Rip
IN MEMORIAM
FLOR1AN CAJOR1
PRIMARY ARITHMETIC
BY
BRUCE M. WATSON
SUPERINTENDENT OF SCHOOLS,
SPOKANE, WASHINGTON
CHARLES E. WHITE
PRINCIPAL OF FRANKLIN SCHOOL, SYRACUSE, M.Y.
D. C. HEATH & CO., PUBLISHERS
BOSTON NEW YORK CHICAGO
Copyright, 1906,
By D. C. HEATH & CO.
1f2
INTRODUCTION
In the preparation of this series of arithmetics the aims have
been:
First, — To secure a high degree of facility in the funda-
mental operations and in those other processes which, in the
actual business of life, are reduced to purely mechanical forms
of computation.
Second, — To cultivate in pupils the habit of forming vivid
mental pictures of the business transactions introduced in the
exercises, and of the commercial and industrial relations of the
numbers involved in the problems.
Third, — To make, at proper times, a clear and rational de-
velopment of so much of the theory of numbers as is necessary
for intelligent arithmetical work.
Fourth, — To grade the work up, from the simple and easy
to the more complex and difficult, by steps so gradual and in
an order so logical, that the pupil will steadily grow in mathe-
matical power and take pleasure in his own progress.
In pursuance of the aims herein outlined, care has been
taken to dwell upon each new process until the child has ac-
quired a considerable degree of skill in it. Then it has not
been permitted to drop out of sight and memory, but has been
kept fresh by continuous and systematic review.
Ill
JV INTRODUCTION
Useless and meaningless distinctions and statements of matter
have been avoided.
The problems of play, of trade, and of industry deal with
things and transactions that are within the experience or knowl-
edge of the child and appeal to his interest.
The numbers used in problems are not so large as to cause
fatigue, discouragement, or waste of time.
In the development work, pupils are directed in a line of
observation or experiment and enabled to obtain their facts
from the numbers and objects studied, rather than from a
printed statement.
The present volume is intended to cover the work usually
accomplished during the first four years of school.
The text-book may be introduced either in the middle of the
second year, or at the beginning of the third. When the
former plan is chosen, the first thirty-one pages, consisting
of oral work involving all combinations of numbers to twenty-
four, will be found to contain sufficient book work for the re-
mainder of the second year. When the latter plan is followed,
the pages covering work that has been accomplished orally in
the second year will serve as review and preparation for the
lessons that follow.
The further distribution of the course through the third and
fourth years must be determined by local conditions, experi-
ence, and age of pupils.
CONTENTS
PAGE
PAGE
Counting ....
1
Quart, Peck, and Bushel .
72
Reading and Writing Numbers
3
Review . . . . .
73
Combinations to 12 .
4
Division
75
Combinations of Two
10
Review
79
Counting by 2's .
13
Multiplication and Division
80
Problems ....
14
Review
81
Yard and Foot .
15
Telling Time . . . .
83
Three. .
16 (^Reading and Writing Numbers
84
One Third . . . .
17 "
Oral Practice in Numbers .
85
Gallon ....
18
Written Practice in Numbers .
87
Two, Three, and Four
19
Review
88
One Fourth . . .
20
Multiplication by 10, 100, 1000 .
89
Five
21
Quick Test . . . .
91
Foot and Inch .
22
Days in the Different Months .
92
Six, Seven, Eight
24
Finding Any Part of a Num-
Combinations to 24 .
27
ber
93
Drill Tables
31
Miscellaneous Problems .
94
Reading and Writing Numbers:
32
Quick Test . . . .
95
Addition ....
33
Review
97
Problems in Addition
43
Miscellaneous Examples .
98
Subtraction
46
Multiplication and Division by
Oral and Written Addition anc
I
Multiples of 10
100
Subtraction
47
Review
101
Problems in Temperature .
54
Pound and Ounce
103
Review ....
56
Review
104
Multiplication .
. 61
Division
105
Review ....
. 63
Quick Test .
107
Roman Numerals
. 64
Review
108
Division ....
. 65
Multiplication and Division
109
Review ....
. 66
Making Questions
110
Multiplication .
. 69
Review
111
VI
CONTENTS
PAGE
Rectangles 112
Multiplication and Division . 114
Making Change . . . . 116
Roman Numerals . . . 116
Miscellaneous Problems . .117
- Halves, Fourths, and Eighths . 122
Miscellaneous Problems . . 123
^Reading and Writing Numbers 124
Review 125
Multiplication and Division . 126
Perimeter 127
Multiplication and Division . 128
Area 131
Division 132
Review 133
Odd and Even Numbers' . . 141
Factors 142
Quick Test 143
Factors 144
Multiples 145
Fractions 146
Whole and Mixed Numbers . 149
PAGE
155
157
161-
163
165
166
175
Review ....
Adding Fifths and Halves
Adding Fourths and Fifths
Adding Fourths and Thirds
Adding Halves and Sevenths
Review and Practice .
United States Money
Review and Practice . . .176
Liquid Measure . . . .179
Dry Measure . . . .181
Time 183
Avoirdupois Weight . . .187
Linear Measure . . . .188
Review and Practice . . . 190
Surface Measure . . .194
Prime and Composite Numbers 199
Prime Factors . . . .200
Factors and Multiples . . 201
Cancellation . . . .202
Review 205
Multiplication Table . . .205
Tables of Denominate Numbers 210
PRIMARY
ARITHMETIC
PRIMARY ARITHMETIC
COUNTING
i. Count to twenty.
2. How many boys are there in your class ?
3. Count the children in the class.
4. How many desks are there in your row ?
5. Find twelve pieces of chalk.
6. Find eleven sticks.
7. Lay four sticks so as to make a square.
8. Lay four sticks so as to make a chair.
9. Lay eight sticks so as to make two squares.
10. How many squares can you make with twelve
sticks ?
Note. — These exercises are suggestive of many that may be given.
ii. Write the figures for one, two, three, four, five, six,
seven, eight, nine.
12. Tell as quickly as "you can the number of spots on
each of these dominoes :
• • •• • • • • • •
• • ••• •••••
WRITING NUMBERS
l. Take ten sticks. Tie them in a bundle, thus, g&
11
2. Count out ten such bundles, and call each
bundle "a ten."
3. Put one bundle on the table.
4. Put one stick beside it, thus, 1 1
How many sticks are there ? Bftjj
5. Put another stick with it, thus,
How many sticks are there ? 12 Sill
6. Take another ten and put three with it, thus, j
How many are there ? 13
Go on in this way to nineteen.
7. What does the figure 1 stand for in the number 12 ?
8. What does the figure 1 stand for ? in 13, 14, 15,
16, 17, 18, 19 ?
9. How many tens are there in 11 ? How many over ?
In 14, 15, 16, 17, 18, 19? g
io. In writing ten we use the figure 1 for the ten m
bundle and O to show that there is none over, thus, ^q
li. Take two tens. How many sticks in all ?
12. To write twenty, we use 2 to stand for 2 tens
and O to show that there is none over, thus, ^q
13. Take two tens and one, thus,
How many ? Write it, thus, 2 1
14. Lay counters for 22, 23, 25, 27, 29.
15. Lay counters for thirty, thirty-one, forty-three.
READING AND WRITING NUMBERS
3
1. Write fifteen ; twenty ; eighteen ; fourteen.
2. Write twenty-five ; thirty-seven ; forty ; ninety-six.
3. Write eighty-two ; seventy ; forty-nine ; sixty-one.
4. Write the number of desks in your room.
5. Write the number of stars on our flag.
6. Write your own age.
7. Count fifty, forward and backward.
8. Write in words 16, 19, 20, 43, 69, 38, 42, 71.
9. Write the number of books on the teachers desk.
io. Write the number of panes of glass in your school-
room.
li. Read 25, 21, 38, 45, 36, 28, 72, 64.
Write them in a column so that the tens will be in a
vertical line.
12. Count forward and backward from 50 to 100.
13. Write in figures all the numbers to one hundred
that have 0's in them.
14. Write in figures and in words the number of desks
in your row.
15. Write in figures and in words the number of letters
in your name. *
is. Read 15, 37, 58, 34, 96, 82, 67, 77, 17, 83, 39, 51.
17. Write in figures, ninety-one, twenty-seven, sixty-eight,
ninety-three, thirty-five, fifty-three.
18. Write the number of squares
in this drawing.
19. Write the number of dots.
• • • •
• • • •
• • • •
• • • •
COMBINATIONS TO 12
1. There are how many drums in this picture ?
2. One is a bass drum. How many other drums are
there ? How many fifes are there ?
3. How many more drums than fifes are there ?
4. Four fifers, one color bearer, and one leader are
how many boys ?
5. Four fifers and six drummers are how many boys ?
6. If the boys march around two squares, how many
blocks will they march ? Draw the squares.
7. If they march three blocks away, and then back to
the starting place, how many blocks do they march ?
8. If they march 2 miles on Monday and 3 miles on
Tuesday, how many miles do they inarch in both days ?
9. When they march 3 blocks with music and 4 blocks
without, how many blocks do they march ?
io. When they march around the square twice, how
many blocks do they go ? Make a picture of the square.
11. If they have marched 9 blocks away from home
and 5 blocks toward home, how far from home are they?
COMBINATIONS TO 12
Keep pint and quart measures before pupils.
What is the first measure ?
For what do we use it ?
What is the second measure ?
For what do we use it? Which
is the larger ?
Fill the pint measure with water. Pour it into the
quart measure. Do it again. How much more will the
quart measure hold ? How many pints does the quart
measure hold ?
1. How many pints make a quart?
2. The quart measure will fill the pint measure how
many times ?
3. Two quarts are how many pints ? Measure and
prove it. Three quarts ? Four, five, six quarts ?
4. How many quarts are there in 4 pt. ? Six, eight,
ten, twelve pints? (pt. stands for pint or pints)
5. Mary bought 3 quarts of milk. How many pints
did she buy ?
6. Alice filled a pint measure four times from a pitcher
of water. How many times would the pitcher of water
fill a quart measure ? Why?
7. How many pint bottles can be filled from five
quarts of cream ?
8. How many quart cans will 12 pints of sirup fill ?
9. How many pints of milk will 3 pint bottles and
one quart bottle hold ?
6 COMBINATIONS TO 12
1. I spent 2 cents for a yeast cake, and 4 cents for
candy. How much, did both cost?
2. Mary had 3 red roses and two yellow ones. How
many had she in all ?
3o Two birds have how many wings ?
4. Four boys have how many thumbs ?
5. Three horses have how many ears ?
6. If we work six days in a week, how many days do
we rest ?
7. Two dogs have how many feet ?
8. A dime is made of silver. It is the same as ten
cents.
A dime less two cents is how many cents ?
9. How many oranges are there in a dozen ?
10. Find the cost of 3 pranges at 2 cents apiece.
11. Add:
4632272125
1122423421
3112213332
12. Subtract :
6475488458
22 3 2457332
13. Count by 2's from 1 to 11.
14. Count by 2's from 2 to 10.
is. Count by 2's from 10 to 2.
16. Count by 2's from 11 to 1.
COMBINATIONS TO 12
1. What two numbers added make 3 ?
2. Add. two numbers to make 5.
3. Add two numbers to make 4.
4. Add two numbers to make 6.
5. What two numbers added make 7 ?
6. What three numbers added make 7 ?
7. What three numbers added make 10 ?
8. What three numbers added make 8 ?
9. What three numbers added make 9 ?
10. Count to 12 by fours.
11. Count to 12 by threes.
12.
6 + ?=8
9-?=3
7 + 2 = ?
5 + ?=9
13.
7 + ?=9
9-?=7
6 + 3 = ?
3 + ? = 9
14.
2 + ?=5
6-?-2
7-2 = ?
5 + ? = 7
15.
5 + ?=9
10-t-4
?-4 = 6
?-6 = 4
16.
3 + ?=6
7-?=2
?+3 = 6
7-5 = ?
17. Name the days of the week.
is. Which is the first day ? The fourth? The seventh?
19. How many working days in two weeks ?
20. How many days are 2 days less than a week ?
2i. A week and 3 days are how many days ?
22. There were 7 apples in a basket. Frank took 1 in
each hand. How many were left ?
23. Eight boys went to the store for milk. Each
bought a pint. How many quarts did they buy ?
8 COMBINATIONS TO 12
Many years ago, the Romans wrote numbers by means
of letters. We use letters to make the numbers on the
face of the clock, to number the chapters in a book, and
for a few other purposes.
The Roman way of writing the first five numbers is
this:
I stands for one. Ill stands for three.
II stands for" two. IV stands for four.
V stands for five.
1. Using letters, write the number of eyes you have ;
the number of thumbs on one hand ; the number of fingers
on one hand ; the number of quarts in six pints ; the num-
ber of school days in a week.
2. When you attend school only 3 days in a week,
how many days are you absent ?
3. When the sun shines only three days in a week,
how many days are cloudy ?
4. Frank earned 10 cents and gave his sister 2 cents.
How much money had he left ?
5. Lucy has 3 cents. How many more cents must she
have to buy a ten-cent jumping rope ?
6. If Will earned 2 cents on Monday, 3 cents on Tues-
day, and 4 cents on Saturday, how much did he earn ?
7. 28329 25365
+ 7 +2 +2 +5 +2 +10 +3 + 7 +4 +5
+J>
+ 2
+ 10
9
-7
7
-_5
7
-2
8. 4 9 5 9 7 7 8 10 11 10
-2-2-3-7 -5-2-3-7-2-5
COMBINATIONS TO 12
4 I *
1
i
1. Draw a line. Cut it into two equal parts. What
is one part ?
2. Fold your paper once in the middle. It is whut
part as large as before you folded it ?
3. Point to one half of the circle at the top of the page.
4. Point to one half of the square at the top of the page.
5. One half of 4 cents is how many cents ? (Picture.)
6. Take six counters. Find one half of them. One
half of six are how many ?
7. Find one half of eight; of 10 ; of 12.
8. Half a dozen apples at a cent each cost how
much ?
9. George bought a half dozen apples and gave 4 to
Rose. How many had he left ?
io. 4 days and how many days make a week ?
li. How many cents in a half dime ?
12. 2 4 3 2 6 3 2 10 12 11
x3x2x3xox2x4x2 -3 -6 -5
10 COMBINATIONS OF TWO
i. Make 6 marks. Group them by 2's. How many
2's in 6 ? Group them again, showing 2 halves of 6.
One half of 6 is how many?
2. Do the same with 8, 10, 12, 14, 16, 18, 20.
3. • Read 42, 89, 76, 98, 73,100.
4. Read I, IV, V, III, II.
5. Add:
6653 4 25843
2326411123
3175432233
2112243223
6. 334289 10 325
^^^x7x^x2x2x3x_3x2
7. 2)6 3)6 2)1 2)8 2)10 3J9" 2)12 4JS
a 3)12 4)12 5)To 3)15 6)12 2)13 7jl?
9. Find J of 6 cents ; l of 14 marbles ; \ of 8 birds.
10. 4 5 7 2 8 2 2 14 10 5
+ 2 +2 +2 +4 4-2 +11 +13 +1 +2 +3
—
—
ii. 5 8
9
5
7
7
8
11
12
11
-2 -3 -
4
-3 -
-4 -
-3
-5
-5
-6
-6
12. Add:
2 3 2
4
8
7
3
2
9
1
1 4 5
3
1
2
2
1
1
2
111
1
2
3
4
2
2
3
2 5 2
2
1
1
1
4
1
6 -
COMBINATIONS OF TWO
11
i. VI = 5 + 1*=6 VII = 5 + 2 = 7 VIII = 5 + 3 = ?
2. X=10 IX=10-1 = 9 XI = 10 + 1 = 11
XII - 10 + 2 = ?
3. How many 2-cent stamps would cost as much as
a 1 2-cent kite ?
4. How many school days in 2 weeks? How many
working days ? How many days in all ?
5.
What did the stamps on these letters cost ?
6.
7.
Five 2's are how many ? Six 2's are how many ?
Write in Roman :
The number of cents in a dime.
The number of feet your cat has.
The number of pints in 4 quarts.
The number of lemons in a dozen.
The number of eggs in a half dozen.
/. The number of days in a week.
g. One less than a dozen.
Grace is reading Chapter X in her book and Frank
is reading Chapter VII. Grace is how many chapters
ahead of Frank ?
a.
b.
c.
d.
e.
8,
12
COMBINATIONS OF TWO
i. Count these dots by 2's: IJt 4 ••••*••••
How many 2's are there ? How many dots are there in
the upper row ? In the lower row ? Twelve dots are
what part of 24 dots ?
2. Make dots to show two 2's ; three 2's ; four 2's ;
five 2's; seven 2's; nine 2's; six 2's; eleven 2's.
3. How many 2's are there in 4 ? In 8 ? In 10 ?
In 14? In 20? In 22 ? In 16? In 24 ? In 6?
4. Show that there are two 12's in 24, thus,
= 12
= 12
5. Show that there are two 8's in 16.
6. Show how many tens there are in 20.
7. This domino shows that 6-4-6 =
12, that 12-6 = 6, that two 6's=12,
that six 2's =12, and that | of 12 = 6.
8. This domino shows that 5 +
4 = , that 9 — 5 = , and that
9-4 = .
9. Tell what is shown by each of these dominos :
• • • •
• • • •
• • • •
• • • •
• • • •
• • • •
• • • •
• • • •
io. 2 4 8 12 7 5
+ 2 +4 +8 +12 +7 +5
• • •
• •
•
• • •
• •
o
3
9 11 10
+ 3
+ 9 +
11 4-10
COUNTING BY 2'S 13
i. count. : : : : :
1 3 5 7 9 11
2. 9 and 2 are how many ?
3. count. :::::::::: 19 + 2 = ?
4. 29 + 2 = ? 39 + 2 = ? 49 + 2 = ? 59 + 2 = ?
69 + 2 = ? 79 + 2=? 89 + 2 = ? 99 + 2 = ?
5. Count by 2's from 1 to 99.
6. Count by 2's from 99 to 1.
7. John had 7 marbles and bought 6 more. How
many had he then? Show by a picture.
8. 7 + 6 = ? 6 + 7 = ? 13-6 = ? 13-7 = ?
9. Arthur paid 8 cents for a tablet and 6 cents for
pens. What did both cost? 8 and 6 are how many?
10. William had 14 cents. He paid 6 cents for a quart
of milk. How many cents had he left ? (Picture.)
11. A boy found 14 eggs in a nest and sold a dozen.
How many were left ? Show by a picture.
12. Add :
6266226211
1 ' 3 2 3 2 24332
353173 1121
2221122233
1113581451
13. Subtract :
4 5 8 11
13
9
8
10
12
13
14
15
2 3 5 6
7
3
2
5
_7
6
8
_7
14 PROBLEMS
1. A year and 3 months are how many months ?
2. Our baby is 11 months old. How old will he be
3 months from now ?
3. A dozen and three oranges are how many oranges ?
4. Make dominoes that count 5, 7, 10, 9, 11.
5. A dozen and 4 eggs are how many eggs ? (Picture.)
6. Alice is 16 years old and Ethel 4 years younger.
How old is Ethel ?
7. James picked 9 quarts of cherries and Donald 4
quarts. How many quarts did both pick ?
8. A boy earned 14 cents and gave his sister 11 cents.
How many cents had he left ?
9. How many evening papers at 2 cents apiece will
18 cents buy ?
10. How many shoes in 10 pair? In 12 pair?
n. Nine robins have how many feet ?
12. How many 2's in 14 ? 20 ? 22 ? 24 ? 18 ? 16 ?
13. Find \ of 8 books; of 12 pints; of 16 cents; of
10 dollars.
14. Answer each of these questions in three ways :
? + ?=10
? + ?=
16
?
+ ? =
14
?+?=15
3-? = ?
14-? =
?
13
-? =
?
16-?= ?
17. Add
•
6 6
5
3
4
3
1
7
3 7
2 3
2
6
4
5
2
3
2 1
3 1
7
2
4
2
3
4
4 2
2 1
1
5
2
1
4
6
3 8
YARD AND FOOT 15
Note. — If possible, let each pupil be provided with a yardstick. At
/east have several. Let pupils have much practice in estimating and meas-
uring.
i. Draw a line 1 yard long on the blackboard.
2. Find something in the room a yard long or wide.
3. How long do you think the schoolroom is ? How
wide ? Measure it. Find something 1 yard high.
4. Name some things that are always measured by the
yard.
5. Without the yardstick draw a line one yard long.
Measure and correct it. A line 2 yards long.
6. How long do you think the blackboard is ? Meas-
ure it, and see how nearly correct your estimate is.
7. Hold your hands 1 yard apart. Hold them 1 yard
above the floor.
Note. — yd. stands for yard or yards.
8. What will 2 yd. of ribbon cost at 7 cents a yard ?
9. How many yards of ribbon will 22 cents buy at
2 cents a yard ?
10. Draw a line 1 yd. long. Divide it into 3 equal
parts. What is one of these parts ?
n. Hold your hands one foot apart. Draw a line 1 foot
long. Hold your hand one foot above your desk.
12. How many feet high are you ?
13. Without a rule draw a line 2 feet long. Measure
and correct it. Do the same with lines 3, 4, 5, and 6 feet
long.
16 THREE
i. How many feet are there in 2 yd. ? In 3 yd. ? In
4 yd. ? In 5 yd. ?
Note. — ft. stands iorfoot or feet.
2. How many yards in 15 ft. ?
3. A line 6 yd. long is how many feet long ?
4. A line 6 ft. long is how many yards long ?
5. Count by 3's from to 24 and back to 0.
6. Two 3's are how many ? Four threes ? Seven 3's ?
Six 3's? Three 3's? Five 3's? Eight 3's?
7. Nellie's father is 6 ft. tall. His height is the same
as how many yards ?
a
beven yard
Is 01 cl<
oth are
ikm
v many
lei
et li
ongT
9.
7 + 3 = ?
9-t
-3 = ?
12
+ 3 =
= ?
13 + 3 = ?
10.
5-3 = ?
11-
•3 = ?
8
-3 =
= ?
9-3 = ?
n.
Add:
4
4 3
4
2
3
4
5 7
3
6 5
7
1
4
6
1 2
5
3 3
3
3
2
3
2 3
3
12.
3 7
Subtract :
2
4
3
1
1
1
2
3 1
1 4
13
12 15
16
11
11
12
10
9 10
7
6 3
_4
_9
2
3
_T_
5 J
13.
8
Multiply :
3 4
11
12
9
10
3
2 7
2
5 3
2
2
2
2
3
4 3
14. DimVfe; 2)6 3)6 4)12 3)12 3)15 8)16 2)14
ONE THIRD 17
i. Divide a yard into feet. One foot is what part of
a yard ? One third of 3 ft. is how many feet ?
2. One third of 6 cents are how many cents ? 2 ! 2 i 2
3. How many 3's in 6 ? $ of 6 = ? §§§
How many 2's in 6 ? $ of 6 = ?
4. J of 9 feet are how many feet ?
5. ^ of 3 yd. are how many yards ?
6. Three 3's are how many ?
7. ^ of 9 dots are how many dots ?
8. How many 3's in 9 ?
• • •
• • •
• • •
9. IJour times 3 are how many ?
• • •
• • •
10. How many 3's in 12 ? 1 of 12 = ? HI
11. A ribbon 12 ft: long is how many yards long ?
12. Five 3's are how many ? Show this by a picture.
13. | of 15 = ? How many 3's in 15 ?
14. Six 3's are how many ? ^ of 18 = ? How many 3's
in 18 ? Show this with dots.
15. An orchard has 3 rows of trees with 8 trees in a
row. How many trees in the orchard ? Make a picture
of it.
18 GALLON
Keep the measures before the class.
1. What measures are these?
For what is the quart measure
used? For what is the gallon
measure used ?
