARIES' LIQUID MEASURE 60 minims 8 fluid drams 16 fluid ounces
8 pints
=1 =1 =1 =1
fluid
dram
(f 3) ounce (fS.) pint (O.) gallon (cong.)
fluid
COUNTING 12 things = 12 dozen = 12 gross = 20 things =
dozen (doz.) gross (gro.) 1 great gross (G. gr.) 1 score
1 1
APPENDIX 24 sheets (paper) 20 quires, or 480 slieets
379
=1 =1
quire
ream
TIME
=1 =1 =1 =1 2 weeks =1 30 (31, 28, 29) days =1 3 months, or 13 weeks =1 12 months, or 365 days =1 365 days 5 hrs. 48 mins. 49.7 sees. = 1 366 days =1 =1 10 years 100 years =1 60 seconds (sees.) 60 minutes 24 hours 7 days
minute (min.) hour (hr.) day (da.) week (wk.) fortnight
month (mo.) quarter year (yr.) (common) true or solar year leap year decade century (C.)
VALUE U.
S.
Money
10 mills 10 cents 100 cents or 10 dimes 10 dollars
=1 =1 =1 =1
c, or ^) dime (di.)
ct. (ct.,
dollar (I) eagle
Canadian Monet
100 cents
=1
dollar
= 11
English Money
12 pence (cZ.) 20 shillings
=1 =1
= *0.243+ = * 4. 8665
shilling (s.)
pound (£)
Ekench Money
100 centimes
=
1 franc (fr.)
= $0,193
German Money
100 pfennigs
=
1
mark (i\I.)= 10.238
PEACTICAL ARITHMETIC
380
Russian
Money
100 copecks
=1
ruble
AUSTEO-HUNGAKIAN MONET
100 kreutzer
=
1 florin
VALUE OF FOREIGN COINS IN UNITED STATES MONEY (Proclaimed by the Secketaky of the Treasury)
Country
APPENDIX
NEGOTIABLE PAPERS
381
382
PEACTICAL AlilTHMETIC
TABLE OF COMPOUND INTEREST Periods
APPENDIX
383
METRIC TABLES MEASURES OF LENGTH 10 10 10 10 10 10 20
millimeters centimeters decimeters
(mm.)=
centimeter (cm.)
1
= 1 decimeter (dm.) = 1 meter (m.) = 1 dekameter (Dm.) = 1 hektometer (Hm.) = 1 kilometer (Km.) = 1 myriameter (Mm.)
meters dekameters hektometers kilometers
MEASURES OF SURFACE 100 100 100 100 100 100
sq. millimeters (sq.
mm.) =
1 sq.
=1 =1 =1 = =1
sq. centimeters sq. decimeters
meters sq. dekameters sq. hektometers sq.
1
sq.
centimeter (sq. cm.) decimeter (sq. dm.)
sq.
meter (sq. m.) dekameter (sq. Dm.) hektometer (sq.Hm.)
sq.
kilometer (sq.
sq. sq.
Km.)
MEASURES OF VOLUME 1000 cu. millimeters (cu. 1000 cu. centimeters 1000 cu. decimeters
mm.)= 1 cu. centimeter (cc.) = 1 cu. decimeter (cu. dm.) = 1 cu. meter (cu. m.)
MEASURES OF CAPACITY 10 10 10 10 10 10
milliliters
(ml.)
centiliters deciliters liters
dekaliters hektoliters
= 1 centiliter (cl.) =1 deciliter (dl.) = 1 liter (1.) = 1 Dekaliter (Dl.) = 1 Hektoliter (HI.) =
1 Kiloliter
(Kl.)
PRACTICAL ARITHMETIC
384
MEASURES OF WEIGHT 10 10 10 10 10 10 10 10 10
milligrams (mg.) centigrams decigrams
grams dekagrams hektograms ,
kilograms
myriagrams quintals
=1 =1 =1 =1 =1 =1 =1 =1 =1
centigram (eg.) decigram (dg.)
gram (g.) dekagram (Dg.) liektogram (Hg.) kilogram ( K.)
myriagram (Mg.) quintal (q.)
tonneau (T.)
METRIC EQUIVALENTS OF ENGLISH MEASURES acre= .4047 hectare. 1 bushel = 35.24 liters. 28.316 liters. 1 cubic foot 1 cubic inch = 16.39 cubic centimeters. 1 cubic yard = .7645 cubic meter. 1 foot = 30.48 centimeters. 1 gallon = 3.785 liters. 1 grain = .0648 gram. 1 inch = 25.4 millimeters. 1 mile = 1.609 kilometers. 1 ounce (avoirdupois) = 28.35 grams. 1 ounce (Troy) = 31.1 grams. 1 peck = 8.809 liters. 1 pint =.4732 liter. 1 pound = .4536 kilo. 1 quart (dry) = 1.101 liters. 1 quart (liquid) = .9464 liter. 1 square foot = .0929 square meter. 1 square inch = 6.452 square centimeterSc 1 square yard = .8361 square meter. 1 ton (2000 lbs.) = .9072 metric ton. 1 ton (2240 lbs.) = 1.017 metric tons. 1 yard = .9144 meter. 1
=
•
APPENDIX
385
ENGLISH EQUIVALENTS OF METRIC MEASURES
=
1 centimeter .3937 inch. 1 cubic centimeter .061 cubic inch. 1 cubic meter 35.31 cubic feet, or 1.308 cubic yards.
=
=
=
1 gram 15.43 grains. 1 hectare 2.471 acres. 2. 205 pounds. 1 kilo 1 kilometer .6214 mile. 1 liter .9081 dry quart, or 1.051 liquid quarts.
=
=
1 1 1 1
= = meter = 3.281 feet. millimeter = .0394 inch. square centimeter = .155 square inch. square meter = 1.196 square yards, or
10.76 square
feet.
1 metric ton
= 1.102
short tons, or .9842 long ton.
CATTLEMEN'S NOTATION Explanation of the Valuk of the Various Notches.
A notch in bottom of the animal's left ear equals 1, two notches equal 2. A notch in top of left ear equals 3, two notches equal 6, three notches equal 9. A notch in bottom of right ear equals 10, two 200 notches equal 20. A notch in top of right ear equals 30, two notches equal 60, three notches equal 90.
A notch
in
end of
left
ear SOOi
equals 100.
A
notch in end of right ear equals 200. A hole in end of left ear equals 400. hole in end of right ear equals 500. A hole in bottom of left ear equals 1000. Numhers can thus he made from 1 to 1999.
A
PRACTICAL ARITHMETIC
386
LUMBERMEN'S NOTATION In marking lumber the following characters are used
A
Al
All
Alii
S
6
7
8
X\
Al
All
15
16
17
X X
XII
XIII
11
1«
13
XIX
X'
/I
X'll
XIII
19
2(}
21
22
23
10
18
Xf
X\
X\l
XMI
XXIil
XMIII
2t
25
26
27
28
29
70
80
50
60
yn
XI
9
Alll
^
90
100
14
)f 30
200
I 40
