A PRACTICAL ARITHMETIC STEVENS
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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....