2. Fiji the quart measure with
water. Pour it into the gallon measure. Repeat till the
gallon measure is full. How many times did you empty
the quart measure? How many quarts make a gallon
(gal.) ? Write on the blackboard what you have learned.
3. How many quarts in 2 gallons ? In 3 gallons? In
6 gallons ? In 5 gallons V In 4 gallons ?
4. How many pints in 1 gallon? In 2 gallons?
5. A gallon of milk costs how much at 5 cents a
quart ?
6. Two quarts were spilled from a gallon of water.
How much remained?
7. What must I pay for a gallon of vinegar at 6
cents a quart ?
8. Eight quarts are equal to how many gallons? 16
qt. ? 24 qt. ?
9. Count by 4's from to 24 ; from 1 to 13 ; from 2
to 18; from 3 to 15 ; from 2 to 26.
10. -| of 4 qt. are how many quarts ? How many quarts
in a half gallon ?
li. Count by 3's from 1 to 37 ; from 2 to 38.
12. Count by 2's from to 50 and back ; from 1 to 51
and back.
TWO, THREE AND FOUR 19
1. 9 + 2 = ? 19+2 = ? 29 + 2 = ? 39 + 2 = ?
2. 11-2 = ? 21-2 = ? 31-2 = ? 41-2 = ?
3. When you buy 5 quart bottles and 2 pint bottles of
milk, how many quarts do you get ?
4. 234353246
+ 2 +2 +1 +4 +2 +4 +3 +2 +2
5. 754768656
-2 -4 -2 -4 -3 -3 -1 -4 -4
6. XIII = 10 + 3 = 13. XIV = 10 + 4 = ?
7. Express 13 and 14 in Roman notation.
8. Copy in figures and give answers :
III + II = ? V-III = ? V-II = ? IY + VIII = ?
V + III = ? II + X = ? V + VII = ? VIII + V = ?
9. 3 4 3 4 4 2 12 10 11
x6 x4 x8 x6 x5 x8 x2 x2 x2
10. 4)12 3)15 4)20 3)21 4)24 4)16 4)l2 3)18
n. XV = 10 + 5 = 15. XVI = 10 + 6 = ?
12. Express in Roman all the numbers to 16.
13. Copy in figures and give answers:
V + V = ? VIII + IV = ? III + IX = ?
14. Add: 15. Subtract:
46324 697548
11232 233245
34424
16. Count by 3's from 1 to 22.
20
ONE FOURTH
i. How many fourths are there in the square ? In the
line ? In the circle ? In the orange ?
2. Draw a foot line and divide it into four equal parts.
What is each part called ?
3. One quart is what part of a gallon ?
4. One fourth of 8 is how many ? J | J | J | J
5. Show with dots J of 12 ; of 20 ; of 16 : of 24.
6. How many 3's in 12 ? How many 4's in 12 ?
7. How many 4's in 20 ? How many 5's in 20 ? How
many 4's in 24 ? How many 6's in 24 ?
8. How many are three 4's ? Four 5's ? Four 6's ?
9. If a pound of candy costs 20 cents, what does \ of
a pound cost ?
10. 16 + 4 = ? 8-2 = ? Jof8 = ? £ofl6 = ?
n. XVII = 10 + 7 = 17. XVIII = 10+ 8 = ?
XIX = 10 + 9 = 19. XX = 10 + 10 = ?
12. Write in figures : I; III; V; X; IX; XI; VIII;
XIII; XV; XIV; XII; II; VI; VII; XVI; XX.
Note. — Enlarge and fix the idea of fourth by having papers cut in
various forms, and then cut or folded into fourths.
FIVE 21.
i. Count by 5' s to 50 and back ; from 1 to 36 and back.
2. A nickel is equal to a half dime. Two nickels are
the same as how many cents ?
3. Three lives are how many ? Seven fives ?
4.5 + 4 = ? 4 + 5 = ? 9-4 = ? 9-5 = ? 5+? = 7
5. 5 + 5 = ? 10-?=5 6 + 5 = ? 8 + 5 = ? 7 + 5=?
6. Give answers in Roman : Two fives = ? Four 5's= ?
7 + 2 = ? 6 + 6 = ? 5 + 5 = ? 9 + 2 = ? 10 + 2 = ?
7. How many school days are there in one week ?
Three weeks ? Four weeks ? Six weeks ? Five weeks ?
8. How many working days in 4 weeks? In 1 week?
In 3 weeks ? In 2 weeks ?
9. How do you find \ of anything ? \ ? \ ? \ ?
10. Draw a line and divide it into 5 equal parts. What
is one of these parts ?
n. What is i of 10 ? Of 20 ? Of 25 ? Of 15 ?
12. Count by 3's from 1 to 37 ; from 2 to 35.
13. Find \ of 18 ; \ of 6 ; \ of 12 ; \ of 22 ; \ of 15.
14. Find \ of 24; \ of 12; \ of 6; \ of 16; \ of 15.
15. How many cents had Dick when he had earned 5
cents and his father had given him a nickel ?
16 Nina's bank contained 13 cents and she took out
a half dime. How much remained ?
17. Jack had 3 cents. How much more did he need to
buy a 10-cent ball ?
is. 9 + 5 = ? 10 + 5 = ? 12 + 5 = ? 11 + 5 = ? 13 + 5 = ?
22 FOOT AND INCH
i. With a rule, draw a line one foot long. Divide it
into 12 equal parts. What is one of these parts ? How
many inches make one foot? (in. stands for inch or
inches.)
2. Divide the foot line into halves. How many inches
in one half of a foot ?
3. Divide the foot line into thirds. How many inches
are ^ of a foot ? -^ of 12 inches are how many inches ?
Four is what part of 12? How many 4's in 12?
4. Divide the foot line into 4 equal parts. What part
of a foot is one of these equal parts ? How many inches
in J of a foot ? How many 3's in 12 ? What part of 12
inches is 3 inches ?
5. How many inches in 2 ft. ? 2x12 = ?
6. A foot and 2 in. are how many inches ?
7. A foot and 3 in. are how many inches? A foot
less 3 in. ? Hold your hands 3 in. apart ; 6 in. ; 10 in.
8. How many inches wide do you think your desk is ?
Measure it and see.
Note. — Have much estimating and measuring to fix ideas.
9. A chalk box is 8 in. long and 4 in. wide. How
many inches of string would reach around it ?
io. How many inches around an inch square ? A 2-inch
square ? A 3-inch square ? A 4-inch square ? A 5-inch
square ? A 6-inch square ? Draw these squares.
n. How many feet in 24 inches ? 12 inches are what
part of 24 inches ?
12. Count by 3's to 36. How many 3's in 36 ?
FIVE
23
mu)
1 Q^tf ufj£(L£
30 ! L—
-t'/ a pml
bJ ' «&L,
JwBfsi
^■^^» m»-^
mfm
^^^te^^,
^^s=-— - -
1. This picture shows 9 girls and their teacher, starting
for the park, which is 12 miles from the city. The car
passes through a village 7 miles from the city. That is
how far from the park ? Draw a line to show the railroad,
and make crosses on it to show the city, village, and park.
2. Each seat in the car will hold 5 persons. Count by
5's and find how many persons can be seated in the car.
3. How many seats were needed for this party ?
4. How many persons will 6 seats hold ?
5. At the village 5 more girls joined the party. How
many girls were there in the party then?
6. The fare from .the village to the park is 5 cents.
How many cents did the 5 girls pay ?
7. How many fares would 2 dimes pay ?
8. The entire trip was made in 1 hour. How many
miles did the car go in a half hour ?
9. Mary had 14 cents to use at the park. She bought
a bag of peanuts for a nickel and some candy for 4 cents
What did she pay for all ? How much had she left ?
24 SIX
1. Count by 6's from to 24 ; from 2 to 20 ; from 3
to 21 ; from 5 to 23 ; from 4 to 22.
2. How many working days in 2 weeks ? In 4 weeks ?
In 3 weeks ? In 5 weeks ?
3. Count by 6's from 24 to 0.
4. Julia bought a tablet for 6 cents. She gave the
clerk a dime. How much change should she receive ?
5. Sarah is 12 years old. Mary is 6. What is the
difference between their ages ?
6. If Grace is 6 years older than Sarah, how old is
Grace ?
7. What must be paid for a slate worth a dime and a
picture worth 6 cents ?
8. How many papers must Frank sell at 2 cents apiece
to get 10 cents ?
9. Eleven marbles and six marbles are how many ?
10. If you can buy 6 marbles for a cent, how many can
you buy for 4 cents ?
n. Twelve is what part of 24 ? 6 is what part of 24 ?
12. Six inches are what part of a foot ? 3 inches ?
13. Six is 1 of what ? ^ of what ? 1 of what ?
14. Add :
6666626662
6666265122
666664537
6612346C
6 6 3 2 2 2 1
SEVEN 25
1.
Count by T
s fro
m to 28 ;
from
28 to 0.
2.
Add:
7
7 7
7
5
7
6
7
4
1
7
7 7
3
2
5
2
3
7
9
7 7
4
6
7
3
7
2
3
7
2
7
3
. 7
1
7
7
3.
Midtiply :
7
7 7
6
5
3
5
3
2
4
2
3 4
4
6
6
4
5
7
4
4.
Subtract :
7
9 11
14
19
16
12
13
10
15
7
7 __7
J7
__7
J_
J_
_7
J7
J7
5
7)14 7)28
7)21 \
iyf 3)i5
3)18
6)18
4]2i
6.
Add:
'7
2 2
7
t
7
6
7
5
7
7
2 2
3
4
5
3
3
7
6
4
7 7
3
3
3
2
3
2
5
3
2 6
6
4
2
7
3
2
4
7. Count by 7's from 1 to 29 ; from 5 to 26.
s. 17-7 = ? 19-7 = ? 19-12 = ? 7 + ? = 14
9. | of 14 marbles are how many marbles ?
10. 7 is J of what number ? \ of what ?
' n. How many days are there in 2 weeks ? In 3 weeks ?
In 4 weeks ? A week is what part of 21 days ?
26 EIGHT
i. Count by 8's to 24. 8 + 8 + 8 = ? Three 8's are
how many?
2 . 8 + 8 = ? 16-8 = ? 8 + ? = 16. 16 + ? = 24.
3. What is J of 24? How many 8's in 24?
4. 8 cents and a half dime are how many cents? A
dime and 8 cents? 8 cents and what make a dime?
5. A dozen pencils are how many more than 8?
6. How many quarts in a gallon? How many pints
in a quart? How many pints in a gallon?
7. How many pints in 2 gallons? In 3 gallons?
8. A dozen and 8 lemons are how many lemons?
9. Draw on the blackboard a figure like
this, making it 10 inches long and 8 inches
wide. How many inches across both ends?
Across both sides? Across one end and one side?
io. 10 + 10 = ? 8 + 8 = ? 10 + 8 = ? 18-10 = ?
11. Mary is 11 years old and Helen 8. What is the
sum of their ages? 11 + 8 = ? 19-11 = ? 19-8 = ?
12. Dorothy is 11 years old and Helen 7. What is the
sum of their ages? 18-7 = ? 18-11 = ? ? + ?=18.
13. A foot and 7 inches are how many inches? A foot
and 9 inches? A foot and 11 inches? A foot and 10
inches?
14. 13
15
16
17
23
21
18
17
-8
-7
-8
-9
-11
-11
-10
-10
is. 3)24 6)24 12)24 8)24 4)24 6)12 2)16
COMBINATIONS TO 24 27
1. My rule is 2 feet long. How many inches long is it ?
2. 14 oranges are how many more than a dozen ?
3. Harry visited his uncle, 15 miles from Harry's home.
He rode 12 miles and walked the rest of the way. How
far did he walk ?
4. Willie had 16 marbles and lost 4. How many had
heleft? 16-4 = ? 12 + 12 = ? 12x2 = ? 14-12 = ?
5. 12 cents and a half dime are how many cents ?
6. A half dozen cakes are how many cakes? How
many are a dozen and a half dozen ? 12 + 6 = ? 12 + 5 = ?
7. Jennie had 2 dimes. How many cents had she ?
She bought a pad for 8 cents. How many cents had she
left? 20-8 = ? 12 + 8 = ? 20-12 = ?
8. To-day is the 12th day of the month. A week from
to-day is what day of the month ? 12 + 7 = ? 19 - 12 = ?
19-7 = ?
9. Ralph has 21 chickens; 9 of them are white and
the rest are brown. How many are brown ? 21 — 9 = ?
10. A dime and 12 cents are how many cents ?
n. A foot and 11 inches are how many inches ?
12. Add :
11
4
2
2
13.
4
9
3
6
3
2
5
6
5
2
2
5
4
4
5
2
3
1
7
6
5
6
5
3
6
9
12
5
12
3
5
6
17
16
21
23
19
18
15
13
-9
-7
-11
-12
-11
-12
-9
-7
28 COMBINATIONS TO 24
i. XXI = 10 + 10 + 1 = 21 XXII = 10 + 10 + 2 = ?
XXIII= 10 + 10 + 3 = 23 XXIV = 10 + 10 + 4 = ?
2. Write in Roman all the numbers to 24.
3. 6 gallons of cream are how many quarts ?
4. 24 cents will buy how many 8-cent tablets ?
5. 24 peaches are how many dozen ? (Picture.)
6. How many pints of milk in 12 quarts?
7. A rule is 2 ft. long. How many inches long is it ?
How many 6-inch pieces would it make ? 4-inch pieces ?
8. Add :
884 12 11 2854
712 3 32425
316 2 49366
285_3J8235
9. 8 2 3 2 4 8 12 5 6
x3 xll x8 x8 x6 x2 x2 x4 x3
10. Multiply :
6 6 6
5
4
4
8
9
3
3 4
5
4
3
5
2
2
5
11. Add :
5 2
2
2
1
2
2
2
5
6 2
2
9
5
5
5
2
2
3 5
8
4
7
5
5
5
10
2 7
5
1
3
6
4
9
10
12. 5)25 5)20 5)10 4)20 3)15 2)10 5)15 6)12
COMBINATIONS TO 24
29
1. How many tenpins are there in this game? They
were set in 2 rows ; how many were there in each row ?
2. If they were set in 3 rows, how many would there
be in each row ? (Picture it.) If they were set in 4 rows ?
(Picture.) If they were set in 6 rows ? (Picture.)
3. Each boy has four plays. Charles puts down 3 ? 7,
5, 2. James puts down 8, 6, 4, 2. Which wins ?
4. Here is the score. Find who wins in each game.
a.
James
Charles
James
Charles
James
Charles
8
9
b.
8
2
c.
6
4
3
5
5
2
2
6
5
2
7
3
4
3
2
3
3
12
6
4
7
6
e.
6
4
/•
10
11
3
4
7
11
3
2
8
3
5
1
7
2
5
2
10
11
Note. — Play more games, varying them.
30 COMBINATIONS TO 24
i. Helen has a half dime. May has 3 times as much.
How much money has May ? How much have both ?
2. Jennie earned 14 cents and paid a dime for note
paper. How much had she left ?
3. Divide 20 cents among 4 girls. How much does
each get ?
4. A dime, a half dime, and 2 cents are how many
cents ?
5. How many shoes do 9 children wear ?
6. If a lady writes one letter a day, what do her postage
stamps for a week cost ?
7. How many candles are there in 3 boxes if each box
holds six ?
8. How many feet in 8 yards ?
9. In a rose bed are 3 rows of bushes, with 8 bushes
in each row. (a) How many rosebushes in the bed?
(Picture.) (b) How many bushes in 2 of the rows? If
there were 4 rows, how many bushes would there be in
each row ? (Picture.)
DRILL TABLES
Note. — The drill tables on page 31 contain those additions and sub-
tractions that require most repetition. It is a waste of time to repeat com-
binations that are perfectly known.
Copy these tables on the blackboard and go through them daily as a
rapid drill exercise. Vary the order, sometimes going across and sometimes
up and down. Occasionally let pupils take turns in pointing while others
answer.
In the subtraction table, let results be given in both forms "4 from
12 leaves 8 " and " 4 aud 8 are 12."
DRILL TABLES
31
See note, page 30.
ADDITION DRILL TABLE
9
2
7
4
12
8
9
11
3
6
5
2
11
s 8
12
7
11
12
11
12
8
4
11
5
10
5
9
12
5
8
9
5
2
12
9
11
7
4
12
11
12
11
8
12
6
3
12
6
6
7
7
6
4
3
6
9
8
5
7
11
4
7
4
11
9
5
8
9
11
8
7
10
3
8
6
5
6
4
9
7
8
9
12
11
9
12
7
6
SUBTRACTION DRILL TABLE
12
4
18
9
18
7
16
8
22
12
16
9
14
11
17
9
18
12
10
6
19
9
15
9
11
8
17
5
13
7
17
11
11
4
14
7
10
4
15
11
12
9
11
5
23
12
14
9
21
11
12
7
13
4
24
12
16
11
20
12
20
11
13
8
14
12
11
2
13
11
15
8
16
12
19
7
19
11
21
12
22
11
15
12
17
7
9
4
12
8
20
9
18
11
19
8
16
7
22
10
14
3
17
8
18
6
8
5
14
8
15
6
11
3
17
12
13
6
17
6
11
7
10
5
16
6
15
4
10
3
11
6
23
11
14
5
21
10
12
5
13
9
8
3
16
5
20
8
7
4
13
5
14
2
11
9
13
2
15
7
16
4
19
12
12
6
21
9
8
4
12
3
9
6
9
5
32 READING AND WRITING NUMBERS
1. One hundred is written 100 ; two hundred is written
200 ; five hundred is written 500.
Write four hundred ; seven hundred ; eight hundred.
2. Read 300 ; 600 ; 700 ; 400 ; 200 ; 500 ; 900.
3. 324 is read, three hundred twenty-four.
642 is read, six hundred forty-two.
Read 759; 483; 279; 585; 986; 361; 416; 313.
4. Write four hundred twenty-one ; three hundred
forty-nine ; six hundred fifty-two ; one hundred forty-one ;
two hundred ninety-one ; seven hundred sixteen ; nine
hundred seventy-seven.
5. Six hundred nine is written 609.
Eight hundred ten is written 810.
Write three hundred eight : four hundred six ; nine hun-
dred one ; two hundred fifteen.
6. Read 749 ; 982 ; 507 ; 308 ; 701 ; 209 ; 685 ; 420.
7. Read 385 ; 769 ; 835 ; 429 ; 651 ; 910 ; 203 ; 519.
a Read 999; 807; 666; 342; 111; 405; 612; 711.
9. Read 359 ; 460 ; 580 ; 307 ; 222 ; 809 ; 980 ; 630.
10. Write five hundred ninety ; five hundred nine ; nine
hundred forty-one; three hundred sixty; four hundred
six ; eight hundred seventy ; five hundred fifty-five.
n. The right-hand figure is called units' figure, the
second, tens' figure, the third, hundreds' figure.
634 is 6 hundreds, 3 tens, and 4 units.
Tell the number of hundreds, tens, and units in 246 ;
321; 245; 807; 650; 718; 320; 510; 408; 907.
Written ADDITION 33
i. Add 59 and 8.
59 8 units and 9 units are 17 units.
8 17 units = 1 ten and 7 units.
g^ 1 ten and 5 tens are 6 tens. 67
2. Add 68 and 96.
68
96
164
6 units and 8 units are 14 units.
14 units = 1 ten and 4 units.
1 ten, 9 tens, and 6 tens are 16 tens.
16 tens == 1 hundred and 6 tens. 164 Answer.
Note. — Explanations of processes in addition, subtraction, multiplica-
tion, and division should not be dwelt upon unduly. Yet it is well for
children to see how results are obtained, though they may not be required
to repeat an intricate analysis of the operation.
Add:
3. 28 4. 36 s. 93 6. 29 ?. 43 a 78 9. 66
4 7 8 9 9 3 8
10.
42
8
ii.96
_9
12.28
3
13. 46
5
14.29
_6
15.37
_8
16.42
9
17.
86
33
.is. 42
69
19.96
25
20. 18
73
21. 16
46
22. 19
43
23. 86
44
24.
35
48
25. 96
57
26. 98
63
27. 99
34
28. 10
48
29. 70
30
30. 52
19
31.
87
24
32.85
49-
33.18
14
34. 17
15
35. 67
24
36. 45
85
37. 93.
29
34 ADDITION Written
Add:
i. a. 7 6. 5 c. 4 d. 2 e. 12 /. 22 g. 22 h. 12
4 4 7 4 17 31 11 11
3 6 2 6 30 42 33 11
213 520^42124
2. a. 41 J. 51 c 41 <?. 51 6. 61 /. 72 g. 33
13 42 20 62 33 80 55
21 63 75 73 40 61 40
13 12 32 80 54 53 61
30 4 units, 6 units, 5 units, and 8 units, are units.
45 23 units = tens and units.
16 2 tens, 3 tens, 1 ten, 4 tens, and 2 tens are tens.
34. tens = hundred and tens. 123 Answer.
4. a. 15 6. 24 c. 17 d. 15 e. 54 /. 12 g. 19
24 16 34 34 47 24 82
35 33 23 26 32 16 41
14 12 52 41 23 35 63
5. a. 22 b. 24 c 17 d. 15 e. 56 /. 17 g. 46
43 33 26 25 34 25 20
14 17 34 37 12 34 32
37 26 43 12 29 40 55
6. a. 23 b. 14 c. 26 £ 25 e. 46 /. 29 g. 92
42 ' 18 13 43 34 41 8
25 22 47 58 55 32 31
12 14 12 64 42 68 40
Oral ADDITION 35
1. Find the whole cost of a pencil at 5 cents, a tablet
at 8 cents, and a stamp at 2 cents.
2. 5 cents, 2 cents, 4 cents, and 12 cents are — — cents.
3. If a peach cost 2 cents, an orange 6 cents, and a
pineapple 12 cents, they all cost — ■ — cents.
4. Add 2 to 9 ; 19 ; 29 ; 39 ; 49 ; 59 ; 69 ; 79 ; 89 ; 99.
5. Add 3 to 8 ; 18 ; 28 ; 38 ; 48 ; 58 j 68 ; 78 ; 88 ; 98.
6. 7 + 4 = ? 17 + 4 = ? 27 + 4 = ? 37 + 4 = ? 47 + 4 = ?
7. 7 + 5 = ? 17 + 5 = ? 27 + 5 = ? 37 + 5 = ? 57 + 5 = ?
8. Add:
7 17 27 37 47 57 67 77 87 97
$. Count by 3's from to 30 ; from 1 to 31 ; from
2 to 32.
10. Count by 4's from to 40 ; from 1 to 37 ; from
2 to 38.
n. Count by 2's from 50 to ; from 49 to 1.
v>. Count by 5's from 1 to 31 ; from 3 to 33.
13. Count by 6's from 30 to ; from 5 to 29.
14. Count by 6 J s from 1 to 31 ; from 3 to 27.
15. Count by 7 J s from to 35; from 1 to 29 ; from
2 to 30.
16. A kite, an orange, a ball, and a top each cost 5 cents
How much did all cost ?
36 ADDITION Oral
i. Add :
7
17
37
47
57
67
77
87
27
7
7
7
7
7
7
7
_7
_7
2.
7
17
27
37
47
57
77
87
67
9
9
9
9
9
9
9
9
9
3.
7
17
57
87
67
37
47
27
77
8
_8
8
8
8
8
8
_8
8
4.
6
16
26
46
36
86
56
76
66
5
_5
_5
5
5
5
5
5
5
5.
6
16
56
86
96
5
15
85
45
4
4
4
4
4
_5
5
5
5
6.
6
16
26
36
56
86
66
46
76
6
6
6
6
6
6
6
6
6
7.
6
16
26
36
46
86
56
66
76
7
7
J_
J_
7
7
_7
7
7
8.
6
16
36
86
56
76
66
46
26
9
9
9
9
9
9
9
9
9
9.
6
16
36
56
26
86
46
76
66
8
8
8
8
8
8
8
_8
8
10.
5
15
25
35
85
75
45
65
55
6
_6
6
_6
6
6
6
6
6
11.
5
15
35
65
85
75
45
25
55
7
J_
J_
_7
7
7
_7
7
j
Written ADDITION 37
i. Add :
24 ] The numbers added are addends.
12 I a 7 7 -J The result of addition is the sum.
36 f
Note. — In adding, do not repeat the figures. In
14 J
86 Sum exara P lel > sa M
4, 10, 12, 16.
2, 5, 6, 8.
2. a. 12 b. 23 c. 24 d. 37 e. 97 /. 54 g. 61
36 27 58 35 35 33 32
24 45 32 46 56 25 45
15 56 46 25 87 29 37
3. a. 13 b. 21 c. 33 d. 39 e. 83 /. 66 g. 98
42 42 24 40 21 42 32
25 31 44 8 40 81 43
67 56 55 60 _9 38 37
4. a. 88 6. 66 c. 99 d. 22 e. 90 /. 42 g. 98
42 42 88 39 88 66 21
36 91 32 42 19 37 32
77 33 41 ^0 18 41 14
5. a. 62 b. 22 c. 32 d. 33 e. 21 /. 61 g. 64
14 44 45 25 15 28 38
28 91 16 40 17 33 21
33 18 94 28 83 25 45
6. a. 22 I. 39 c 29 d. 88 e. 96 /. 24 g. 81
33 41 38 64 38 86 28
44 80 50 49 80 19 72
55 16 96 82 19 81 19
38 ADDITION Oral
l. Add :
5
15
25
65
85
55
75
35
45
9
_9
9
9
9
9
9
_9
9
:. 5
15
85
75
25
55
35
65
45
8
8
8
_8
J8
J5
8
8
8
:. 7
7
7
7
7
7
7
74
7
4
14
34
54
84
64
44
7
24
4. 4 4 4 4 3 13 23 7 7
6162646 7 _7 _7 53 63
5. 4
7
6. 4
8
7. 4
9
s. 3 13 23 8 8 73 8 83 8
i J* _§. i£ 3£ _1 M _1 63
9. 3
14
24
34
44
54
84
64
74
_7
7
7
7
_7
_7
7
7
8
8
54
8
64
44
8
24
14
34
8
74
8
_8
84
_8
14
24
34
9
9
74
9
9
9
9
9
44
54
_9
84
64
13
53
23
73
9
9
33
9
9
9
9
43
83
9
63
12
32
22
52
72
9
9
9
9
9
9
9
_9
82
62
42
io. 2
n. 17+4 = ? 48 + 5 = ? 39 + 7 = ? 56 + 8 = ?
Oral ADDITION 39
1. Count by 2's from to 50 ; from 1 to 51.
2. Count by 3's from to 51 ; from 2 to 47.
3. Connt by 4's from to 100; from 2 to 102.
4. Count by 4's from 1 to 101 ; from 3 to 103.
5. Count by 5's from 2 to 97 ; from 1 to 101.
6. Mrs. Smith buys a pint of cream every day. How
many quarts does she buy in 24 days ?
7. One half of a foot is how many inches? \ of a
foot? \ of a foot? \ of a foot? (Picture.)
8. Five gallons of milk will serve how many customers
if each takes a quart ? If each takes a pint ?
9. Count by 6's from to 96; from 2 to 98; from
5 to 95.
10. Add:
17 7 27 15 29 38 25 33 56
JlI-IAJL-IJL-IJL
li. Count by 7's from to 98 ; from 4 to 95.
12. Count by 7's from 2 to 100 ; from 5 to 96.
13. Go through the addition drill table, page 31.
14. Count by 6's from 1 to 97 ; from 3 to 99.
is. Find l of 24; i of 24; | of 24; J of 24; J of 24.
16. Count by 7's from 1 to 99 ; from 6 to 97.
17. Add:
888888888
19 27 35 46 92 75 43 54 28
40 ADDITION Written
The fourth figure in a number, counting toward the left,
is thousands' figure. 9000 = nine thousand. 3000 = three
thousand. 6241 = six thousand two hundred forty-one.
1. Read 2128; 4521; 7938; 8000; 8106; 2300; 5840;
6007; 9017; 2307; 8111.
2. Write five thousand; one thousand three hundred
sixty-seven ; one thousand nine hundred nine ; four thou-
sand eight ; two thousand ninety-three.
Add up, then down :
3. a. 324 b. 142
132 353
c. 612
225
d. 416
527
e. 423 / 324
576 521
4. a. 351 6. 254 c. 341 d. 649 e. 894 /. 342
460 165 205 427 783 643
243 342 370 583 527 845
5. a. 786 b. 483 c. 213 d. 138 e. 923 / 238
483 547 426 24 761 182
765 592 325 805 302 302
293 384 136 41 50 56
6. a. 314 b. 517 c. 514 d. 235 e. 216 /. 932
280 281 283 415 31 18
179 305 107 800 58 271
250 490 920 70 814 526
303 235 116 J9 _76 _32
Read the addends and the sums in the above examples.
MONEY 41
1. 100 cents make one dollar. We write it $1.00.
200 cents make two dollars. We write it $2.00.
500 cents make five dollars. How would you write it ?
2. 125 cents make one dollar and 25 cents. We write
it $1.25. Seventeen cents is written $.17, 17 ct., or 17^.
349 cents make three dollars and 49 cents. We write it
$3.49. Six cents is written $.06, 6 ct., or 6£ Two hun-
dred twenty-five cents make how many dollars and cents ?
How would you write it ?
3. Read $4.00
4. Read $1.25
5. Read $4.32
.00; $15.00; $25.00; $49.00
,16.
$.08.
$.10.
$.95.
$2.25; $4.35; $6.23; $17.53
$7.50; $8.40; $1.05; $16.10
6. Read $27.20; $8.07; $3.01; $2.10; $30.01
7. Read $2.52; $1.37; $2.49; $3.65; $4.03; $81.20.
8. Read the numbers in question i as cents.
9. Read the numbers in question 4 as cents.
10. $2.43 Read these addends as cents, then as
1.25 dollars and cents. Add them and read the
6.47
sum.
5.81
6.35
n. Read and add :
a. $ 4.23
b. $ .42
c. $3.81
d. $1.86
e. $2.35
6.87
1.37
.59
2.35
4.16
4.19
.58
.47
4.81
.89
12.15
.69
.33
7.63
5.71
8.52
4.73
4.44
.48
.60
42
ADDITION
Oral
l. James had $.29 and found $.02. He then had
— cents.
2. There were 57 sheep in one field and 5 in another.
In both fields there were sheep.
3. How many pupils in a class composed of 23 girls
and 8 boys ?
4. A yard of cloth cost 56 cents and a yard of ribbon
9 cents. They both cost cents.
5. William is 18 years old and Frank is 7. The sum
of their ages is years.
6. Two fours and five threes make how many ?
7. Add:
36 49 36 42 38 64 85 39
78596979
PROBLEMS 43
1. There are 26 pupils in one class, 26 in another, and
40 in a third. How many pupils in the three classes?
2. A farmer raised 387 bushels of corn the first year,
293 the second, 468 the third, and 99 the fourth. How
many bushels did he raise in the four years ?
3. A boat is loaded with 927 bushels of corn, 383
bushels of wheat, 898 bushels of barley, and 629 bushels
of oats. How many bushels in the load ?
4. During the month of June, the meat for our family
cost $7.18, the flour $3.88, the butter $2.79, the sugar
$2.18, and the rent $25. What did all of them cost ?
5. Our lot is 66 ft. wide and 168 ft. long. Make a
picture of it. How far must I go to walk around it ?
6. A girl paid 48 cents for stamps and 37 cents for
postal cards. What did both cost ?
7. Write and add :
Seventy-eight cents ; two dollars and seventy-nine cents ;
16 dollars and eight cents ; eighty-three dollars and seven
cents ; thirty-one dollars and sixteen cents. What are
these numbers called ? What is the answer called ?
8. Henry spent 47 cents for tea, 69 cents for potatoes
and 93 cents for apples. How much money did he spend ?
9. Shoes for $3.50, a hat for $2.50, a suit of clothes
for $17.75, an overcoat for $12.98 and underwear for
$6.56 cost in all how much?
10. Sarah had $ .89 after buying a 50-cent book and a
25-cent comb. How much had she at first ?
44 ADDITION Oral and Written
i. 7 + 7 + 3 + 8 = 2. 6 + 5 + 7 + 2 + 6 =
6+8+6+2= 5+7+6+9+9=
5+3+9+5= 4+6+8+7+4=
8+9+7+7 = 8+8+5+8+3 =
+ + + = ? + + + + =
3. 9 + 6 + 5 + 6 = 4. 7 + 8 + 9 + 6 + 8 =
4+7+8+3= 6+9+4+4+7=
2+5+4+9= 9+5+3+5+5=
8+4+7+5= 5+4+1+3+4=
7+7+6+4 = 3+3+7+8+8 =
+ + + = ? + + + + =
5. 3 + 6 + 4 + 8 = 6 . 9 + 3 + 8 + 10 + 5 = —
5 + 2 + 9 + 6 = 6 + 4 + 2+ 4 + 8 = —
4 + 3 + 2 + 1 = 7 + 8 + 3+ 9 + 2 = —
8 + 6 + 9 + 5 = 6 + + 5+ 7 + 3 = —
+ + + = ? + + ++ =
7. Add :
a. 783 b. 492 c. $6.07 d. % .96 e. $12.10
472 18 .49 4.71 3.19
921 96 .63 5.83 .29
687 439 4.07 6.92 17.00
432 897 _^21 _^88 6.31
8. a. $ 4.83 "6. $8.49 c. $19.07 d. $ 8.36
.79 6.72 10.50 .48
6.85 .36 .18 .90
12.92 4.07 3.98 4.07
13.07 5.60 7.62 16.00
Oral SUBTRACTION 45
i. Take 5 from 7; 13; 17; 15; 10; 9; 12; 11; 8.
2. Take 4 from 9; 11; 13; 16; 12; 7; 15; 10; 14.
3. There are 11 seats in a row. Children sit in all
but two of them. How many children in the row ?
4. Take 3 from 8; 12; 9; 15; 13; 7; 10; 14; 11.
5. Take 7 from 9; 14; 16; 18; 13; 19; 15; 17; 11.
6. May planted 39 rosebushes. Two of them died.
How many lived ? Picture them in 3 rows.
7. Count by 2's from 49 to 1.
8. Take 11 from 15; 13; 17; 11; 21; 19; 22; 23.
9. Take 2 from 11; 21; 31; 51; 61; 81; 71; 41.
10. Take2froml0; 20; 30; 80; 90; 60; 40; 70; 50.
11. John bought some raisins for 12 cents and gave the
clerk 2 dimes. How much change should he receive ?
12. Take6froml2; 14; 18; 9; 11; 17; 15; 16; 10.
13. Take 9 from 12; 10; 13; 15; 17; 18; 21; 19.
14. A half dime and cents make 17 cents.
15. Take 12 from 15; 18; 12; 24; 20; 23; 19; 21.
16. Take 10 from 20; 19; 22; 16; 21; 18; 15; 17.
17. Take8froml0; 9; 13; 20; 15; 19; 16; 18; 17.
18. Luther and John earned 20 cents shoveling snow.
John earned 12 cents. How many cents did Luther earn ?
is. 8 + 7 = ? 15-8 = ? 15-7 = ? 8 + ?=17 7 + ?=17
20. 4 + ? = 12 ? + 8 = 12 12-4 = ? 12-8 = ?
2i. + = 18. + =15.
22. A foot less 7 inches are how many inches ?
46 SUBTRACTION Written
1. From 378 take 135.
378 Minuend 5 units from 8 units leave 3 units.
135 Subtrahend 3 tens from 7 tens leave 4 tens.
243 Remainder 1 hundred from 3 hundreds leaves 2 hundreds.
The number from ivhich we subtract is the minuend.
The number subtracted is the subtrahend.
The result of subtraction is the difference or remainder.
2. From 948 take 716. Which of these numbers is
the minuend? Which is the subtrahend? What shall
we call the result?
3. 836 4. 956 5. 507 6. 738 7, 89 8. 938
-423 -25 -203 -607 -26 -817
9. 769 10. 807 ii. 486 12. 985 13. 631 14. 639
-553 -503 -375 -474 -420 -317
15. 863 is. 347 17. 450 is. 892 19. 298 20. 847
-751 -216 -320 -660 -162 -516
21. The subtrahend is 342 and the minuend 483.
What is the difference?
22. The minuend is 98 and the subtrahend 48. Find
the remainder.
23. What is the difference between 837 and 206 ?
24. How much larger is 984 than 863 ?
25. What number added to 48 makes 89 ?
26. A kite string 897 feet long is how much longer
than a kite string 492 feet long ?
Oral and Written ADDITION AND SUBTRACTION
47
2
5
8
10
7
11
3
12
6
4
9
a. Add 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 to each of
the numbers in the squares.
b. Subtract every number in the squares from 14 ;
from 15; from 16; from 17; from 18.
Add:
2. 5 15 25 35 85 75 45 65 55
666666666
•—
3. 5
15
35
65
85
75
45
25
55
7
J_
7
7
7
7
7
7
jr
4. 2
12
32
22
52
72
9
9
9
9
9
9
9
9
9
82
62
42
5. 38
99
28
85
23
92
86
49
52
74
43
95
95
87
88
78
35
71
6. How much farther is 296 miles than 85 miles ?
7. A bushel of apples cost % 1.25
A box of oranges cost 4.35
A box of soap cost 3.45
A dozen cans of corn cost 1.44
They all cost
8. Find the difference between 104 and 507.
9. $14.28 io. $85.92 n. $86.27 12. $12.86
-12.06 -15.70 -16.15 -9.10
48 SUBTRACTION Oral
1. 30 30 = 20 + 10
-2 2= 2
28 Difference 20+ 8 =28 Difference
2. 73 73 = 60 + 13
-8 8= 8
65 Difference 60 + 5 = 65 Difference
3. Subtract 2 from 10 ; 20 ; 30 ; 40 ; 50 ; 60 ; 70 ; 80.
4. Subtract 3 from 10 ; 20 ; 30 ; 40 ; 50 ; 60 ; 70 ; 80.
5. Subtract 4, 5, 6, 7, 8, and 9 from the same num-
bers as those given in question 4.
6. Subtract 2 from 11, 21, 31, 41, 51, 61, 71, 81, 91.
7. From the same numbers, subtract 3, 4, 5, 6, 7, 8, 9.
8. 12 22 32 42 52 62 72 82 92
^^_2_2_2_2_2_2_2
9. Subtract 3, 4, 5, 6, 7, 8, and 9 from the minuends
given in question 8.
io. 13 23 33 43 53 63 73 83 93
li. Subtract 4, 5, 6, 7, and 9 from the minuends given
in question io.
12. 14 24 94 14 24 34 44 54 64 74
-4
-4
-4 -
_5 _5 _5 _5 _5 _5
-5
13.
84
94
14
24 34 74 84 94
14
-5
-5
-6
-6 -6 -6 -6 -6
-7
Written SUBTRACTION 49
i. One ten = how many units ?
2. One hundred = how many tens ?
3. One thousand = how many hundreds ?
4. From 473 take 135<
473 = 4 hundreds + 6 tens + 13 units.
135 = 1 hundred +3 tens + 5 units.
338 = 3 hundreds 4- 3 tens + 8 units. Difference.
We cannot take 5 from 3. So we take 1 ten out of 7 tens, put it
with 3, making 13 units, and subtract 5 units from 13 units. We
then take 3 tens from 6 tens, and 1 hundred from 4 hundreds. How
do -we get 6 tens ?
5. From 629 take 237.
629 = 5 hundreds + 12 tens + 9 unitSo
237 = 2 hundreds + 3 tens + 7 units.
392 = 3 hundreds + 9 tens + 2 units.
Can you tell how this is done? How do we get 12
tens ? How do we get 5 hundreds ?
6. 981 7. 352 a. 764 9. 662 10. 816 11. 236
-732 -135 -545 -254 -623 -52
12. 149 13. 918 14. 732 15. 608 is. 983 17. 536
-56 -48 -313 -27 -874 -435
is. 439 is. 906 20. 382 21. 641 22. 319 23. 709
-247 -514 -174 -512 -258 -358
50 SUBTRACTION Oral
i. From 15, 25, 35, 45, 55, 65, 75, 85, 95, take 6, 7,
8, and 9.
2. Take 7, 8, and 9 from each of the following num-
bers : 16, 26, 36, 46, 56, 66, 76, 86, and 96.
3. 17 27 37 47 57 67 77 87 97
_8 -8 -8 -8 -8 -8 -8 -8 -8
4. 17
27
37
47
57
67
77
87
97
-9
-9
-9
-9
-9
-9
-9
-9
-9
5. 18
28
38
48
58
68
78
88
98
-9
-9
-9
-9
-9
-9
-9
-9
-9
6. Twenty boys went camping. All but 9 of them
caught cold. How many boys caught cold ?
7. A mother hen hatched 13 chickens. Only 8 of
them lived. How many died ?
8. i I ° If it
is 24 miles from A to C, and 8 miles from A to B, how
far is it from B to C f
9. Ted rode his bicycle 18 miles from home. He
turned about and had ridden 12 miles toward home when
his tire burst, so that he had to walk. How far had he to
walk ? (Picture.)
10. 5 yards are how much more than 9 feet ?
n. Anna bought a tablet for 8 cents. If she gave the
clerk a quarter of a dollar, how much change should she
receive ?
Oral SUBTRACTION 51
i. 18-10 = ? What can you do with 10 and 8 to
get 18 ?
2. What can you do with 12 and 5 to get 7 ? With 5
and 7 to get 12 ?
3. 13-?=9 9 + ?=13 13?9 = 4 9?4 = 13
4. Henry earned $15. He bought some clothes for $7
and put the rest of his money in the bank. How much
did he put in the bank ? How do you find it ?
5. If Henry put $8 in the bank and spent $7 for clothes,
how would you find the number of dollars he had at first ?
6. 12, 18, 6. Show all the things that you can do with
two of these numbers to get the other.
Written
1. 467 Find the remainder. Add the remainder and
325 subtrahend. What do you get ? If you should not
get the minuend when }^ou add the subtrahend and
remainder, what would you think was the reason ?
Since you do get the minuend by adding the subtrahend and re-
mainder, what does it tell you about the remainder ? How can you
find out whether any remainder is correct ?
In the following examples, find the remainders and test your work
by adding the remainder and subtrahend.
2. 342 3. 987 4. 658 5. 709 6. 917
-121 -603 -435 -209 -615
7. $52.63 a $82.49 9. $16.81 10. $12.81
-12.91 -26.39 -7.19 -9.35
52 SUBTRACTION Written
Find the remainders and test your work :
1. 763 2. 307 3. 625 4. 653 5. 719
528 164 218 435 217
6. 947 7. 456 a 887 9. 715 10. 984
615 295 479 263 237
11. $9.35 12. $2.19 13. $9.10 14. $17.25
2.48 1.36 3.50 9.32
15. $59.20 is. $49.37 17. $81.79 is. 865
28.30 25.66 15.63 429
19. $12.93 20. $2.06 21. $4.37 22. $19.28
5.09 1.96 .85 15.00
23. Mr. Brown bought a horse for $245 and sold it for
$190. How much did he lose ?
24. Clarence bought a sheep for $3.75 and sold it for
$5.80. How much did he gain ?
25. Six hundred seven pupils are enrolled in our school.
Five hundred ninety-three are present. How many are
absent ?
26. There are 956 men in a parade ; 784 of them are
on foot. How many are riding ?
27. 1296 28. 4381 29. 981 30. 7120
-473 -2073 -973 -500
31. 2013 32. 408 33. 607 34. 370
-1005 -231 -583 -219
Oral ADDITION AND SUBTRACTION 53
i. 9 and 8 are the two parts of . 8 is one part
of 17 ; the other part is .
2. One part of 25 is 7. What is the other ?
3. William earned $.01 on Monday, $.02 on Tuesday,
$.03 on Wednesday, and so on through the week. How
much did he earn ?
4. Tom and Joe caught 23 trout. Joe caught 12 of
them. Tom caught .
5. Jessie and her mother pared 32 apples. Jessie pared
six. Her mother pared .
6. A postman had 15 days' vacation. He went away
for 8 days. How many days did he stay at home ?
7. Ethel earned two dimes and 2 nickels. In all she
earned cents.
Written
Add toward the top, then toward the bottom :
i. 621
2. 106
3. 264
4. 563
s. 462
143
342
341
692
153
254
260
173
118
247
326
406
462
209
321
243
347
374
712
145
6. 598
7. 390
s. 635
9. 264
io. 246
321
408
962
324
314
607
761
48
149
270
53
29
307
254
186
908
382
42
326
409
54
PROBLEMS IN TEMPERATURE
Written
l The degree of heat that anything has is
called its temperature. What is it that measures
temperature ? When the liquid in the thermom-
eter rises> is it growing warmer or colder ? When
the liquid goes down ?
2. Find zero (0) on this thermometer. What
temperature does this thermometer show now ?
3. Find the freezing point. That is how many
degrees above zero? It is how many degrees
below the boiling point?
4. When the thermometer out of doors shows
10 degrees (10°) below zero, what do you think
the season is ? It is how many degrees below the
freezing point ? What is the season when it
shows 90 degrees (90°) above zero?
5. When it is 49° above zero at sunrise and 18°
higher at noon, what is the temperature at noon ?
6. When the city water is at 58°, how much
must it be heated before it boils? How many
degrees must it cool before it freezes ?
7. The temperature of the body is 98° above 0.
It is how much above the freezing point ?
8. Look at the schoolroom thermometer and
tell how warm the room is. It is how much
cooler than your body?
Note. — Many more exercises may be given, using the
schoolroom thermometer in various locations.
Written ADDITION AND SUBTRACTION 55
1. Subtract and test your work :
a. 6324 b. 4713 c. $78.21 d. $63.92
4516 2804 34.05 44.08
2. Add two hundred nine, five hundred thirty-two,
thirty-six, one thousand three hundred twenty-five, and
eight hundred ten.
3. Add $564.32, $34.27, $248, $6.03, and $48.27.
4. A tank held 634 gallons of oil. 218 gallons leaked
out. How much remained ?
5. A grocer sold 539 pounds of coffee and had 756
pounds left. How many pounds had he at first ?
6. $465.32 + $234.16 4- $72.18 + $8 + $5.01 = ?
7. Separate 506 into two parts, one part being 153.
8. The two parts of a number are 479 and 1088. Find
the number.
9. Claude has $5.08 in the school bank, $16.24 in the
city savings bank, and $1.38 in his purse. How much
money has he ?
10. A farmer sold a load of potatoes to a grocer for
$23.20. He bought some sugar, tea, and flour for $14.18.
How much money should he receive ?
n. A man sold a harness for $12.75, receiving for it a
load of wood and $7.80. What was the wood worth ?
12. Find the difference between :
a. 589 and 692. d. $345.16 and $192.95.
b. 437 and 928. e. 3246 and 8109.
c. $52.26 and $16.19. /. 235 and 1047.
56 REVIEW Oral
i. Some of the things that we have learned :
a. pints make a quart.
b. There are quarts in a gallon.
c. inches make 1 foot.
d. One yard is the same as feet.
e. One dollar is equal to cents.
/. A half dime is cents.
g. Ten cents make one .
h. The numbers added are .
i. The result of addition is the .
j. The number from which a number is subtracted is
the .
k. The remainder or difference is .
Z. We may test our work in subtraction by
2. A house that is 8 yd. wide is feet wide.
3. A cow that gives 12 qt. of milk gives gallons.
4. A rule that is 24 inches long is feet long.
5. Two dimes and a half dime make cents, or
one of a dollar.
, 6. Express your age in Roman numerals.
7. There are 24 rosebushes in 3 equal rows; how
many in a row? (Picture.)
8. How many oranges at 4 cents apiece can I get for
2 dimes ?
9. Harold is 9 years old. How old will he be 8 years
from now? 12 years? 16 years? 7 years? 13 years?
10. Count by 8's to 32 ; by fours ; by 2's.
Written REVIEW 57
i. A merchant bought 459 yd. of silk, 847 yd. of flan-
nel, 1027 yd. of muslin, 439 yd. of prints, and 2348 yd. of
broadcloth. How many yards did he buy ?
2. A city has 429 miles of streets. If 238 miles are
paved, how many miles are unpaved ? Test your work.
3. Add three thousand forty dollars fifteen cents ; two
hundred twenty-seven dollars fifty-six cents ; and ten dol-
lars forty-nine cents.
4. Two men start from the same place ; one travels east
983 miles; the other travels west 479 miles. They are
then how many miles apart ? (Picture.)
5. A man earned $ 581 in one year, $ 748 the next,
and $857 the next. a. How much did he earn in the
three years? b. If he spent $1479, how much did he
save ?
6. Express in Roman numerals :
a. The number of feet in a yard.
b. The number of quarts in a gallon.
c. The number of feet in 7 yards.
d. The number of inches in a foot.
e. The number of cents in a dime.
/. The difference between 25 and 8.
g. The number of cents in two dimes.
A. Your age.
i. The number of pints in 2 gallons.
j. The number of school days in 3 weeks.
7. Write in figures VI, VIII, IX, XI, XIII, XIV, XVIII,.
XXII, XIX, XXIV.
58 REVIEW Oral
i. Eight years from now May will be 20 years old.
How old is she now ?
2. What coin is J of 20 cents ? | of 20 cents ? \ of
a dollar ?
3. Nellie had 21 cents and spent J- of it. a. How
many cents did she spend ? b. How many cents has she
left?
4. There are 24 hours in one day. How many hours
in £ of a day ?
5. Eight 2's less five 3's are how many ?
6. Five kittens have how many paws?
7. Six squares have how many corners? Cut them
from paper, then fold them into halves and quarters.
8. Kate had 33 peaches and gave away 9. How many
had she then ?
9. If 3 pounds of dates cost 21 cents, what will one
pound cost ? What will 2 pounds cost ?
10. 12 + ? = 22 ? + 9 = 21 12 + 11 = ? 10 + ? = 22
ii. Read 5007; 2010; 5080; XIX; XIV; XXIII;
XIII; IX.
12. 24 lemons are how many dozen ?
13. Make a problem for 7 + 6 ; for 3x6; for 21 — 11 ;
for 15-*-3; for 2x7; for 12-5-2; for 10 + 5.
14. 2 dozen oranges less 6 are how many ?
is. Add and subtract:
14 35 49 85 76 27 68 53 93
853753497
Oral MULTIPLICATION AND DIVISION 59
i. How many 2's in 10? 18? 20? 12? 14? 24? 22?
2. What is i of 8? 4? 10? 16? 12? 14? 24? 20?
3. Count by 3's to 24 and back; from 2 to 26 and back.
4. How many 3's in 24, 18, 12, 21, 15, 9, 6?
5. What is £ of 6? 9? 15? 21? 12? 18? 24?
6. 4 + 4 + 4 + 4 + 4 = ? How many 4's did yon add to
get 20? Then 20 is how many 4's? In what other way
than by addition can you find five fours ?
7. Count by 3's until you have the sum of five 3's.
8. In what other way could you have found the value
of five 3's ? Which is the shorter way ?
9. Find, by addition, seven 4's; eight 4's; nine 4's;
ten 4's ; eleven 4's ; twelve 4's.
io. How many 4's in 40 ? 28? 36? 44? 16?
ii. What is J of 24? 12? 16? 44? 36? 28?
12. How many are three 4's? Five 4's? Ten 4's?
Twelve 4's? Nine 4's? Eleven 4's? Eighths? Six 4's?
13. 20
16 How many 4's are there in 20? How did
— 4 we find it ?
12 In the same way, find how many 3's there
-4 are in 12; 3's in 27; 4's in 32; 5's in 30;
8 5's in 40; 4's in 48; 5's in 60.
4
60
MULTIPLICATION AND DIVISION
Oral
28 12 30 6's
2. What is the cost of twelve 2- cent stamps?
3. Jessie is 9 years old ; her brother is twice as old.
How old is her brother ?
4. How many pints will a 10-quart pail hold ?
5. How many pints in a gallon ? In 2 gallons ? In
3 gallons?
6. a. Our schoolroom is 36 feet long. How many
yards long is it ? b. It is 9 yards wide. How many feet
wide is it ?
7. Five gallons of oil will fill a quart lamp how many
times?
8. If 3 lemons will make a pitcherful of lemonade,
how many such pitchers of lemonade will a dozen lemons
make?
9. Twenty-four eggs are how many dozen ? 48 eggs ?
10. 5 10 5 6 12 5 5 4 6
x2 x5 x4 x5 x5 xll x3 x6 x5
Written MULTIPLICATION M
i. If one cow costs $ 42, what will 4 cows cost ? Find
it by addition.
We may also find it by multiplication, thus:
$ 42 4 times 2 units are 8 units.
4 4 times 4 tens are 16 tens, or 1 hundred and 6 tens.
diQgg $ 168. Answer.
Multiply and test your work by addition :
2. 64 3. 82 4. 51 5. 94 6. 93
J? A A A A
7. 71 8. 82 9. 41 10. 83 u. 71
_5 _3 _6 _2 __6
12. 843 is. 544 14. 932 is. 510 is. 811
_2 _2 _2 J> _5
17. 802 cents is. 601 cents 19. 712 cents 20. 433 cents
A A A A
21. 510 cents 22. $8.02 23. $6.01 24. $7.12
_6 4 5 4
25. If John's coat cost $4.20, what must be paid for 3
such coats ?
26. Find the cost of 5 colts at $41 apiece.
27. Find the cost of :
a. Three bushels of apples at 63 cents a bushel.
6. Four pounds of steak at 22 cents a pound.
c. Five baskets of peaches at $1.10 a basket.
d. Two city lots at $ 940 apiece.
62
MULTIPLICATION
Written
73 4 times 3 units are 12 units = 1 ten and 2 units.
a 4 times 7 tens are 28 tens.
292
28 tens + 1 ten = 29 tens = 2 hundreds and 9 tens.
292. Answer.
2.
48 Multiplicand.
2 Multiplier.
96 Product
The number multiplied is the
multiplicand.
77ie number by which we multi-
ply is the multiplier.
The result of multiplication is
the product.
Multiply and test your work by addition :
3. 69 4. 79 5. 65 6. 78 i. 431 a 243 9. 45
2 2 3 3 4 3 6
10.
82 11.
531 12. 263
13.
984 14. 782 15. !
85 16. 873
4
3 3
2 3
3 2
17.
$2.83
2
is. $4.84
2
19.
$3.82 20. $6.51
4 5
21. $5.18
3
22.
$7.19
3
23. $1.62
4
24.
$5.91 25. $8.09
5 4
26. $4.15
6
27.
$7.19
28. $66.21
29.
$2.47 30. $921
31. $450
3
4
2 4
3
32.
$17.08
3
33. $16.05
4
34. $42.83
2
35. $34.84
2
36. Read:
a. The multiplier in example 35. b. The product in
example 32. c. The multiplicand in example 25.
Oral REVIEW 63
i. Add 7 to 4, 8, 9, 5, 17, 16, 2, and 11.
2. Subtract 8 from 14, 24, 34, 44, 54, 64, 74, 84, 94.
3. 24
34
44
54 64
74
84
94 104
-7
-7
— 7 -
-7 -1
-7
-7
-7 -7
4. Subtract 9 from 14, 24, 34,
44, 54
,64,
74, 84, 94.
5. 21
42
73
56
32
71
54 81
-7
-8
-9
-8
-3
-7
-6 -7
6. 33
71
83
96
73
52
42 61
-4
-2
-4
-9
-8
-5
-3 -9
7. 4)32 5)25 4)28 4)48 3)21 3)27 3)24 2)24
8. 3)36 5)45 2)22 4)36 4)40 4)24 4)28 7)28
Written
9. 813 10. 493 li. 290 12. 840 13. 237 14. 800
-633 -234 -164 -650 -156 -720
15. 931 is. 815 17. 790 is. 841 19. 126 20. 371
-702 -442 -683 -724 -86 -232
21. Find the difference between :
a. 234 and 986. 6. 642 and 437. c. $29.38 and $46.91.
d. 834 and 1052. e. 293 and 86. /. 6428 and 9275.
64 ROMAN" NUMERALS
i. XXV = 20 + 5 = 25. XXVI = 20 + 6 = 26.
XXVIII = 20 + 8 = ?
2. XXIX = 20 + 9 = 29. XXX =10 + 10 + 10 = ?
XXXI = 31. XXXII - ?
3. XXXIII = 30 + 3 = 33. XXXIV = 30 + 4 = 34.
XXXV = ?
4. XXXVI = 30 + 6 = 36. XXXVII = 30 + 7 = ?
XXXVIII = ?
5. 39 = 30 + 9. Write it in Roman.
6. L = 50. LI = 51. LIV = 50 + 4 = ?
7. Write 55 in Roman. Write 56, 57, 58, 59.
8. XL = 50 - 10 = ? XLI = 40 + 1 = ? XLII = ?
9. Write in Roman 43, 44, 45, 46, 47, 48, 49.
10. LX = 50 + 10 = ? LXV = ? Write 66, 68, 69.
ii. LXX = 50 + 20 = ? Write 72, 74, 75, 76, 78, 79.
12. LXXX = 50 + 30 = ? Write 81, 83, 84, 86, 87, 89.
is. C = 100. XC = 100-10 = 90. XCII = 90 + 2 = ?
14. Write 93, 94, 95, 96, 97, 98, 99.
Read the following examples in class.
Copy them in figures and find the products.
is. XXVIII x IV is. XIX x III 17. XLxV
is. LVxIV 19. LXV x III 20. XLIVxVI
21. LXXVIIIxIII 22. XCVIIxII 23. XCIVxIV
24. LXXXIXxIII 25. XLIXxII 26. LIXxV
27. A set of books consists of 3 volumes. Each, volume
contains LXXXV chapters. How many chapters in all
the volumes ?
Written DIVISION 65
i. A farmer raised 864 bushels of oats and sold half of
them. How many bushels did he sell ?
432 bushels ■£ of 8 hundreds = 4 hundreds.
n\ool h 11 i °f °* tens = ^ tens *
■| of 4 units = 2 units. 432 bushels. Answer.
2. 2)426 3. 2)284 4. 2)648 5. 2)886 6. 3)936
7. 3)630 8. 4)884 9. 4)408 10. 5)550 11. 6)606
12. } of' 660 = ? 13. J of 933 = ? 14. J of 840 = ?
Dividend Divisor Quotient
15. 682 divided by 2 =
The number divided is the dividend.
The number by ivhich ice divide is the divisor.
The result of division is the quotient.
Find the quotients :
Dividend Divisor Dividend Divisor
is. 480 4 is. 336 3
17. 606 6 19. 505 5
20. A farmer brought 248 eggs to market. -J- of them
were broken. How many eggs were broken ?
21. Two hundred sixty-six pupils attend a certain school.
There are just as many boys as girls. How many boys are
there ? How many girls ?
cents cents cents
22. 4)448 cents 26. 3)933 cents 30. 2)228 cents
23. 4)$T48 27. 3)$ 9.33 31. 2)$2^8
24. 8446-2 28. 6060-3 32. 6060-*- 6
25. $5.50-*- 5 29. $6.93-*- 3 33. $24.88-*- 2
66
REVIEW
Oral
i. One orange for 5 ^, a lemon for 2 f, and a pineapple
for 15^ cost how much? (Picture.)
2. 11 ft. is how much more than 3 yd. ?
3. Three quarts more than 4 gal. are how many quarts ?
4. 30 boys are arranged in 5 equal lines. How many
boys in each line ? (Picture.)
5. If 1 man can build a wall in 27 days, in how many
days ought 3 men to build it ?
6. In 4 weeks there are how many school days ?
7. How many weeks in 21 days ?
a 40 + 20 = ? 50 + 30 = ? 16 + 12 = ? 57 + 9 = ?
9. \ of 24 cents are how many cents ?
10. Add 2, 3, 4, 5, and 6 to 14, 25, 36, 47, and 58.
11. Add 6, 7, 8, and 9 to 14, 25, 36, 47, 58, and 69.
12. Add 5, 6, 7, 8, and 9 to 16, 38, 57, 89, and 65.
13. Count by 6's from to 72.
14. One pint more than 12 qt. is how many pt. ?
Add each of the numbers
in the outer ring to every
number in the inner ring.
Written REVIEW 67
i. 369 + 483 + 754 + 96 + 9 = ?
2. 432x2 = ? 561x2 = ? 823x3 = ? 483x3 = ?
3. There are 144 pencils in a gross. How many are
there in 2 gross ?
4. Lucy divided 486 beads equally between Mabel and
Sarah. How many did Mabel receive ? Sarah ?
5. a. Some of our expenses for a year are :
Food $462.23 b. If our income is $1292.50,
Clothing 154.35 how much have we left?
Doctor and Medicine 48.54* c. How much is our income
Taxes 61.08 for 3 years ?
Books and Papers 28.40 d. What are these expenses
Fuel and Light 68.39 for 2 years ?
Total
6. Albert has collected 191 postage stamps. Ralph
has 5 times as many. How many has Ralph ?
7. 237 + ? = 543. 543-? = 237. 306 + ? = 543.
8. How many quarts in 862 gallons ?
9. How many quarts in 862 pints ?
10. How many pints in 232 gallons ?
n. Find by addition twelve 5's ; seven 4's ; twelve 3's ;
four 8's ; five 10's ; four ll's ; eleven 4's.
12. Find by subtraction how many 4's in 48 ; 7's in 35;
5's in 35 ; 4's in 32 ; 8's in 32 ; ll's in 44 ; 4's in 44.
13. Write the table of 2's to 2 x 12.
14. Write the table of 3's. 15. Write the table of 4's.
16. Write the table of 5's.
68 MULTIPLICATION AND DIVISION Oral
1. Add five 6's ;. add six 6's ; add seven 6's; eight 6's;
nine 6's ; ten 6's ; eleven 6's ; twelve 6's. Learn the
sums, and recite them, thus : Six 6's are , etc.
2. How many 6's in 30 ? How many 5's in 30 ?
30 + 6=? 30-5=?
3 . 30 = 6x ; 30 = 5x ; 7x6 = ;
42 + 6 = ; 42 + 7 = .
4. How many 6's in 42 ? How many 7's in 42 ?
5. =6x9; 54 + 6 = ; 54 + 9 = .
6. How many 6's in 54 ? *How many 9's in 54 ? -^ of
54= ? £of 54= ?
7. Eight 6's are ; 6 eights are ; \ of 48
; lof 48 = ; 6x = 48; 8x = 48;
there are 6's in 48 ; there are 8's in 48.
8. How many 6's in 60 ? How many 10's ? \ of
60= ? T Vof 60= ?
9. There are 6 arithmetics in a package. How many
arithmetics in 7 such packages? In 5,. 6, 8, 10, 9 such
packages ?
10. If Arthur can walk 6 miles in a day, in how many
days can he walk 24 miles ? 36 miles ? 42 miles ?
li. 60 is how many 6's? What must we add to 60
to get eleven 6's ? Twelve 6's ?
12 . 6x11 = ; 12x6 = ; 72 + 6 = ;
72 + 12 = ; l of 72 = ; ^ of 66 = ;
6x =66; xl2 = 72; 11 x =66.
13. Write the table of 6's through 6 x 12.
Written MULTIPLICATION 69
6 times 8 units = 48 units = 4 tens + 8 units.
1. 438 6 times 3 tens = 18 tens.
6 18 tens -f 4 tens = 22 tens = 2 hundreds -f 2 tens.
2528 ^ times 4 hundreds = 24 hundreds.
24 hundreds -f- 2 hundreds = 26 hundreds = 2 thousands
+- 6 hundreds. 2628 Product.
Find products and test your work by addition : fy\At VK
376x6. is. $8.90x4. *£^£J*a
207 x 6.
$18.06x6. ~ smkJ-a
$15.21x6.
$14.06x5.
$.79x4.
$.93x6.
$2.18x5.
26. Six rows of peach trees, 58 in a row, are how
many trees?
27. 219 tons of coal at $6 a ton cost how much ?
28. Find 4 times 763 by addition ; by multiplication.
29. a. 653 h. 462 c. 325 d. 433 6. 529
3 4 5 4 6
2.
341 X 6.
10.
3.
79x6.
li.
4.
88x6.
12.
5.
72x6.
13.
6.
537 x 6.
14.
7.
169 x 6.
15.
8.
635x6.
16.
9.
249 x 6.
17.
18.
$8.90x4.
19.
$359.87x6
20.
385 x 6.
21.
706 x 6.
22.
395 x 6.
23.
617x6.
24.
534x6.
25.
729 x 6.
— —
~- —
30. a. 453
4
I. 632
3
c. 725
5
d. 634
4
e. 426
3
3i. a. 405
6
b. 327
4
e. 309
3
d. 630
6
6. 743
5
32. How many working days in 349 weeks ?
70 MULTIPLICATION AND DIVISION Oral
1. Find in two ways the value of seven 7's ; eight 7's ;
nine 7's ; ten 7's.
2. 7x9 = ; 7x7= ; 7x10= .
3. 35 is the product of what two numbers ? 56 ? 63 ?
70? 42? 49? 28? 21? 14?
4 . 1 of 70 = ; i of 49= ; 1 of 63 = ;
l f 28 = ; iof 35= ; 1 of 56= .
5. 7xll = ? How did you find it ? 7x12 = ?
6. 8is|ofwhat? 9? 11? 6? 7? 12? 5? 4?
7. How many 7's are there in 21? 35? 49? 70?
84? 63? 77? 56? 42? 28?
8. A schoolroom has 7 rows of desks with 8 in a row.
How many desks in all ? (Picture.)
9. If there were 42 desks in 6 rows, how many would
there be in a row ? (Picture.)
io. Seven boys gathered 49 qt. of nuts and shared them
equally. How many quarts were there for each boy ?
Written
1. Multiply by 7: a. 32. b. 45. c. 67. d. 53.
e. 86. / 95. g. 123. h. 84. I $42.90. / $13.28.
k. .$.99. I 548 pints. m. 764 yards. n. 196 feet.
2. Multiply 841 : a. by 3 ; b. by 4 ; c. by 5 ; d. by 6.
3. Multiply $29.12: a. by 5 ; b. by 6 ; c by 7.
4. Multiply $4.09: a. by 3; b. by 4; c. by 7.
5. How many days in 98 weeks ?
6. If a man earns $ 725 a year, how much will he earn
in 7 years ?
Oral MULTIPLICATION AND DIVISION 71
i. The multiplicand and multiplier are factors of the
product. In 7 x 9 = 63, which number is the product ?
Which are factors?
2. Name two factors of 21; 28; 15; 42; 63; 56;
44; 55; 77; 32; 40; 72; 49; 48.
3. 4x =36; 5x =60; 4x = 44.
4. 7 is a factor of 35. What is another factor ?
5. Answer the following without writing either question
or answer :
42x2 56x2 81x4 92x5 321x2
421x3 32-S-2 93-3 408-4 609 + 6
6. Count by 8's from to 96 and back.
7. Find eight 8's by addition. Name 2 factors of 64.
8. Add 8 to 64. How many 8's in 72 ? 8x? = 72.
9. 8x10 = ? 8xll = ? 8x12 = ? 8x? = 80.
io. 8 and 12 are factors of what number ? 8 and 10 ?
8 and 11? 8 and 7 ? 8 and 9 ? 8 and 6 ? 8 and 5?
li. When a product and one of its factors are given,
how can you find the other factor ?
12. 9x8 = ? 9x9 = ? 9x10 = ? 9xll = ? 9x12 = ?
13. How many 9's are there in 36 ? 54 ? 45 ? 63 ? 81 ?
14. How many 9's in 72 ? 108 ? 90 ? 99 ?
15. Give the multiplication table of 9's ; of 8's ; of 7's ;
of 6's; of 5's; of 4's; of 3's; of 2's.
16. Give the missing factor :
108 = 9x -; 81 = 9x ; 63 = 9x .
72 MULTIPLICATION
Jl
Quart Peck Bushel
Note. — These measures should be before the class and used by
the pupils. Sawdust, oats, or any other light, dry material may be
used to advantage.
1. Which measure is largest ?
2. Which is next ? 3. Which is the smallest ?
4. How many times do you think a bushel of oats
would fill the peck measure ? Try it and see.
5. How many quarts do you think would be needed
to fill the peck measure ? Try it and see.
6. How many quarts make a peck? How many
pecks make a bushel ?
7. Name some things that are measured with these
measures.
8. bu. stands for bushel, ph. for peck, and qt. for
quart. The dry quart is a little larger than the liquid
quart. A half peck is how many dry quarts? How
does it compare with a gallon?
9. Find the number of quarts in a. 53 pk. ; I. 49 pk. ;
c. 85 pk. ; d. 136 pk. ; e. 841 pk. ; /. 79 pk. ; g. ,257 pk.
10. Find the number of pecks in a. 908 bu. ; b. 568 bu.;
c. 912 bu.; d. 846 bu.; e. 932 bu.;/. 711 bu.; g. 894 bu.
Oral
REVIEW
73
i. Count by 7's to 84; by 8's to 96 ; by 9's to 108.
2. What two factors make 36? 44? 55? 48? 64? 72?
3. The product of two numbers is 84. One of them
is 7. What is the other ?
4. A two-bushel bag will hold how many pecks ?
5. 36 pecks of apples will fill how many bushel crates ?
6. A quart is what part of a peck ?
7. What will a peck of berries cost at 12 $ a quart?
8. Answer at sight :
2)486 3)933
4}880
5)105
6)660
986 323 249
-475 +921 +120
86
-24
405
x_4
422 622
x3 x3
Multiply every number in Subtract each number in
the outer ring by each num- the outer ring from every
ber in the inner ring. number in the inner ring.
74
REVIEW
Written
i. See how quickly you can get these .
a. 169 6.980 c. $4.07 A 691 e.-396pk.
x6 x7 x8 -384 x8
2. a. If a sleeping car is 69 ft. long, how long is a train
of 9 such cars? b. If the engine and tender are 57 ftc
long, what is the entire length of the train ?
3. Seven coal trains have 47 cars in each train.
a. How many cars in all ? b. If each car carries 9 tons
of ccalj how many tons are carried by all the cars ?
4. Copy this diagram. Wherever a column and a line
cross each other, write the product of the numbers given
at the top of the column and at the left of the line, as,
10x8 = 80; 4x5 = 20.
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
20
6
7
8
9
10
80
11
12
Oral DIVISION 75
1. How many 2's in 5, and how many over ? In 7 ?
In 11? In 19?
2. How many 3's in 8, and how many over ? In 11 ?
In 16? In 14? In 22 ?
3. How many 4's in 23, and how many over ? In 33?
In 15 ? In 21 ? In 38 ?
4. In 47 there are 5's and over. Recite in
the same way about 16; 23; 39; 18; 46; 33; 64; 57.
5. Tell how many 9's and how many over in 11; 46 ;
87; 39; 43; 86; 98; 53; 69; 76; 49; 108; 32.
The number left over when the dividend does not exactly
contain the divisor is called the remainder.
Dividend Divisor Quotient Remainder
26 -*• 6 = 4 and 2 over
Test : 6 x 4 + 2 = 26 Dividend.
6. Divide each of the following numbers by 2, 3, 4, 5, 6,
7, 8, and 9, and test your answers as above :
7 12 14 38 23 30 19 13 11 17 28
34 32 29 15 10 8 24 31 26 39 35
7. Divide each of the following numbers by 5, 6 ? 7, 8,
and 9, and test your answers :
44 40 52 49 55 42 46 50 59 61 41
51 43 45 53 57 60 48 56 47 54 58
8. Divide each of the following numbers by 7, 8, and 9,
and test your answers :
62 72 75 67 65 70 73 74 66 63 76
71 68 64 81 79 82 78 80 77 69 83
76 DIVISION Written
1. 64 Quotient Process
8)512
48 tens 5 hundreds does not contain 8 any hundred
32 units times ; 5 hundreds and 1 ten make 51 tens; 51
tens divided by 8 equals 6 tens and 3 tens over ; 3 tens and 2 units
make 32 units. 32 divided by 8 = 4. 64 Quotient.
The figures and words below the dividend may be omitted, and
64 Quotient 8)512
the work expressed thus 8)512 or 64 Quotient
2. Find J of 81; 168; 261; 195; 294; 1488; 1971.
How can you test your work? The quotient and
divisor are what of the dividend?
3. Find the number of gallons in 236 qt. ; 148 qt. ;
112 qt. ; 244 qt. ; 216 qt. ; 944 qt.; 2324 qt.
4. How many school weeks in 165 school days ? 245
school days ? 445 school days ? 625 school days ?
5. Lucy's father worked 348 days. How many weeks
did he work ?
6. a. 4)232 b. 3)311 c. 4]SS2
d. 5JH3F e. 5)2iTU /. 3J720
Find the quotients and test your work by midtiplication.
7. £of 39; 45; 51;. 57; 63; 69; 72; 78; 81; 102.
8. J of 56; 64; 72; 76; 84; 92; 104; 112; 120.
9. Icf 65; 75; 80; 95; 125; 140; 150; 145; 160.
10. \oi 78; 90; 102; 114; 120; 132; 144; 168; 180.
n. lof 91; 105; 119; 133; 147; 161; 175; 189.
12. \ of 104; 120; 136; 152; 168; 184; 200; 232.
is. h of 486; 298; 754; 9312; 8476; 7352; 3578.
Oral
MULTIPLICATION AND DIVISION
77
1. Divide by 3
36; 24; 15
2. Divide by 4
36; 24; 16
3. Divide by 5
20; 25; 45
4. Divide by 6
48; 24; 55
5. Divide by 7
21; 14; 84
6. Divide by 8
32; 48; 80
; 18; 9; 21; 27; 6; 24; 39; 42.
40; 20; 32; 8; 44; 48; 28; 52.
50; 35; 60; 40; 30; 55; 65.
12; 42; 18; 72; 60; 30; 66; 120.
70; 56; 35; 77; 28; 42; 49; 98.
56; 64; 24; 96; 88; 40; 72; 144.
7. Divide by 9
81; 72; 54; 45; 18; 36; 90; 108; 63; 135.
8. A bushel of cranberries cost $ 2.52. What was the
cost of a peck ? (^ of 252 cents.)
9. Give two factors whose product is 12; 8; 24; 18;
21; 36; 42; 84; 108; 72; 81; 56; 63; 54; 42; 32; 16.
10. Find by addition and multiplication : three 7's ;
four 8's ; five 5's ; three 12's ; three ll's ; six 12's.
11. A table has 4 sides, each 4 ft. long. How far is it
around the table ? (Picture.)
12.
Multiply each number in the upper row by every number in the
lower row.
2
3
5
8
7
10
6
9
4
12
1
11
11
6
2
10
3
1
4
7
12
9
5
8
78 MULTIPLICATION AND DIVISION Written
i. 3)552 2. 4)164 3. 6)738 4. 3)222 5. 8)336
6. 5)400 7. 6)336 a. 5)785 9. 7)287 10. 5)670
11. 4)816 12. 6)378 13. 7)245 14. 3)267 15. 8)432
is. 5)575 17. 4)356 is. 5]63o 19. 5)490 20. 6)804
21. Four boys bought a boat for $ 140. What should
each pay?
22. 185 books were put on 5 shelves. How many was
that for each shelf?
23. A room has 7 rows of chairs with 19 chairs in each
row. How many chairs in the room ? (Picture.)
24. Multiply by 3 :
28; 65; 47; 124; 253; 769; 483; 204; 910.
25. Multiply by 4 :
49; 385; 769; 428; 349; 206; 908; 839.
26. Multiply by 5 :
563; 721; 432; 86; 742; 938; 701; 650.
27. Multiply by 6 :
432; 591; 763; 284; 315; 91; 38; 409; 840.
28. Multiply by 7 :
63; 40; 51; 48; 39; 415; 521; 230; 408; 916.
29. Multiply by 8 :
41; 13; 76; 83; 44; 26; 715; 403; 847; 936.
30. Multiply by 9 :
17; 21; 42; 35; 40; 56; 123; 235; 368; 987.
31. Divide by 7 and test your work :
105; 133; 154; 217; 392; 469; 595; 651; 623; 952.
Oral REVIEW 79
i. Count to 80 by5's; 6's; 7's; 8's; 9's; 10's; ll's.
2. Four books at $ .08 apiece cost how much ?
3. $.20 for 4 oranges is how much apiece ?
4. A half dollar, 2 quarters, a dime, and 2 nickels are
how much money ?
5. a. How much will I have left out of $ 32 after
buying a coat for $11 ? b. 64 quarts = how many pecks ?
6. 4 dolls at $ .15 apiece cost how much ?
7. 28 eggs sold out of 4 dozen leave how many ?
8. 3 dimes will buy how many bananas at 3 1 apiece ?
9. Bananas at $ .48 a dozen are how much apiece ?
10. From a rope 24 ft. long, Joe cut 8 ft. for a jumping
rope and 7 ft. for hammock ropes. How many feet were
cut , off ? How many feet were left ? How many inches
long was the jumping rope ? The piece that was left ?
li. If mother needs 2 dozen buttons for Grace's dress
and has 17 buttons, how many must she buy ?
Written
1. a. Subtract 723 from 1213. h. Subtract 24 from £
of 96.
2. Add $4.20, $3.24, $2.16, $.21, and $2.43.
3. One factor of 168 is 6. What is the other?
4. 29 and 5 are the factors of what number ?
5. See hoiu quickly you can get the answers to these :
a. 232 + 467 + 229. c. $36.45 d. 672 e. 4]3B
6. 306 4-184-200. -14.29 -280 /. 5]M5
80 MULTIPLICATION AND DIVISION Written
1. Multiply each of these numbers by 7, 8, 9, and, 10:
a. 37; 36; 31; 35; 34; 33; 32; 38; 39.
b. 63; 65; 64; 62; 67; 68; 61; 69; 66.
c. 84; 82; 85; 89; 86; 83; 81; 88; 87; 80.
d. 93; 94; 95; 96; 92; 97; 99; 98; 91.
2. Find | of 104; 120; 136; 152; 168; 184; 200.
3. Find 1 of 117; 135; 153; 171; 189; 207; 225.
Find quotients and remainders. Test your work.
4. DicidebyS: 41; 43; 46; 49; 53; 56; 79; 94.
5. Divide by 4: 53; 58; 62; 70; 74; 98; 106; 138.
6. Divide by 5: 78; 83; 94; 102; 112; 118; 123.
7. Divide by 6: 81; 88; 93; 99; 165; 110; 136.
8. Divide by 7: 95; 99; 107; 115; 120; 129; 145.
9. Divide by 8: 108; 115; 124; 138; 147; 165.
io. Divide ly 9: 121; 128; 138; 156; 167; 187.
n. Lewis's hens laid 154 eggs in a week. That was
how many eggs a day ?
12. Copy in figures and find the product : LXVIII x IX.
13. Find the cost of 9 carriages at $ 257 apiece.
14. At how much apiece must 8 cows be sold to bring
$368?
15. Copy in figures and find the quotient : XCVI -s- IV.
16. How many weeks in 161 days ; 245 days ; 448 days ;
623 days ; 497 days ; 945 days ?
17. 8)232 9)441 7)651 5)335 5)2410" 9)1107
18. 426 is : a. \ of what number ? b. ^ of what ?
Oral REVIEW 81
i. 8 + 3 + 2 + 5 + 7 + 6-8= ? 4 + 8 + 9-6 + 10=?
2. Lewis bought a pencil for 3 cents and a writing pad
for 8 cents. How much change should he get from a
quarter ?
3. In a flock of 57 sheep 9 died. How many lived ?
4. Give two factors which make 81 ; 64 ; 49 ; 36 ; 56 ;
63; 72; 96; 84; 48; 77; 99; 144.
5. One factor of 121 is 11. What is the other?
6. Write in Roman the numbers of the chapters in a
book from Chapter XXXVIII to Chapter LX.
7. Two peaches at 2^ apiece and 5 oranges at 3^ apiece
cost how much ?
8. a. 3 + 9 + 5-4-2 + 9= ? 6.4x9-3=?
c. 6x8-12= ?
9. How many months in 11 years ?
10. Make a problem for 8 x 7 ; for 6x5; for 4x12.
li. 9 x 12 = - . Make a problem.
12. A half-peck of chestnuts at 5^ a quart cost how
much ?
13. 12 bu. of oats will feed how many horses if each
horse eats a peck ?
14. a. 1 gal. = pt. ; h. 1 yd.= in.; c. 1 bu.
= qt.
15. If we sing 7 exercises every day, how many shall
we sing in a week ?
16. The sum of two numbers is 24. One of them is 6.
What is the other ?
82 REVIEW Written
i. Add.
Write
sums
only.
Do not copy the addends.
Can you get
correct
sums
: in 3 minutes ?
a. 749 b
83
. 476
584
c.
754
326
d.
$ 128.04
36.12
e. 1271
564
365
693
473
17.49
329
872
227
538
216.20
613
574
456
842
538.52
706
633
843
695
6.37
473
497
709
972
49.59
856
2. From 8293 take
a. 467; b. 548; c. 2439; d. 7584; e. 3965;/. 684.
3. a. 714 b. 1264 c. 207 d. 273 e. 807 /. 561
x8 x7 x9 x9 x8 x7
4. a. 7]3l7 b. 8)268 c. 9)288 d. 6)2454 e. 5)170
5. a. 5)6700 6. 4)196 c. 7)658 d. 9)T683 e. 8)1184
6. Three ranchmen own 3978 sheep. If their shares
are alike, how many sheep does each man own ?
7. A peddler's sales for a week are: Monday, $6.18;
Tuesday, $4.23; Wednesday, $7; Thursday, $16.85;
Friday, $3.98; Saturday, $27.39. a. Find the total for
the week. b. At the same rate, what would be the total
for 9 weeks ? c. For 7 weeks ? d. For 8 weeks ?
8. Mr. Jones raised 583 bu. of corn, which was 276 bu.
more than Mr. Brown raised. How many bushels did
Mr. Brown raise ?
TIME
83
l. Which is the hour hand?
Which is the minute hand ?
What is the other hand?
To what number does the hour
hand point? The minute hand?
How many hour spaces are
there on the dial? How many
hours is it from noon to mid-
night? From midnight to noon? How many hours in
a whole day?
2. How long does it take the minute hand to go around
the dial ? How many minute spaces between XII and I ?
Between X and XI ? How many minute spaces on the
whole dial ? How many minutes make an hour ?
3. How many times will the minute hand pass around
the dial between 12 o'clock and 1 o'clock ? Between 12
and 4 ? Between 2 and 5 ? Between 4 and 9 ?
How many minutes are there in 2 hours ? In 7 hours ?
4. The second hand passes around the circle once every
minute. How many seconds make a minute ?
5. What time is shown on the dial ?
6. When the minute hand reaches VI, where will the
hour hand be ? What time will it be ? When the minute
hand reaches I, what time will it be? When it reaches
II; III; nil; V; VI; VII; VIII; IX; X; XI; XII?
7. When the hour hand is after V and the minute hand
is at III, what is the time ? (Picture.)
84 TIME
Summary
seconds (sec.) make 1
minutes (min.) make 1
hours (hr.) make 1 (da.)
BEADING AND WKITING NUMBERS
|
JLJL
467,507 is read four hundred sixty-seven thousand five
hundred seven.
10,450 is read ten thousand four hundred fifty.
- l. Read :
512,239 42,000 639,010
759,283 354,000 420,216
569,351 20,514 25,004
306,429 1,006 106,000
26,381 150,213 70,016
10,450 40,208 236,700
2. Write : a. One thousand five hundred seventy-four.
6. Two hundred thirty-four thousand six
hundred ninety-seven.
c. Fifty-nine thousand.
d. Sixty thousand four hundred thirty.
3. Make a watch dial showing half-past ten.
4. Write in Eoman the number of hours in a day;
seconds in a minute ; hours in half a* day ; minutes in half
an hour ; minutes in a quarter of an hour ; hours in two
days ; hours from 5 in the morning to 7 at night.
ORAL PRACTICE
85
i. 20 + 10
2. 40 + 20
3.
20 + 70
4. 40 + 50
30 + 10
40 + 30
20 + 80
60 + 40
20 + 20
50 + 20
20 + 90
70 + 40
30 + 30
60 + 20
50 + 30
50 + 80
30 + 20
70 + 10
30 + 60
90 + 60
5. 70-20
6. 80-40
7.
60-40
8. 50-30
90-10
90-30
70-50
70 - 60
50-20
70-10
30-20
90-40
30-10
60-20
80-50
70-40
60-30
90-80
90-60
80-20
9. 10x8
10. 30x4
11.
50x7
12. 6 x 20
20x2
50x3
60x8
3x80
60x3
70x3
30x6
5x90
40x5
60x2
40x9
2x60
70x2
90x4
80x2
7x30
is. 25 + 10
14. 16 + 40
15.
39 + 10
16. 76 + 20
45 + 20
27 + 30
84 + 10
24 + 50
35 + 30
58 + 20
21 + 30
19 + 80
65 + 10
85 + 10
35 + 20
72 + 20
35 + 20
17 + 40
42 + 30
61 + 30
it. 26-10
is. 73-50
19.
89-50
20. 83-50
42-10
84-20
72-40
79-20
83-20
96-30
99-70
92-80
56-30
88-50
83-40
61-30
27-10
79-60
64-50
82-60
7x90
8x40
6x70
2x80
86 PRACTICE IN ADDITION AND SUBTRACTION Oral
1. Add 2, 3, 4, 5, 6, 7, 8, 9 to each of the following
numbers :
a.
b.
c.
d.
e.
/•
g-
h.
i.
57
19
55
72
74
58
26
77
82
44
69
98
42
35
68
37
56
53
52
74
75
83
54
38
49
89
62
64
15
66
46
17
36
28
48
96
85
105
63
88
87
73
16
92
93
59
18
47
76
39
45
67
78
27
86
29
99
84
65
95
79
25
97
2. Subtract 2, 3, 4, 5, 6, 7, 8, 9 from each of the above
numbers.
3. Pupils by turn add columns aloud, one pupil writing
the sums on the blackboard.
65 + 27 = ? Say 65, 85, 92.
4. i 65 + 20 = 85.
85+ 7 = 92. An*.
In the same way give the sums of the following :
5. 24 + 25. 9. 37 + 58. is. 64 + 27. 17. 63 + 29.
6.
38 + 43.
10.
23 + 34.
14.
81 + 19.
18.
34 + 38.
7.
72 + 19.
11.
58 + 45.
IS.
59 + 21.
19.
33 + 68.
8. 1
35 + 16.
12.
43 + 59.
16.
58 + 34.
20.
92 + 19.
65-27<
= ?
Say 65,
45,
38.
21.
65-20
45- 7
= 45
= 38
Ana.
22. '
72-19.
25.
76-29.
28.
82-44.
31.
45-18.
23. !
35-16.
26.
93 - 37.
29.
91-23.
32.
37-19.
24. 1
S3 -25.
27.
64-35.
30,
78-31.
33.
92-78.
Written SUBTRACTION - 87
l. Mr. Emerson bought a stock of groceries for $ 3897
and sold them for $ 5296. How much did he gain ?
_ . After we have taken 1 ten from 9 tens in the minuend,
^ how many tens are left ? We cannot take the 9 tens
g iQnrt A in the subtrahend from the 8 tens left in the minuend,
so what must we do ?
Test all your work. The subtrahend + the remainder = ?
2. 842 3. 435 4. 583 5. 694 6. 803 7. 715
647 238 245 598 654 678
a 5643 9. 4521 10. 3462 u. 3573
2738 2618 2548 1628
la. 6411 13. 5343 14. 4701 is. 3603
2508 2517 2654 1672
16. 5007 17. 3541 is. 4504 19. 4791
2548 2496 1576 2432
20. $421.35 21. $846.30 22. $6937.15 23. $2341.17
143.29 298.41 486.29 1935.48
24. 1200 25. 1000 26. $439.21 27. 8435 28. 4605
1199 983 248.41 6598 2719
29. How much money must be added to $ 436 to make
$1321?
30. In the year 1895 Mr. Finch had $ 4378 in the bank.
In 1903 he had $ 5247. a. How much did he save in
that time ? b. In how many years did he save it ?
88 REVIEW Written
Can you get the first five right in tivo minutes f Write
only tlie answers.
1. 403
2. $12.50
516
1.35
940
6.23
768
1.79
24
7.00
3.
419
-263
6.
708
x7
4.
576
x9
7.
375
x9
2)8642
, 467
x6
9. Mr. West is 6 ft. tall. How many inches tall is he ?
10. A window sill is 84 inches from the ground. How
many feet above the ground is it ?
li. A merchant bought goods amounting to $ 530 and
paid $ 260 down. How much did he still owe?
12. If a steamboat goes 512 miles in a day, how far
will it go in 6 days ?
13. $42.10 14. $39.24 is. $18.19 ie. $4.93
x6 x5 x4 x3
17. The subtrahend is $ 375.39, the minuend $ 483.29.
Find the remainder.
is. 1476 is the difference between 4325 and what other
number ?
is. 5462 20. 2000 21. 4605 22. $30.06 23. 2741
-2735 -729 -2719 -12.74 -659
24. A train of 9 cars has 79 passengers in each car.
How many passengers in all the cars ?
25. An ocean steamer can carry 789 passengers at each
trip. How many can she carry at 7 trips ?
MULTIPLICATION 89
The value of any figure depends on its place ; and every
time a figure is moved one place to the left its value is
multiplied by ten, thus:
60 = 6 tens=6xl0 =6x10
600 m 6 hundreds =6x10x10 = 6 x 100
6000 = 6 thousands = 6 x 10 x 10 x 10 = 6 x 1000
1. 5x10 = ? 5x100 = ? 5x1000 = ?
2. 9x10 = ? 9x100 = ? 9x1000 = ?
3. When we multiplied 6, 5, and 9 by 10, we an-
nexed what to them ? By 100 ? By 1000 ?
4. How can we multiply a number by 10 ? By 100 ?
By 1000?
5. Multiply by 10 :
7; 43; 55; 79; 3; 436; 581; 3245; 4823.
6. Multiply by 100 :
8; 9; 7; 4; 3; 2; 14; 81; 37; 40; 324; 561.
7. Multiply by 1000 :
1; 2; 5; 8; 12; 61; 19; 83; 10; 425; 306; 420.
8. If one horse is worth $ 225, what are 30 such horses"
worth ? How shall we find it ?
*225
Qfk 30 = 3 X 10 ; therefore, multiplying by 30 is the same as
multiplying by 3 and then by 10.
$6750
9. Multiply 248 by 30 ; 50 ; 60 ; 80 ; 70 ; 90 ; 40
10. 29
700 29 X 700 = 29 X 7 X 100.
20300
11. Multiply 34 by 700 ; 500 ; 200 ; 9000 ; 8000.
90 MULTIPLICATION Written
l. Mr. Johnson sells threshing machines at $ 537
apiece. How much does he receive for 39 machines ?
What must we do to find it?
537 39 = 30 + 9 ; therefore, we may multiply 537
39 by 30 and by 9 and add the products.
4833 = 537 X 9 4833 and 16110 are called partial products.
1611 = 537 x 30 The may be omitted from units' place in the
20943 = 537 x 39 second partial product
2. 127 3. 206 4. 346 s. 710
34 25 15 32
6. 532
21
7. 712
33
s. 543 9. 673 10. 274 u. 148
22 13 16 14
12. 714
25
13. 324
34
14. 212 is. 742 is. 632 17. 427 is. 654 19. 475
16 24 70 63 37 38
20. 749 21. 746 22. 807 23. 237 2*. 415 25. 474
67 78 89 78 69 68
26. 7 sacks of flour at $1.35 cost how much ?
27. 6 pounds of coffee for $1.32 is how much a pound ?
28. At $ 1.75 a day, how much can a man earn in a
week ?
29. $ 7.35 paid on a debt of $ 10.00 leaves how much
unpaid ?
30. How many chapters from chapter XXVIII to chap-
ter XCIV?
31. From 120 apples, take 7 dozen apples.
REVIEW 91
Quick Test
Teacher dictates questions. Pupils write answers. Pass papers,
mark them, and make report.
1. How many months are there in 11 years ?
2. J of a day is how many hours ?
3. On what number is the minute hand at 20 minutes
past two ?
4. How many seconds are there in £ of a minute ?
5. At 20 f a gallon, what will 1 qt. of milk cost ?
6. Bought 10 qt. of cherries at 9 ^ a quart and gave
the clerk a silver dollar. What change should I receive ?
7. Potatoes at 48 ^ a bushel are how much a peck ?
8. Hickory nuts at 5 ^ a quart are how much a peck ?
9. How many pints in 11 gallons ?
10. How many days in 12 weeks ?
Oral
1. From 100 subtract 30 ; 20 ; 50 ; 80 ; 10 ; 70 ; 40.
2. 65-28 = ? (Say 65, 45, 37.)
3. 84-28 s. 93-54 i. 59-29 9. 83-26
4. 76-37 6. 46-38 8. 81-17 10. 48-29
11. 49x10 = ; 73x100 = ; 8x1000 = .
12. How many dresses will 36 yd. of silk make if 9 yd.
will make one dress ?
13. 3 dozen eggs cost $.39. One dozen costs .
14. How many minutes in 8 hours ? In 7 hours ?
92 MISCELLANEOUS
Numbers of Days in the Different Months :
January 31 April 30 July 31 October 31
February 28 May 31 August 31 November 30
March 31 June 30 September 30 December 31
February has 29 days once in four years (Leap year).
1. a. How many days in a common year ?
&. How many days in a leap year ?
c. Hew many June days have you seen? July days?
d. How many December days have you seen ? April
days ?
e. How many days in 57 common years ?
/. How many days in 89 leap years ? 44 leap years ?
g. How many hours are there in a common year ?
h. How many hours are there in a leap year ?
L How many hours are there in 9 leap years ?
2. How many seconds are there in an hour?
3. How many minutes are there in a day ?
4. How many seconds are there in a day ?
5. How many school weeks in 475 school days ?
6. If there are 8 grades between the kindergarten and
the high school, and it takes 200 days to pass each grade,
how many days must you attend school to go through all
the grades ?
7. Find the cost of 5 books at $ 1.87 each.
8. $203 paid for 7 cows is how much apiece ?
9. $152 will buy how many washing machines at
$ 8 each ?
FINDING ANY PART OF A NUMBER
I cent
r 7 ^
cent I
I cent I
cent
of 6 cents =
cents.
1. Here are how many cents ? -J
cents, -§ of 6 cents = 2 x cents =
2. Make 12 cents. Find \ of 12^; § of 12*.
3. Draw a line 20 in. long.
Find J of 20 in. ; £ of 20
in. ; | of 20 in. ; £ of 20 in. ; f of 20 in. ; £ of 20 in.
4. Draw a line 1 yd. long. Mark the inches. J yd. is
inches ; £ yd. = in. ; £• yd. = in.
\ of a yard is inches ; -| yd. = in.
are
^ of a yard is inches ; |- yd. = in.
Picture 10 marbles. Mark off £ of 10 marbles ; f.
|- of 10 marbles are marbles ; f of 10 marbles
— marbles ; ^ of 10 marbles are marbles.
9. Take 21 splints, beans, or marbles. Find ^> f> f?
f , f, f of them.
io. How many eggs in f of a dozen ? £ of a dozen ?
li. A pie is worth 20 cents. What is \ of it worth ?
|? |? i? s? 4 ? Make two pi c t ur es of the pie. Cut
one into fourths, the other into fifths.
12. How many hours in f of a day ? f ? f- ? | ? f ? £ ?
13. If you are awake J- of the time, you are awake how
many hours each day ? How many hours do you sleep ?
94 MISCELLANEOUS Written
1 Find 1233425567 5 2 5 7 8 n f 0^90
2. a. If an acre of land costs $175, what would 84
acres cost ? b. J- of an acre ?
3. Mr. Rich earns $25.76 per week. His son earns f
as much. a. How much does the son earn ? b. How
much more does the father earn than the son ? c. How
much do both earn ?
4. Multiply twenty-nine thousand four hundred sixty-
three by fifty-seven. Write the product in words.
5. A man had 196 books. He gave his son f- of them.
a. How many books did the son receive ? b. How many
did the man keep ?
6. The Revolutionary War began in 1775, and the
Spanish War in 1898. How many years between the
two wars ?
7. a. Find the product of 842 and 76. b. 27684-^9 = ?
8. Bought a carriage for $125 and sold it for $98.
How much did I lose ?
9. a. 448-7 = ? 5.390-5 = ? c. 863x9 = ?
10. A man having 320 sheep sold 284. How many
had he left?
li. A boy had saved $2 and then spent $.60 for pres-
ents. How much had he left ?
12. Leo had $3.68 and his father gave him enough to
make $5.00. How much did his father give him?
13. A man owed $265 and paid $199. How much
did he still owe?
QUICK TEST 95
i. 5 + 8 + 7 + 6 + 9 = ?
2. Write 19 in Roman.
3. Find the cost of 8 pounds of sugar at 5 cents a pound.
4. Add 62 and 31.
5. Subtract 49 from 83.
6. Find f of 28.
7. How many quarts in 3 pk. of onions?
8. 120 minutes are how many hours?
9. How many inches in 9 feet ?
10. 7x9 + 8-7 = ?
Oral Problems
1. If 7 oranges cost 21 cents, 1 orange costs cents.
5 oranges cost cents. Make the question.
2. a. When Bessie picked 5 qt. of berries on Monday,
8 on Tuesday, and 7 on Wednesday, in the three days she
picked quarts.
b. If she sold 10 quarts and gave the rest to her mother,
she gave her mother quarts.
3'. If a dozen oranges cost 48 cents, 1 orange costs
cents. 11 oranges cost cents. Question.
4. In 10 quarts there are pints. If 1 pt. of milk
costs 3 cents, 20 pints will cost cents. Question.
5. If eggs are $.24 a dozen, 1 egg costs cents.
7 eggs cost cents. Question.
6. If 10 eggs cost 30 cents, 1 egg costs cents.
A dozen eggs cost cents. Question.
96 PROBLEMS Oral
Answer to yourself these questions about each problem :
a. What is asked? b. What is told? c. What must 1
find first ?
1. A lady bought 3 dozen buttons at*8 cents a dozen,
and a yard of ribbon at 10 cents. What did she pay for
both?
2. John walked 4 miles and Eoy walked five times as
far. How far did Roy walk ? How far did both walk ?
3. A man earned $8 one week, $ 9 the next, $10 the
next. How much money did he earn in the three weeks ?
He put $20 in the bank and spent the rest. How much
did he spend?
4. At 6^ a quart, what will 3 gal. of oil cost?
5. How many 5-cent car fares can be paid with a quar-
ter, a dime, and a half dime ?
6. Elsie bought a tablet for 8 cents, a stamp for 2 cents,
and some pencils for 9 cents. She gave the clerk a quar-
ter. How much change should she receive ?
7. A man earned $42 and used f of it. How much
did he use ? How much had he left ?
8. Four oranges cost 12 cents. At the same price,
what must be paid for 8 oranges?
9. A man earns $ 15 a week and saves \ of it. How
much does he save in one week ? How long will it take
him to save $ 27 ? How much will he save in 12 weeks ?
How much does he spend in a week ? In 4 weeks ?
10. Ned has three rabbits and Ted four times as many.
How many has Ted ? How many have both ?
Oral
REVIEW
97
1. A milkman had 2 cans of milk with 6 gallons in
each can. How many quarts of milk had he ?
2. If 5 pencils cost 15 cents, what will 1 pencil cost?
What will 3 pencils cost? 10 pencils? 11 pencils?
3. f of a yard of ribbon is how many inches long ?
4. A four-foot rule could be cut into how many sticks,
each six inches long ?
5. 3 min. = sec. 2 hr. = min.
4 wk. = -
ihr.= -
9 qt. and 1 pt. =
4 doz. + 3 =
6 doz. + 11=
da. 5 yr. =
mo.
min,
7 gal. and 3 qt.
-pt.
8 doz. + 2 = —
11 doz. + 6 = -
qt.
39?
10.
11.
How many dozen, and how many over, in 17 ? 27 ?
46? 54?
Multiplication table, page 73.
Read each number in the inner
square before every sign in the outer
squares, and find the result
12. 4x8 + ? = 35. 7x9 + ?=69.
is. 7x7 + ?= 58. 8x6 + ? = 54.
14. What is the time when the hour hand is at VIII ?
Where is the minute hand then ?
is. What is the time when the hour hand is between
V and VI and the minute hand is at III ? When the
minute hand gets to IX ?
16. What is the cost of 2 bu. of potatoes at 10^ a peck ?
+5
-f2
-7
+18
-t-3
36
72
108
xio
-r-6
-29
-^9
-7-4
-11
4-9
98 MISCELLANEOUS Written
1. Find 7 times 389 by addition and by multiplication.
2. Find by subtraction how many 16's in 176; in 96;
in 144; in 80; in 160; in 112; in 128.
3. Copy answers only. Add up and down. How long
will it take t
a. 463
b. 453 c
•. $478.45
d.
$165.35
e. $ 4.10
274
224
85.46
48.64
467.20
632
35
300.18
8.03
254.18
49
368
63.24
6.00
325.16
548
74
.65
17.40
49.21
231
989
49.85
5.84
8.00
598
6785
237.46
97.68
77.56
4. a. 3642 x 24; b. 4832 x 34; c. 2356 x 43; d. 805 x 96.
5. At our festival we used 125 gallons of ice cream.
a. How many quarts were used ? b. If each quart was
served to 6 persons, how many persons ate of the cream ?
6. a. A market man bought 1057 pounds of beef, 538
pounds of mutton, and 457 pounds of veal. How many
pounds of meat did he purchase ? b. After he had sold
986 pounds of meat, how many pounds remained ?
7. Find the quotient and remainder : a. 347 h- 5 ;
b. 643 + 6; c. 487 + 8; d. 3067 <- 9; e. 4234 -*- 7;
/. 613 + 9 ; g. 4134 -*- 8.
8. 48 bushels of potatoes at $.55 a bushel cost how
much ?
9. A grocer has 432 bu. of potatoes. How many
customers can he supply with a peck apiece ?
Written
MISCELLANEOUS
9
Papers
sold by seven hoys during one week :
Mon. Tues. Wed. Thur.
Fri.
Sat
Henry
, . . 36 28 24 14
26
32
Carl .
. . . 24 35 25 16
18
26
Jerry .
. . 18 23 26 24
28
29
Frank ,
. . 29 18 21 32
27
35
Charles ,
. . 15 26 18 27
34
36
Roy . ,
, . . 34 31 30 28
26
27
Edward
, . . 12 23 20 19
27
28
1. Find the number of papers sold on Monday ; Tues-
day; Wednesday; Thursday; Friday; Saturday.
2. Find the number sold by Henry; Carl; Jerry;
Frank ; Charles ; Roy ; Edward.
3. Find : a. The number sold on all the days. b. The
number sold by all the boys. c. How do these two num-
bers compare ?
4. a. 714 b. 1264 c. 207 d. 740 e. 1273 /. 6701
x8 x7 x9 x6 x4 x5
5. a. 9)3T7 b. 8)2657 c. 9)2890 d. 9)3069
6. At 3^ each, how many lemons will 72^ buy ?
7. $ 6.28 out of a $ 10 bill leaves how much change ?
8. There are 27 daisies in one vase and 3 times as
many in another. How many in both vases ?
9. Find the cost of 7 tons of coal at $4.75 a ton.
10. John earned $18 during the vacation and spent
% 12.75. How much did he save ?
100 MULTIPLICATION AND DIVISION Oral
1. Moving a figure to the left one place multiplies its
value by 10. Moving a figure one place to the right does
what to its value ?
2. 9x10 = 90. 90-10 = ? 23x10 = 230. 230-10 = ?
3. To multiply a number by 10 we annex a 0.
How can we divide a number by 10 ?
4. Divide by 10 :
80; 60; 130; 740; 800; 4360; 560; 1300; 2080.
5. To multiply a number by 100 we annex two ciphers.
How can we divide a number by 100 if it has ciphers
at the end ?
6. Divide by 100 :
600; 900; 1200; 2300; 6000; 48000; 64500; 360000.
Written
32
7. 8P)25W. 80 = 8 x 10, To divide by 80 we divide
by 10 and then by 8. How do we divide by 10 ?
8. a. 30)34920 b. 40)2480 c. 50)4750 d. 60)720
9. Divide by 90 :
a. 1620; b. 4770; c. 71100; d. 108000; e. 17280.
iOo 500 = 5 x 100. How may we divide 4500 by 500 ?
n. a. 500)1500 b. 500)7500 c. 700)11200 d. 600)72000
12 a. 342x60 is. a. 490-70 14. a. 4800-80
b. 34 x 90 b. 34600 - 40 b. 62500 - 500
c 81 x 700 c. 27900 -* 90 c. 91000 -*- 700
d. 495 x 310 d. 6420 - 60 d. 34000 - 2000
Written REVIEW 101
i. Add up, then down. Write only the sums. 5 minutes f
a. $548.42 b. 4835 e. 4782 d. 63854 e. $381.15
57.54
724
95
9763
42.81
6.00
89
398
427
68.73
.84
38984
27579
5106
59.42
346.99
35
49895
78243
486.53
24.63
672
6879
4675
79.49
51.06
4897
4623
1016
83.26
2. Find the differences and test results :
a. 7821 b. $200.14 c. $800.00 d. 7421 e. 8402
6459 89.27 256.13 1695 1673
3. Multiply: a. 763 by 42. b, 529 by 44. e. 862 by 31.
d. 720 by 43.
4. Find : a. | of 2982. b. •§- of 2832. c. 1 of 5715.
d. i of 2732.
5. a. If our living expenses are $7.56 a week, how
much are they for 1 day? b. For 9 days? c. For 5 days?
d. For 4 weeks ?
6. Fiud : a. i of 651. b. f of 651. c. £ of 5640.
d. i of 5640.
7. a. 43x500. b. 691x70. c. 39x3000.
d. 865x80. e. 196x39.
8. How many days in the first six months of the year ?
9. Counting 30 days for a month, how many months
in 180 days?
10. How many quarts in 798 bushels ?
102 MULTIPLICATION Written
i. If a grain car will carry 756 bu. of corn, how
many bushels will 243 such cars carry ? What operation
must be performed ?
756
92T8 — 7^6 3 What is the answer? What
OAni ^r a Af\ have we omitted from the second
3024 =756x40 . , 9
i en o - Y^fi 900 a ™*ird partial products f
183708 = 756x243
2. Henry's kite string is 648 ft. long. How many
feet of twine would it take to make 207 such kite strings ?
How many partial products will you have ? Where will
you write the first figure of the second partial product ?
3. A tract of land is laid out in 248 lots, each one
for sale at $375. If the owner sells all of them at that
price, how much will he receive for them ?
4. Multiply 239 by 158. Multiply 158 by 239. How
do the products compare ?
5. Find how 412 times 653 compares with 653 times
412.
Find the products in two ways :
6.
385x209
10.
209 x 506
14.
854 x 305
7.
842 x 351
ii.
983 x 786
15.
907x635
8.
496 x 258
12.
428 x 732
16.
294 x 687
9.
324 x 807
13.
356 x 271
17.
839 x 594
18. If a baggage car goes 248 miles every day, how
many miles will it go in a year ?
AVOIRDUPOIS WEIGHT 103
Note. — Have scales before the class.
i. For what are the scales used ?
2. Find the pound weight.
3. Let each pupil take the pound
weight in his hand.
4. Name articles that weigh about a pound. Weigh
them.
5. Put sand in a bag until you think you have a
pound. Weigh and correct it.
6. Use the bag of sand for a pound weight. Find the
ounce weight. Weigh out several ounces of sand in bags.
Find how many ounce bags are needed to balance the
pound bag.
7. There are ounces (oz.) in 1 pound (lb.).
8. Name articles that are sold by the pound ; by the
ounce.
9. How many ounces are there in 2 lb.? 3 lb.? 5 lb.?
10. How many ounces in i lb. ; J lb. ; |- lb. ?
11. How many ounces in 1J lb. ; 2J lb. ; 1J lb. ?
12. Mr. Jolly, the candy maker, gave away 25 lb. of
candy, putting 1 oz. into each bag. How many bags of
candy did he give away ?
13. a. How many days will 7 lb. of sugar last you if
you eat an ounce every day ? h. How many weeks ?
14. If the average weight of the plums on a certain tree
is 1 oz., how many plums will it take to weigh 395 lb. ?
476 1b.? | lb.? fib.? | lb.?
104 REVIEW Oral
i. How much is | of a peck? ^ of $ 150?
2. If I give a dollar in payment for 9 qt. of peaches at
10^ a quart, what change should I receive ?
3. Find the sums and differences :
68 54 78 49 51 63 58 41 53
2926 16 27 33 37292439
4. How many feet in 108 inches? How many yards?
5. How many times can a two-quart measure be filled
from a bushel of walnuts ?
6. I have 12 rows of strawberry plants with 12 plants
in each row. How many plants have I ?
7. Find the cost of 8 tons of rye straw at $ 20 a ton.
Written
1. At Mann's store 85 crates of Georgia peaches, each
crate containing 6 baskets, were sold in 1 day.
a. How many baskets were sold ? b. If there were 34
peaches in each basket, how many peaches were sold ?
2. a. If a boy can ride his bicycle 6 miles an hour,
how many hours will it take him to ride 288 miles ?
b. If he rides 6 hours a day, how many days will it take ?
3. From the sum of 4623 and 5498 subtract their dif-
ference.
4. If 3 horses cost $ 678, what will 12 horses cost at
the same rate ? (12 is how many times 3 ?)
s. 43 6. 231 7. 435 8. 9)649 9. 6)435
x280 x 600 x309
Written DIVISION 105
l. A dealer bought 13 carriages for $ 3055. What
did each cost?
235
13)3055 Process
26 ^ of 30 hundreds is 2 hundreds and 4 hundreds over.
45 4 hundreds and 5 tens are 45 tens. ^ of 45 tens is 3 tens
§9 and 6 tens over. 6 tens and 5 units are 05 units, ^ of
65 65 units is 5 units.
85
Find the quotients and test your work by multiplication :
2. 13)2015 9. 13)1599 is. 14)6818 23. 15)3765
3. 13)2327 10. 13)234 17. 14)5026 24. 15)4575
4. 13)5993 11. 13JT742 is. 14JT344 25. 15)6420
5. 13)2769 12. 14)T890 19. 14)7322 26. 15)1845
6. 13)42l2 13. 14)3430 20. 14)364 27. 15)3l95
7. 13)975 14. 14)6342 21. 14)3234 28. 16)688
8. 13)5577 15. 14)3556 22. 15)2025 29. 16)1984
30. One factor of 247 is 13. What is the other factor ?
31. The product of two numbers is 6804. One of the
numbers is 14. What is the other number?
32. In one mile there are 5280 ft. ^ of a mile = ? ft.
33. Find ^ of 364 ; ^ of 5005 ; Ji of 1638 ; f of 3556.
34. ^ of 1190 = ? T \ of 3332 = ? if of 6314 = ?
35. Findf of 2730; |; f; &; &; &J &J &.
36. How many pounds in 48 oz. ? 832 oz. ? 144 oz. ?
106 MULTIPLICATION AND DIVISION Written
- i. How many quart boxes can be filled from 25 bu. of
peaches ?
2. ^ bu. = qt. How many half-bushel baskets
could be filled from 288 qt. of chestnuts ?
3. A four-gallon can holds qt. How many four-
gallon cans could be filled from 272 qt. of oil ?
4. If William earns $ 16 a month, how many months
must he work to earn $ 576 ?
5. See how quickly you can get correct answers :
a. 3421 x 45 ; ft. 4326 x 51 ; c. 5678 x 55 ; d. 9834 x 43.
6. Find quotients and remainders and test your work :
a. 5)393; 6.6)497; c. 7)899; d. 8)943; e. 9)4875.
7. How many pounds in 2112 oz. ?
8. 42 lb. and 12 oz. are how many ounces ?
9. At $ .06 a quart what will 65 gal. of milk cost?
io. One factor of 675 is 15. What is the other?
u. In 3600 seconds how many minutes ?
12. Find quotients and remainders and test your work :
a. 439 + 13; ft. 513 + 14; c. 1835 + 8; d. 459 + 7.
is. Find : a. { of 675 ; ft. | of 732 ; c. £ of 580.
14. Multiply: a. 472 by 69; ft. 803 by 105.
is. Divide: a. 8320 by 20; ft. 7960 by 40.
16. Find the number of hours in the month of October.
17. Find the number of minutes in the month of October.
18. If a man works 9 hours a day, in how many days
will he work 3681 hr. ?
QUICK TEST 107
1. How many ounces in a half pound ?
2. How many ounces in J of a pound ?
3. How many 12's in 52 and how many over ?
4. 12 gal. and 3 qt. are how many quarts ?
5. At 5 f a foot, what will a yard of picture moulding
cost?
6. A half hour is how manj minutes ?
7. If you buy a book for $.15, how much change
should you get from a quarter ?
8. Four dimes and a half dime are how many cents ?
9. How many inches in a yard ?
10. Two quarts of berries at 10 ^ a quart and a loaf of
bread at 5^ cost how much ?
Oral
1. How many pints in 4 gal.?
2. A quart is what part of a gallon ? 2 qt.? 3 qt.?
3. f of a yard is how many inches ?
4. Charles was punctual at school every morning for
20 weeks. How many times was he punctual ?
5. | of 40 = ? J of 40 = ? What part of 40 is 5 ?
6. How many 6's in 12 ? 6 is what part of 12?
6 months is what part of a year ?
7. Sarah's brother earns $ 16 a week and saves \ of it.
In how many weeks can he save % 20 ?
8. Candy at 2 / an ounce is how much a pound ?
What is a quarter of a pound worth ? A half pound ?
108 REVIEW Written
1. In 48 pecks there are how many quarts ?
2. The Pilgrims came to America in 1620. How
long ago was that?
3. Bought a lot for $ 598. For what must I sell it to
gain $59?
4. A milkman sells 36 gallons of milk every day.
a. How many pounds does it weigh if a pint weighs a
pound ? b. How many ounces does it weigh ?
5. Robert bought some clothes for $5.45. He gave
the clerk a $5 bill and a silver dollar. How much
change should he receive ?
6. 5 tons of coal cost $27.50. Find the cost of 1 ton.
7. 423 s. 524 9. 4031 10. 4706 11. 5072
-297 -349 -1234 -927 -3095
12. Write in words: 31,605; 270,040; 341,005; 104,500.
13. Write in figures : three hundred thousand twenty ;
eighteen thousand fourteen ; six thousand three hundred
thirty ; one hundred fifty-seven thousand nine.
I*, a. f of 1032; b. | of 992; c. f of 560; d. f of 1675.
15. • From seventy dollars and twenty-nine cents take
fifty-two dollars and sixty-nine cents.
16. At 30 cents a peck, what will 3 bu. of apples cost ?
17. A lady had $135. She paid $45 for a sewing
machine and $ 22 for cloth. How much has she left ?
is. There are 7 dozen lemons in one box and 83 lemons
in another. How many lemons in both boxes ?
Written DIVISION AND MULTIPLICATION 109
i. Divide 1134 by 21. To find the first figure in the
quotient, ask yourself, " How many 2's in 11 ? "
2. Divide by 21:
a. 8883; b. 6515; c. 19677; d. 9639.
3. Divide 2573 by 31. To get the first quotient fig-
ure say, " How many 3's in 25? "
4. Divide by SI:
a. 2635; b. 2883; c. 3875; d. 14353.
In examples 5-19, find the quotients and test your work
by multiplication :
5. 1599 + 41 10. 814 + 22 15. 2108-62
6. 6068-41 11. 2912-32 is. 6912-72
7. 2346 + 51 12. 768-32 17. 4756 + 82
8. 2275 + 91 13. 3486 + 42 is. 1288 + 92
9. 1386 + 22 14. 4992 + 52 .19. 2511 + 93
Find the products and test your work by division:
20. 46x31 22. 124x32 24. 93x52
21. 53x21 23. 63x61 25. 242x71
26. One factor of 3844 is 62. Find the other factor.
27. 43x? = 5203. 2a 11070 + ? = 82. 29. ? x 61 = 1159.
30. The multiplier is 42. The product is 3444. What
can you find ?
31. The divisor is 78, the quotient 467. What can you
find?
32. Lucien sold 806 papers in the month of May. That
was how many per day ?
110 MAKING QUESTIONS
Every problem tells us something and asks us to find
something. We use what is told, to find what is asked.
The following exercises tell you something. Ask the
question in each one and answer it.
1. Berries are 10 cents a quart. John bought 7 qt.
2 Mary had 21 cents. Oranges cost 3 cents apiece.
3. Seven pounds of maple sugar cost 84 cents.
4. Chester is 5 ft. tall. There are — — inches in a foot.
5. There are seconds in a minute. It takes Leah
5 seconds to answer a question.
6. Chocolate creams cost 3 ^ an ounce. There are
ounces in a pound.
7. Frances earned 11 cents on Friday, 9 cents on Tues-
day, and 10 cents on Wednesday.
8. Richard earned 41 cents and paid 5 ^ for car fare.
9. Nina took a music lesson twice a month for a whole
year. There are months in a year.
10. Robert is 14 years old. His sister Dorothy is ten.
li. Mary is 19 years old. Frederick is 7 years younger.
12. Lemons are 24 cents a dozen. Ethel bought 6
lemons.
13. There are 8 hours in a working day. Philip worked
72 hours.
14. Make a problem for $ .05 + $ .06 + $ .07.
15. J of 16 = ? Make a problem.
16. f of 36 = ? Make a problem.
17. 10x2 = ? Make a problem.
Oral
KEVIEW
111
i. John paid $.36 for 9 packages of flower seed.
Question.
2. Wilbert has a strip of oak 5 ft. long. He is making
6-inch rules. Question.
3. Make a problem for 4 times 12 in.
4. A bushel of potatoes is worth. 60 cents. A peck
is of a bushel. Question.
5. Alice made a dozen pop-corn balls. Lena made three
times as many. How many did both make ?
3
6
2
12
11
4
10
8
5
9
7
x 7, 8, 9.
7. At $ .06 a pound, find the cost of 3 lb. of starch ;
81b.; 10 1b.; 9 1b.; 12 1b.; 50 1b.; 111b.; 20 1b.; 7 1b.
8. 33 bananas were sold from a bunch containing
7 dozen. How many were left?
Written
1. January, March, May, July, August, October, and
December have each 31 days. How many days in all
these months? Find it in two ways.
2. A man in Vermont made 388 qt. of maple sirup.
He put it into gallon cans. Question. Answer ?
3. Make a problem for $ 84.50 - $ 13.27.
4. Make a problem for 38 x 7 da.
5. Write in words : 304,091; 20,040; 100,001; $50.03.
6. I saw an ocean steamship 499 feet long. There are
inches in a foot. Question. Answer ?
112
KECTANGLES
Fig. 1.
Fig. 2.
1. What is the shape of Figure 1 ? How long is it ?
How wide ?
What is it called ? Describe a square inch (sq. in.).
2. Without a rule, draw a square inch. Measure and
correct it.
3. The corners of a square are right angles. This is a
right angle I — How many right angles has a square ?
4. What kind of angles has Figure 2 ?
5. How many right angles has Figure 1 ? Figure 2 ?
6. Figure 1 and Figure 2 are rectangles. Describe a
rectangle.
7. A rectangle may be either square or oblong. Make
an oblong rectangle 3 in. long and 1 in. wide. Draw
lines catting it into square inches. How many square
inches are there ?
8. Find out how many square inches in an oblong 1 inch
wide and 3 inches long ; 4, 5, 6, 10, 11, 13 inches long.
9. Draw a rectangle three inches long and 2 inches
wide. Mark it off into square inches and count them.
10. Draw a square 3 in. long. Mark it off into square
inches and count them.
RECTANGLES
113
_j , 1
i ] !
1. What is the name of this figure ? How wide is it ?
How long ? Its size is 3 in. by 4 in.
2. The dotted lines drawn from left to right divide the
rectangle into oblongs how long and how wide ? How
many of them ?
3. Each oblong 4 in. long and 1 in. wide contains how
many square inches ? How many square inches in all of
them ? Three times 4 sq. in. are how many square inches?
4. The dotted lines from top to bottom divide the rec-
tangle into how many oblongs ? Each of these oblongs
is how long ? How wide ? It contains how many square
inches ? All of them contain how many square inches ?
114 MULTIPLICATION AND DIVISION Written
1. Draw a rectangle which you think is 6 in. by 5 in.
Measure and correct it. Mark out a row of square inches
along one side of it. How many square inches in this
row? How many such rows could you make from the
whole rectangle ? How many square inches in the rec-
tangle ? 5 times 6 sq. in. = ?
2. Make a rectangle 7 in. by 4 in. Mark it off into
square inches. How many square inches in the rectangle ?
How do you find it ?
3. Make a rectangle 8 in. by 6 in. How many square
inches does it contain ? How do you find it ?
4. On the blackboard, draw a rectangle 18 in. by 7 in.
How many square inches does it contain ?
5. How many square inches in an oblong 24 in. by
12 in. ? Make the drawing.
6. Find the number of square inches in the top of a
table which is 22 in. by 38 in.
Find the number of square inches in each of the following
rectangles :
7.
39 in. by 42 in.
12.
62 in. by 37 in,
8.
68 in. by 29 in.
13.
41 in. by 48 in,
9.
47 in. by 33 in.
14.
36 in. by 19 in,
10.
59 in. by 28 in.
15.
38 in. by 40 in,
11.
39 in. by 2 feet.
16.
3 ft. by 20 in.
17. a. A blackboard 2 ft. 6 in. wide is how many inches
wide ? b. A blackboard 4 ft. long is how many inches
long ? c. How many square inches in a blackboard 4 ft.
by 2 ft. 6 in. ?
Written DIVISION 115
1. Mr. Wilson bought a farm for $ 9044. How much
must he save each year to pay for it in 19 years ?
476
19)$ 9044 19 ig almost 20. Think how many 2's in 9.
(20) 76 To get the next quotient figure, think how many
144 2's in 14. To get the next quotient figure, think
233 how many 2's in 11. 5 is a little too small, because
11 a it gives a remainder 19, the same as the divisor.
What is the correct figure ?
114
2. Divide 12499 by 29. (29 is almost 30. Let 3 be
your guide figure and think how many 3's in 12, etc.)
3. Divide 2808 by 39. (39 is almost 40. What will
you take for a guide figure?)
4539-89 is. 14732-58
2772-99 19. 4420-68
792-18 20. 6318 + 78
10584-28 21. 45056-88
10353-29 22. 6174 + 98
2242 + 38 23. 3315 + 39
8064 + 48
ng cars is 522 ft. long. How
long is each car?
25. How many coal cars 31 ft. long would make a train
1395 ft. long?
26. When you have a product and one of its factors,
how do you find the other factor ? What is the length of
a rectangle 12 in. wide that contains 840 sq. in.?
4.
2808 + 39
11.
5.
24708 + 29
12.
6.
11837-*- 19
13.
7.
4508 + 49
14.
8.
36639 + 59
15.
9.
16008 + 69
16.
10.
64148 + 79
17.
24.
A train of 9
sleer
116
MAKING CHANGE
Oral
In paying the amounts given below, how much change
should you receive from $ 1 ?
To find the change for 64 cents, —
64+ 6
= 70.
Think
70 + 30
= 100
.
Say 6, 36.
t 30 + 6
= 36
Am.
$.12
$.14
$.16 $.18
$.13
$.15
$.17
$.19 $.11
.25
.27
.29 .25
.21
.22
.24
.26 .28
.31
.33
.35 .37
.39
.32
.34
.36 .38
.48
.46
.44 .42
.41
.43
.45
.47 .49
.56
.58
.52 .-> 1
.59
.57
.55
.53 .51
.61
.69
.67 .65
.63
.64
.64
.66 .62
.76
.78
.77 .72
.73
.71
.75
.74 .79
.81
.88
.83 .87
.84
.85
.86
.82 .89
.95
.96
.99 .97
.94
.93
.98
.91 .92
Add the (
jolumns. Add the lines.
Add the sums of
the columns.
Add the sums of the lines. Compare.
ROMAN NUMERALS
i. C = 100. CC = 100 + 100 = 200. CCC = 100 + 100
+ 100 = ?
2. D = 500. CD =500 -100 = 400. DC = 500 + 100 = ?
3. M = 1000. CM = 1000 -100 = ? DCCC = ?
4. C = ? XXVI = ? CXXVI = ? DC = ? LXV = ?
5. Read: DC; MC; MCC ; CM; CCXX; CCCX; CXXX
6. Eead : DCCCXX ; CDXXX ; CCLXI ; CXLVITI.
7. Write in Roman : 1000; 500; 300; 400; 600; 900
a Write in Roman : 140; 260; 320; 550; 450; 195
ritU
m MISCELLANEOUS
117
1.
See how quickly you can get correct sums :
a.
$173.25 b. $ 836.42 c. $7000.42 d. 497
92.47 1521.50
83.92 6839
9.38 936.08
6214.83 709
407.25 42.53
807.15 598
92.16 1006.27
78.26 763
57.84 83.44
9287.42 6908
9.26 64.29
383.52 89718
2.
Find the missing numbers. Test your work :
a.
645071 b. 48356 c.
58605 d. ?
-280693 + ?
- ? x59
? 97403
29567 708
3.
Solve in figures DCLIX x CCXII.
4.
273018-3 io. 362416-4
is. 342x290
5.
452124-*- 3 ii. 122028-4
17. 4506x206
6.
151824-3 12. 253540-5
is. 1928x453
7.
4243x260 13. 312x600
19. 364218-*- 6
8.
4506x206 14. 3424x60
20. 4530-5
9.
192x453 is. 3642-6
2i. 3206x700
22. Find, the number of square inches in a rectangle
98 hi. by 70 in.
23. A rectangle contains 1710 sq. in. It is 30 in. wide.
How long is it ?
24. The product is 6447, one factor is 21. Find the
other. Make a problem.
25. 392x508 26. 36048-8 27. 875x900
118 PROBLEMS Oral
1. In 17 pt. there are qt. and pt.
2. In 23 qt. there are gal. and pt.
3. In 34 qt. there are pk. and pt.
4. 3 ft. and 2 in. are in. 3x12 + 2 = .
5. In 39 pk. there are bu. and pk.
6. Wilfred picked 3 pk. 6 qt. of cherries. How many
quarts did he pick ?
7. I bought a piece of rope 36 ft. long and used § of it
for a swing. How many feet of rope did I use ?
8. Harold picked a peck basket full of apples 29 times.
How many bushels did he pick and how many pecks over ?
9. If your tablet is 8 in. by 10 in., how many inch
squares can you make on one page ?
Written
1. One box holds 2 dozen lemons, and another 37
lemons. How many lemons in both boxes?
2. At $ .05 an ounce, what will 2 lb. of candy cost ?
3. Find the cost of 24 gal. of ink at 12^ a pint.
4. 12 gal. 3 qt. of maple' sirup at 25^ a quart would
cost how much ?
5. A man bought coal for $ 4.75 and wood for $ 3.50.
How much change should he receive from a $ 20 bill ?
6. April, June, September, and November have each
30 days. How many hours in these months all together ?
7. What is the cost of 288 oranges at 36 cents a dozen ?
8. What number multiplied by 70 will make 1330 ?
Oral MULTIPLICATION 119
1. When steak costs 18^ a pound, a half pound costs
cents. 1J pounds cost 9j^ + 18^ or cents.
What would 21 pounds cost ? 3 J pounds ?
2. When sugar is 6 cents a pound, 3^ pounds cost 3|
times 6 cents, or cents. (3 x 6 = 18. J of 6 = 3.
18 + 3 = ?)
3. What is the cost of 41 gal. of oil at 12 ^ a gallon ?
4. How many feet in 7 yd. ? In \ yd. ? In 7f yd. ?
5. In 1 da. there are hr. In f da. there are
hr. In If da. there are hr.
Written
1. How many hours are there in 9f days?
24
Q2
16 hr. inf da. (f of 24 = 16)
216 hr. in 9 da.
232 hr. in 9-| da. Answer.
2.
Find how many hours in 2 If days.
3.
32
4. 21 5. 485 6. 485
7. 485
x5f
x8| xli xlf
x7f
8.
252
9. 252 10. 252 ii. 84
12. 24
xl{
x If x 5f x 16i
x7#
13.
205
14. 336 is. 485 is. 204
17. 136
x9f
x 6£ x 4f x 8i
x2|
120 MISCELLANEOUS Oral
i. How many hours in 90 minutes ?
2. How many seconds in 2J minutes ?
3. What will 3 qt. of vinegar cost at $.20 a gallon ?
4. Give the multiplication tables of 7, 8, and 9.
5. Give the division tables of 7, 8, and 9.
6. Give the multiplication tables of 10, 11, and 12.
7. Give the division tables of 10, 11, and 12.
8. How many pecks in 3 bu. 3 pk. ?
9. How many quarts in 3 pk. 3 qt. ?
io. What will 18 lemons cost at $.24 a dozen ?
li. George sold 10 White Leghorn eggs and 14 Plym-
outh Rock eggs at $.30 a dozen. How much did he
receive for them?
Written
i. Divide 8487 by 41.
207
41Jo4o7 28 tens will not contain 41 any tens' times, so we
82 put in tens' place in the quotient and- bring down
287 ^ units. 287 contains 41 seven times.
287
In these examples, think first ivhat the guide figure is:
2. 21112-52 5. 70224-28 8. 56160-27
3. 61676-68 6. 5377-19 9. 399294-42
4. 41457-39 7. 21137-23 io. 470564-*- 94
n. How many ounces in 6J lb. ?
12. Subtract the sum of 486 and 296 from 1000.
Written MISCELLANEOUS 121
1. Albert has $42 in the bank. Franz has 2 J times
as much. a. How many dollars has Franz ? b. How
many dollars have both ?
2. A boy whose age is now 12 years was born in what
year?
3. If a boy earns $ .48 in a week, what does he earn
in 9 days at the same rate ?
4. If a dozen pencils cost 18 cents, what must be paid
for a box holding 6 dozen pencils ? For 4 boxes ?
5. A fruit dealer bought 32 boxes of berries for $2.56.
a. How much did 1 box cost ? b. He sold them at 10
a box. Did he gain or lose, and how much on 1 box ?
c. On all the boxes ?
6. A lame boy rode on the car to and from school every
day. His fare was 3 cents each way. a. What was his
car fare for a week ? b. If he was absent 5 days in a
term of 20 weeks, how much was his car fare for the term ?
7. If a street car makes 15 trips a day and carries 45
passengers each trip, how many passengers are carried
during the day ?
8. Columbus discovered America in the year 1492.
How long ago was that?
9. If a man earns $95 a month and spends $35 a
month, how much does he save in a year ?
10. 31 and 13 are the factors of what number?
li. A door mat 24 in. by 36 in. covers how many
square inches of the floor ?
122
HALVES, FOURTHS, AND EIGHTHS
i
i
X i
i
i
i
T
1
1
1
1
1
1
1
'I'
1
1
i. How many inch spaces are there on this rule ? How-
many half-inch spaces in 1 inch ? In the whole rule ?
2. How many %4nch spaces in 1 inch ? In the whole
rule ? In ^ inch ? How many quarters in an inch ?
How many -|-inch spaces in 1 inch ? In the whole
inch?
3.
rule?
In 1 inch ?
W
4.
1 inch = how many half inches f How
many \
1 inch = | = | = f
inches f How many ^ inches f
5. How many quarter inches in one half inch ?
How
many £ inches in one half inch ? \ inch = J = \.
6. How many \ inches in \ inch ? \ inch = l.
7. Two half inches are how many inches? 4 half
inches ? 6 half inches ? . 8 half inches ? 3 half inches ?
8 - f = i; t = ^5 f make what; f = i
I- make what ?
9.
10.
11.
12.
13.
J inch and \ inch make £ inch ;
\ inch and \ inch make I inch ; i + i = ?
1 4- 1— 9
2 + 4" *
inch make |- inch
2^8*
L inch and -^
J inch and 1 inch make £ inch; }+£»£.
Which is greater \ or i ?
iorl? lor
i? i
or f ?
Oral MISCELLANEOUS 123
1. On the rule (p. 122), find $ + f; J+J; i+|;
ll + |; 31 + 1; 11 + 21
Note. — Children use their own rules also.
2 Find 11 + 1- 14 + 24- 144-4* 1^4-1- "U4.1
3. Find If, then take away J. What is left ?
4. Find 2|, then take away -|. What is left ?
5. 2 + 3 = ? l + i = ? 2i + 3i = ? 1 + 1 = ? 5i + i=?
6. | + i = ? 6 + 2 = ? 6|+'2i = ? 5f-i = ? 7i-i = ?
7. Mary has a hand mirror 4 in. by 6^ in. How
many square inches does it contain ? (Picture.)
8. If the mirror was 3 in. wide and contained 15 sq.
in., how long would it be ? (Picture.)
9. A traveler paid $.25 for breakfast, $.50 for din-
ner, $.25 for supper, and $.50 for lodging. What did
his board and lodging for the day cost him ?
10. If 5 pears cost 15 cents, 10 pears will cost twice as
much, or cents. Why ?
11. 20 pencils cost 60 cents. Five pencils cost \ as
much, or cents. Why ? In what other way could
you get it ?
12. If 2 quarts of milk cost 10 cents, 2 gallons would
cost times as much, or cents. Why ?
13. Henry earned 40 cents in 5 hours. How much
could he earn in 10 hours ? Find it in two ways.
14. Grace can solve 4 problems in 12 minutes. How
many can she solve in 48 minutes ? Find it in two ways.
15. At 2 cents a foot, what will 6 yd. 2 ft. of rope cost ?
124 READING AND WRITING NUMBERS
423,578,600 is read, four hundred tiventy-three million
five hundred seventy-eight thousand six hundred.
i. Bead: 125,791,235; 26,625,130; 4,310,240;
99,000,000; 600,329,842; 100,000,125; 96,000,050.
Find results and read them:
2. Multiply by 10 : 14; 28; 79; 192; 345.
3. Multiply by 100 : 210; 980; 6004; 4250.
4. Multiply by 1000 : 13; 25; 49; 324; 20.
5. Divide by 1000: 98,000; 1,239,000; 4,900,000.
6. 569x3200 12. 2038x490
7. 423x600 is. 950x2400
s. 507x500 14. 3,812,400-900
9. 938x240 is. 180,960 -*- 520
10. 5803x9000 ie. 50,040-60
11. 256x8500 17. 308,000 + 800
18. The sun is 92,000,000 miles from the earth, a. If
you could travel toward the sun at the rate of 40 miles
an hour, you would have to travel how many hours to
reach it ? b. If you should travel 10 hours a day, how
many days must you travel to reach the sun ?
19. It is 25,000 miles around the earth. If you travel
50 miles an hour, how many hours must you travel to go
around the earth ?
Written REVIEW 125
l. How long will it take you to get correct sums f
a, 837 b. 628 c. 8063 cL $26.43 e. $715.30
2964
4307
259
18.75
21.86
418
526
8264
2.93
9.24
3825
8279
1287
4.10
10.16
842
428
428
128.06
7.28
29
4273
3064
563.13
516.00
2. A jar of butter containing 23|- lb. costs how much
at 30 ^ a pound ?
3. At $96 a month, how much can a man earn in 7J
months ?
4. How many quarts in 6-J bushels ?
5. At $1.28 a yard, what will 3f yd. of cloth cost?
6. How many minutes in 7f hours ?
7. 5000 s. $40.12 9. $25.00 10. $38.42 11. 495
-479 -37.84 - ? + ? x 99
$23.59 $96.39
Oral
1. Name all the letters used in Roman notation and
give the value of each.
2. A half inch and a quarter inch are how many
quarters ? A half dollar and a quarter dollar ?
3. Put your pencil at the left end of the rule (p. 122).
Move it 11 inches to the right. Move it f inch farther.
How many inches have you moved it ? 1 \ + f = ?
126 MULTIPLICATION AND DIVISION Oral
l. a. 24x10 2. a. 12x70 3. a. 46x20
6. 45x100 6. 16x30 &. 15x40
c. 16x20 c. 420x20 c. 12x600
d. 18x20 d. 51x100 d. 15x50
e. 30x10 6. 7x1000 e. 90x100
4. a. 160 + 10 5. a. 80-40 6. a. 600-300
b. 230-10 b. 280-40 b. 800-200
c. 40-20 c. 250 + 50 c. 1800-900
d. 80-20 d. 420-70 d. 36000 + 9000
e. 100 + 20 e. 860 + 20 e. 720 + 120
7. A pail weighs If pounds, the cover \ pound, and
the contents of the pail 20 pounds. If you carry it, how
many pounds must you carry ?
8. If George gained 5f lb. during vacation and lost \
lb. during the first week of school, how much heavier was
he then, than when the vacation began ?
ADDITION AND SUBTRACTION
9. a.
2|+i
10.
a.
n+n
11.
a.
2f+9J
b.
H + H
b.
5f + li
b.
6i-i
c.
7i + 8J
c.
2f + |
c.
7-1
d.
4J + 81
d.
7i + i
d.
8J-31
e.
H+i
e.
H+n
e.
fi3 _ 1
U 4 4
12. a.
5J + I
13.
a-
81-1
°2 4
14.
a.
53-29
b.
6| + H
b.
H-t
b.
86-79
c.
n+i
c.
8* + ? =
8*
c.
65-38
d.
H + H
d.
51 + ? =
6
d.
59 + 32
e.
12J + 71
e.
4f-? =
41
^2
e.
86 + 49
Written
PERIMETER
127
Fig. 1.
Fig. 3.
Fig. 5.
Fig. 2.
The sum of all the sides of a
figure is its perimeter.
1. Measure the four sides of
Figure 4. Add them. What is the
perimeter of Figure 4 ?
2. Measure the sides of Figure
5. Find its perimeter.
3. Find the perimeter of Figure
1 ; of Figure 3 ; of Figure 2.
4. Draw on the blackboard a square 9 in. on a side .
a. Its perimeter is how many inches ? o. How many feet ?
5. Draw a square whose perimeter is 48 in. How many
inches long and wide must it be ?
6. Measure your paper and find its perimeter.
7. Draw on the blackboard a rectangle 2 ft. long and
6 in. wide. Find its perimeter.
8. A garden bed is 12 ft. long and 8 ft. wide. Make a
drawing of it, using i in. for 1 ft. What is its perimeter ?
&. A city lot is 150 ft. long and 50 ft. wide. What is
its perimeter ? Draw it, using 1 in. for 50 ft.
128 MULTIPLICATION AND DIVISION Oral and Written
There are 2000 pounds in one ton (T.).
One horse can draw a ton of coal. A two-horse load of
coal usually contains two tons. Farmers usually take to
market about one ton of hay at a load.
A large flagstone may weigh about one ton. Can you
name something else that weighs about one ton ?
1. How many pounds in 2 T. of coal ? In 1^ tons ?
In 12 tons ? In f of a ton ? In J ton ? In -fa of a ton ?
In 6 \ tons ?
2. A load of iron rails weighs 3 tons. The wagon
weighs 1250 lb. The horses weigh 2600 lb. The bridge
that the load is drawn across must be strong enough to
hold up pounds.
3. A car load of coal weighs 28000 lb. How many
wagon loads of 2 T. each will it make ?
4. Mrs. Allen bought a quarter of a ton of coal. How
many poimds did she buy ?
5. A ton of butter was packed in pails holding 50 lb.
each. How many pails were used ?
6. 20 bales of cotton, each containing 500 lb., weigh
how many pounds ? How many tons ?
7. 1000 lb. is what part of a ton ? 500 lb. ? 200 lb. ?
8. How many pounds in 5 T. ? 7 T. ? 21 T. ? \ T. ?
9. How many ounces in 1 ton ? In 7 T. ? In \ T. ?
10. A ton of hay was pressed into bales weighing 200
pounds apiece, a. How many bales were there ? b. How
many such bales would 1\ tons make? c. llf tons ?
Oral DIVISION 129
1. Division is often indicated by writing the dividend
above a line and the divisor beloiv the same line, thus :
¥=12 + 3 = 4; ¥ = 3;-^- = ;|f = ;.¥- •
2. Give the quotients: -*/; ^5 Wi^ifi W-
3. When the dividend does not contain the divisor an
exact number of times, the remainder is written over the
divisor, as a, fraction, thus - 3 ^ = 4§. This means that there
are four 9's in 38, and 2 over, or, that the quotient of 38
divided by 9 is 4f .
Find the quotients : ^ ; V" ; ¥ 5 ¥ 5 ¥ J ¥ 5 W 5 if
4. At 40 cents a pound, what is the cost of ^ lb. of
peppermints and \ lb. of lemon drops ?
Written
i. Divide 26670 by 35.
762
35 1 26670 35 ig midway between 30 and 40. 3 is contained
245 i n 26 eight times. 4 is contained in 26 six times. So
217 the first quotient figure is between 6 and 8, or 7. In
210 a similar manner we get 6 for the second figure of the
^77 quotient.
70
2. 8675 + 25 (use 2 and 3 for guide figures).
3. 3082 -4- 46 (use 4 and 5 for guide figures).
Find the quotients : 1
q 1890 1Q 2.788 ,, 3J111 12 1^_4_8_8 ,3 ,5_1 5 9 &
9 * ¥5 ■ LO - 3 4 *** 8 5 ■ L ^' 4 6 ■ L ' 5 - 8 5
1 Examples 4 to 13 should be read, " 2210 divided by 65," etc.
130 MULTIPLICATION AND DIVISION Oral and Written
i. On the blackboard, make a square 1 ft. wide. How
long is it ? What is it called ? Describe a square foot.
2. Make a rectangle 3 ft. by 7 ft. How many square
feet (sq. ft) does it contain ? Mark off the square feet in
the rectangle.
3. How many square feet in an oblong 9 ft. by 8 ft. ?
7 ft. by 12 ft. ? 11 ft. by 12 ft. ? 6 ft. by 7 ft. ?
4. Measure the length and breadth of your schoolroom
and find the number of square feet in the floor.
Note. — Length and breadth are dimensions.
5. The floors in our house are rectangles and have the
following dimensions :
Reception room 12 ft. by 11^ ft.
Dining room 13 ft. by 16 ft.
Library 18 ft. by 13 ft.
Hall 8 ft. by 18 ft.
Kitchen 12| ft. by 14 ft.
a. Find the number of square feet in each of the floors.
b. In all the floors. Draw the hall, using J- in. for 1 ft.
6. Measure the top of your desk and find the number
of square inches it contains. (Omit fractions.)
7. Mr. Fancher's sidewalk is 5 ft. wide and 66 ft. long*
What did it cost at 11 ^ per square foot?
8. What would it cost to put an oak floor in the li-
brary (question 5) at 17 ^ per square foot ?
9. A skating rink 98 ft. by 212 ft. contains bow many
square feet ? Find its perimeter.
AREA 131
1. Hold your hands 1 yd. apart. Hold your hand one
yard above the floor. Without a rule, draw on the black-
board a square one yard long. How wide is it ? Measure
and correct it. What is it called ? Describe a square yard,
2. The top of your teacher's desk contains about how
many square yards (sq. yd.) ?
3. Estimate the number of square yards in the floor of
your schoolroom. Measure and see how nearly right you
are.
4. A courtyard is 12 yd. wide and 43 yd. long. How
much would it cost to pave it at $ 1\ a square yard ?
5. The number of square units (square yards, square
feet, square inches, etc.) that a surface contains is its area.
How do we find the area of a rectangle ?
6. When the area and one dimension of a rectangle
are given, how can we find the other dimension ?
7. The area of a dining table is 36 sq. ft. Its width
is 4 ft. What is its length ? Draw it, using ^ in. for 1 ft.
8. A pane of glass is 28 in. by 32 in. a. What is its
area? b. A room with 3 windows, each having 2 such
panes, has how many square inches of glass ?
9. Measure a floor in your house and compute the
area. Make a drawing, using J in. for 1 ft.
10. There are 5280 ft. in a mile. If a pavement is a
mile long and 50 ft. wide, how many square feet in it ?
li. A mile is 1760 yd. How many square yards in a
street 1 mile by 20 yd. ?
132
DIVISION
Written
i. Find the value of ^ 3 <p.
599^1 Quotient
49)29366
245
486
441
456
441
15
Proof
599Jf Quotient
x 49 Divisor
5391
2396
29351
+ 15 Remainder
29366 Dividend,
There is a remainder of 15, which shows that 29366 is 15 more
than the product of 599 and 49.
Find the values of the following. Test your work by
multiplying the whole number in the quotient by the divisor,
and adding the remainder.
2. ^>p
10. A||±
14. ^
18. M^
LUi
3. *ft*
7> 18 7 3 6
ii. J^yu
15.
19.
22.
26 6 41_8_8
Zt>. 33
3J7_5_6_1
46
JL06.01
23. l^ftM
4 .2_20_9_
*• 18
« 56803
«*• 92
12 . iu^u
16 . juyyu
20. ^\V=-
642Q
42
5
9
13
17
21.
25
9063
SO
9650
~8"7
8329
31
11 988
14
Hi 1
29.
31053
65
31 . 27_6_8J>
24. 1W*
27. ±1^ 28.
30. - 8 ^
32. If 47 apples will fill a peck measure, how many
peck measures will 4356 apples fill, and how many apples
will be left over ?
33. 2000 ounces of raisins will fill how many pound
packages ?
Oral REVIEW 133
i. Count by 3's from 2 to 101 and back.
2. 33 Brazil nuts were given to a boy and his two sisters.
How many apiece had they, if the nuts were divided equally ?
3. Joseph, raised 42 ducks and sold 15. How many
had he left?
4. A half-dollar, two quarters, a dime, and two nickels
are how much money ?
5. A man earned $32. He paid $12 for a suit and
$ 9 for an overcoat. How much had he left ?
6. What must be paid for 4 dozen peaches at 20 each?
7. Ilin.-f2iin. = ?in.; $1|+$11 = ?
8. Mr. Finch picked 39 plums and divided them
equally among his three sons. How many did Frank and
George receive?
Written
i. $41.72 2. $86.05 3. $32.65 4. $48.37
x8 x_6 -14.87 - ?
$19.48
5. A man earns $20 a week. If he pays $.95 a day
for board and $1.15 a day for other things, how much
can he save in a week ?
6. Divide the product of 27 and 32 by their sum.
7. A man sold 58 cows at $38 apiece and 176 sheep
at $ 4 apiece. What did he receive for all ?
a. One factor of 7659 is 37. What is the other ?
9. Ajjp 10 . A|§A ii. *ftfiP 12 « -W- 9
134 REVIEW Oral
i. A dressmaker bought 4J dozen buttons. When she
has used 20 of them, how many are left ?
19 + 7 + 8 + 6 _ 9 12 + 6-8 ,
10 ' 5
3. What does a year's rent amount to at $ 12 a month ?
4. What is the amount of 6 months' rent at $120 a
year ? Can you find it in two ways ?
5. 3 yd. of gas pipe at 8 cents a foot cost how much ?
6. x =84. x =132.
7. Six feet of chain at $.36 a yard cost how much ?
8. The multiplicand is 42, the multiplier 2. What is
the product ? Make a problem.
Written
i. Mr. Graves receives a salary of $1404 per year.
That is how much a month ?
2. A farmer sold a grocer 235 lb. of butter at $ .24 a
pound and bought of the grocer a barrel of sugar for
(15.75. Which man received some money and how
much?
3.* How many bushels of wheat will a farmer raise in
7J years if he raises 98 bushels every year ?
4. A sidewalk 5 ft. wide contains 485 sq. ft. How
long is it ?
5. 37 and 459 are the factors of what number?
6. How many tons of coal can be put in a bin that
will hold 28000 pounds ?
7. Write in words 400,216.
Oral REVIEW 135
i. From a piece of meat weighing 30 ounces, \ of a
pound was cut. How many ounces remained ?
2. Hazel paid 16 cents for buttons at 24 cents a dozen.
How many did she buy ? How many could she buy for
12 cents ?
3. A rectangle contains 54 square yards. It is 9 yd.
long. Give the question.
4. Charlotte practices music three hours every day.
What part of all the time does she practice ?
5. What part of a minute is 12 seconds ?
6. Give two factors of 63; of 96; of 110; of 32; of 48.
7. Our family uses a half gallon of milk every day at
$ .05 a quart. Give the question and answer.
Written
i. Multiply CLXIX by XCV, expressing the work in
figures.
2. Two boys sold extracts and shared the profits
equally. The first week they took in $17.25. Their ex-
tracts cost them $9.55. How much did each boy make ?
3. Mr. Banker bought a pony for $ 142, a cart for $ 25,
a harness for $13.50, and robes, blankets, etc., for $19.75.
What did they all cost ?
In examples 4-13, find the values and test your work :
a, 3486 ,- 97603 fi 1578 9 n 84936 a 47_6_30
*• 19 °' 2 3 b * 6 5 '* 9 3 *** 8 8
q 12903 , n 12750 ,, 82493 19 28 35 ,,, 4 3 91,
9 - 6 6 10 ' 12J **■ 5 3 12 ' 6 2 13 * ^flP
14. $459.62- $78.36 is. 463x847
136 REVIEW Orai
i. Without measuring, draw a line 4 in. long ; measure
and correct it ; a line 9 in. long ; 12 in. ; 2 yd. ; 1^ ft.
2. Estimate the width and height of doors, windows,
blackboards, ventilators, etc., then measure and see who is
most nearly correct.
3. A bushel and 9 qt. are how many quarts ?
4. ^ in. = how many fourths of an inch ? Eighths ?
5. $f + $i = ? $A + $i = ? liin. + 2iin. = ?
6. What is the time when the minute hand is at IX
and the hour hand is between XI and XII ? (Picture.)
7. Express in words : MDC; CDLX; DCXC.
Written
l. Add up, then down. Time yourself:
a.
123 i
!>. % 6.34
c. 903
d.
4836 e
. % 5.86
12
83.59
74
539
9.73
3
12.70
973
46
81.29
456
893.98
460
930
40.00
89
24.57
23
89
' 1.72
45
806.93
58
98 .
19.38
2. Indicate the sum of 921 and 33 divided by 106.
3. Indicate the product of 1728 and 144 less 5184.
4. a. How many pounds in J- of a ton of corn meal?
b. What is it worth at % 28.64 a ton ?
5. When hops are $ .25 a pound, what should a farmer
receive for 3000 lb. of hops ?
6. Find the value of : a. H^ ; 6. ±£f* ; c. **$£*-.
Oral REVIEW 137
1. What will 2 yd. of cloth cost if 6 yd. cost 48 cents ?
2. If your horse eats 12 qt. of oats a day, how long
will 1$ bu. last ?
3. How many right angles in 11 rectangles ?
4. How much must a man put in the bank each month
to save $ 96 in a year ?
5. A boy received a quarter of a dollar a week for
driving a farmer's cows to pasture. How much could he
earn in 16 weeks?
6. A quart is what part of a gallon ? 3 quarts ?
7. What must be paid for 8 cream puffs when 4 cost
12 cents ? (Two ways.)
8. It takes Willis 5 weeks to earn 10 dollars. In
what time can he earn 18 dollars ?
Written
1. Without partial products, find 83 x 11 ; 421 x 11.
2. By short division, find the value of: a. W£-j b. J ^;
C 4:4:71 . J 42JL4
o. f i , a. 1]L .
3. If Mr. Kent works 300 days in a year at $4 per
day, how much will he earn in 11 years?
4. Without partial products, find: a. 186 x 12; b. 435
xl2; c. 9128x12.
5. By short division, find: a. -^f^; b. ^^; c. *£p.
6. How many years and months in 964 months ?
7. A park is 240 yd. long. How wide must it be to
contain 4320 square yards ?
138 REVIEW Oral
i. How many feet in all the sides of a square yard ?
(Draw it on the blackboard.)
9 9_ . 8 7 __ . 36 .45
18 ' . 18x 5 _ 18h-3 _
3 * 9 ; 9x5 ; 9+ 3
4 . \ . \ « \. Read 80,306 ; 100,100 ; 705,050.
5. How long and wide is a square that contains 16
square inches ? (Picture.)
6. If % 10 is \ of my money, how much money have I ?
7. Irving gathered \ bu. of chestnuts and Horace
gathered 5 qt. more than Irving. How many quarts did
Horace gather ? How many quarts did both gather ?
Written
1. There are XXXI chapters in the book of Proverbs,
CL in the book of Psalms, and LXVI in the book of
Isaiah. How many more chapters are there in the book
of Psalms than in both the others together ?
2. Two men start from the same place. A travels 59
miles north and B travels 63 miles south, a. How far
apart are they? b. If they had traveled in the same
direction, how far apart would they have been. (Picture.)
3. How much greater is J of 86,140 than J of it ?
4. 27,404 has what factor besides 68 ?
5. The product is 7488. The multiplier is 96. Find
the multiplicand. Make a problem.
6. George climbed | of the distance to the top of a
tree 60 feet high. How far from the ground was he ?
TO THE TEACHER 139
TO THE TEACHER
The terras concrete number and abstract number have become
so fixed in arithmetical literature that their propriety, or even
their necessity, is scarcely questioned.
A close examination into the nature of number, however, con-
vinces one that number is essentially abstract, and that the name
or denomination affixed to a number is no part of the number
itself, and is useful merely for the purpose of reference, or as a
mark of identification, and therefore should not be brought
into the mathematical operations performed with numbers.
Possibly the child's intuitive grasp of this truth has made
him so prone to interchange the terms in multiplication, to find
the "number of parts" instead of "one of the parts" in divi-
sion, and to resist the attempt of the teacher to make him use
the larger number for the multiplier in explaining a certain
class of problems.
Is it not possible, indeed, to add unlike numbers ? Is it not
as easy to add 6 trees and 7 books as to add 6 trees and 7 trees ?
We need only to apply the sum to a term sufficiently general
and call it 13 things or 13 objects. In either case, the process
of addition is performed with the numbers 6 and 7, and not
with the objects to which the numbers are applied.
Without prescribing any set form for the analysis of prob-
lems, let us suggest that much time and tribulation may be
saved by such a treatment of the fundamental operations as the
following : —
a. If an apple costs 2 cents and a peach 3 cents, both cost
as many cents as the sum of 2 and. 5, or five cents.
140 TO THE TEACHER
b. If a boy earns 5 dollars and spends 3 dollars, he saves as
many dollars as the difference between 5 and 3, or 2 dollars.
c. Since there are 2 pints in 1 quart, 20 quarts are equal to
as many pints as the product of 2 and 20, or 40 pints.
d. Since there are 16 ounces in 1 pound, 32 ounces are equal
to as many pounds as the quotient of 32 divided by 16, or 2
pounds.
e. If 5 pencils cost 15 cents, 1 pencil costs as many cents as
the quotient of 15 divided by 5, or 3 cents.
This form of analysis recognizes in each case the real nature
of number, namely, the " how-many-ness " of things, and also
the true function of addition, subtraction, multiplication, and
division, as operations with numbers, not with things. It avoids
all difficulty as to the likeness or unlikeness of terms in multi-
plication and division. In every problem involving multiplica-
tion, the question itself indicates to the pupil what unit-name
is to be attached to the product, and he need only observe that
he has two factors to multiply in order to determine the
numerical product. It is wholly immaterial which factor he
uses for the multiplier, or what unit-name either factor may
bear. Likewise, in division, the pupil knows at the outset
what is to be the unit-name of the quotient, and that the divi-
dend represents a product of which the divisor is one factor,
and the other factor is to be found. Whether the dividend
and divisor are like or unlike numbers is of no consequence in
the solution of the problem or the determination of the result.
It is well, however, to label numbers with their unit-names
for convenience in referring to them while solving a problem
or reviewing the work.
ODD AND EVEN NUMBERS 141
1. A number that can be exactly divided by 2 is an
even number, as, 2, 4, 6, 8, 10.
A number that cannot be exactly divided by 2 is an odd
number, as, 1, 3, 5, 7, 9, 11.
2. Divide 98 by 2. What is the remainder? What
kind of a number is 98 ?
3. Divide 97 by 2. What is the remainder? What
kind of a number is 97 ?
4. Write all the odd numbers from 1 to 99.
5. Write all the even numbers to 100.
6. What are the unit figures in the even numbers?
In the odd numbers ?
7. At how many figures of a number must you look
to tell whether it is odd or even ?
8. Tell which of the following numbers are odd and
which are even: 9, 12, 16, 15, 14, 27, 19, 36, 438, 591.
9. What factor is always found in an even number ?
10. In what kind of a number is the factor 2 never
found ?
li. Tell which of the following numbers are odd and
which are even :
The number of
a. Pints in a quart. /. Inches in a foot.
6. Cents in a half dime. g. Quarts in J gal.
c. Quarts in a peck. h. Eighths in J.
d. Minutes in \ hr. i. Square inches in a 5-inch square
e. Hours in f da. /. Quarts in | of a bushel.
142 FACTORS Oral
We have learned that the multiplier and multiplicand
are factors of the product, and that the divisor and quotient
are factors of the dividend. If you have the product and
one of its factors, how can you find the other factor ? If
you have the dividend and one of its factors, how can you
find the other factor ?
One of the numbers that are multiplied to produce a
number is a factor of that number.
So small a number as 2 has factors, for 2x1 = 2. What
are the factors of 2 ?
In telling the factors of a number, we do not mention
the factor 1, because 1 is a factor of every number.
i. Give two factors of 6 ; 9 ; 10 ; 14 ; 15 ; 21 ; 25;
22; 33; 34; 35; 38; 39; 49; 63; 72; 77; 81.
2. Of what number are 12 and 11 factors?
3. 2x3x5 = ? Give three factors of 30.
4. 7x2x5 = ? Give three factors of 70.
5. Name all the numbers that will divide 9 ; 8 ; 10 ;
11; 12; 13; 14.
6. 5 and 2 are factors of 30. What other factors has 30 ?
7. Complete the following statements and tell which
numbers are products and which are factors :
a. 8 pints = quarts.
b. 5 dozen copy books are copy books.
c. 4 bushels = pecks.
d. 5 apples, at 2 ct. each, cost ct.
e. 9x =108.
QUICK TEST 143
1. 25x10 = ?
2. Give two factors of 35.
3. Write the even numbers to 20.
4. There are 120 seconds in 2 minutes. What factor
is not given ?
5. A sheet of wrapping paper 6 ft. by 21 ft. contains
how many square feet ?
6. 6§ + 2f = what?
7. Dan bought a half peck of peanuts at 5 cents a
quart. Give the question and answer.
8. The area of a window shade is 21 square feet. Its
length is 7 ft. Which number is a product ? What are
its factors ?
9. If you sleep f of the time, how many hours a day
do you sleep ?
10. 20 min. is what part of an hour ?
Oral
Complete the following statements and tell which num-
bers are products and which are factors :
11. 32 ounces are pounds.
12. At $ 12 a week, a man can earn % 96 in weeks.
13. A floor is 12 ft. long and 11 ft. wide. Its area is .
14. A man's salary for 10 years amounts to $15000.
He receives dollars per year.
15. At 25 cents per week, Eoger should receive
for shoveling Mr. Abel's sidewalk 4 weeks.
144 FACTORS Oral
i. 12 is what of 4 and 3 ? When 4 and 3 are given,
how can you get 12 ? When 12 and 4 are given, how
can you get 3 ? When 12 and 3 are given, how can you
get 4 ? 4 and 3 are what of 12 ?
2. At 7 cents apiece what will 5 pineapples cost ?
Which numbers are factors ? What is the product ?
3. If 5 pineapples cost 35 cents, how can you find the
cost of 1 pineapple ? If 1 pineapple costs 7 cents, how can
you find the number of pineapples that 35 cents will buy?
5 and 7 are what of 35 ? 35 is what of 5 and 7 ?
4. When two factors are given, what do you do to
find the product ? When the product and one factor are
given, what do you do to find the other factor ?
In each of the following problems, tell ivhich of the things
mentioned in question 4 are given, and ivhich is to be found :
5. What is the area of a rectangle 4 ft. by 9 ft. ?
6. If Clarence earns 12 cents every week, in how
many weeks will he earn 84 cents ?
7. There are 4 pecks in a bushel. How many pecks
in 11 bushels ?
8. 7 days make a week. How many weeks in 63 days ?
9. 4371-? = 47. 10. 75x? = 2025. 11. 38x99 = ?
12. If $5.10 is divided equally among 3 boys, how much
money will each receive ?
13. An apple tree bore 128 bushels of apples in 16 years.
That was the same as how many bushels in each year ?
14. One factor of 121 is 11. What is the other ?
Oral MULTIPLES 145
i. 2x3 = ? 6 contains 3 how many times ? 6 con-
tains 2 how many times ?
2. 3x5 = ? 15 contains 3 how many times ? 15
contains 5 how many times ?
3. 5x7 = ? 35 contains 7 how many times ? 35
contains 5 how many times ?
4 . 44^4 = ? 44 + 11 = ? 44 is what of 4 and 11 ?
A number that exactly contains another number is a
multiple of that number.
5. Name a multiple of 2 ; of 3 ; of 5 ; of 7 ; of 4 ; of 11.
6. Name two numbers of which 6 is a multiple.
7. Nine is a multiple of what ?
8. Every even number is a multiple of what ?
9. A number that is not a multiple of 2 is what kind
of a number ?
10. 6 is a multiple of what two numbers ?
li. Give all the multiples of 2 up to 30.
12. Give all the multiples of 3 up to 36 ; of 5 up to 60 ;
of 4 up to 48 ; of 6 up to 72 ; of 7 up to 84.
13. How many different numbers will divide 36 ?
14. The number of cents that 8 tops will cost at 5^
apiece is a multiple of what ?
15. 77 is a multiple of 7. It is a multiple of what
other number ?
16. What is the smallest number of apples that you
could divide equally among either 3 boys or 2 boys with-
out cutting any of the apples ?
146 FRACTIONS Oral
i. Review page 122.
2. Florence bought £ lb. of caramels, \ lb. of pepper-
mints, and \ lb. of butter scotch. How many pounds of
candy did she buy ?
3. What are 10 jackknives worth at %\ apiece ?
4. What are 20 knives worth at % \ apiece ?
5. Cut a pie into 8 equal pieces. What part oi the
pie is 1 piece ? (Picture.)
How many pies, each cut into 8 pieces, are needed to
serve 24 people ? -^ = ?
6. Cut a pie into quarters. Give a piece to each of
two boys. What part of the pie is gone ? What part is
left? (Picture.) f = ?
7. Give half a pie to John and \ to Nellie. What
part is gone ? What part is left ? (Picture.) \ = p
8. Cut a pie into 8 pieces. Give J to Henry (How
many pieces ?) and £ to Frank. What part is gone ?
What part is left ? (Picture.) i + i = s- + ¥ = ? i + 1 = ?
Make a picture of 4 pies cut into 8ths. Each piece
is y. How many pies do 8 pieces make? 16 pieces?
24 pieces ? 32 pieces ? f = ? - 1 /- = ? \ 2 - = ? ^ = ? 9
pieces make how many pies ? 11 pieces? 13 pieces? 15
pieces? 31 pieces? |=? ^=? \ 5 " = ? ¥= ? ¥' = ?
10 pieces are how many pies? 12 pieces? 18 pieces?
20 pieces? 28 pieces? -V° = ? ¥ = ? ¥= ? ¥ = ?
How many pieces in \ of a pie ? ^ ? |- ? J = £ J = i-
Oral FRACTIONS 147
The number written above the line in a fraction is the
numerator.
The number written below the line in a fraction is the
denominator.
Name the numerator and the denominator of ^; f ; J; |-.
The numerator and denominator are called the terms of
a fraction. Name the terms of | ; ^ ; ^.
1. The numerator of a fraction is 5. The denominator
is 9. What is the fraction ? Write it.
2. What is the fraction whose numerator is 8 and
whose denominator is 13 ? Write it.
3. A fraction always indicates division. The numerator
is the dividend. The denominator is the divisor.
^ = 18-5-9 = 2, y- = 17-4-5 = 3f, | inch = 3 inches ^4.
Draw a line 3 in. long. Divide it into 4 equal parts.
Measure one part. How long is it ?
Take 3 apples. Cut a quarter out of each one. Put
together the 3 quarters cut out. What part of an apple
do they make ? How does this compare with the part
that is left of each apple ? The three apples have been
divided into how many equal parts ?
4. Express as fractions : 3 -*- 8 ; 7-5-9; 4-f-5; 15-5-3;
124-4-17.
18 = 2 18-5-3 _ 9 42 = 9 42-s-2 _ 9 4 = 9 4 ± 4 = ?
5 * 9 ' 9-3 ' 14 * 14-*-2 8 ' 8h-4
6. Write the fraction whose terms are 3 and 5 ; 4 and 7 ;
5 and 8.
148 FRACTIONS Oral and Written
1. A fraction whose terms cannot both be divided by
the same number is in its lowest terms. Thus f is in its
lowest terms, because 2 and 3 cannot both be divided by
the same number. |- is not in its lowest terms, because
both 4 and 6 can be divided by the same number. What
number will divide 4 and 6 ?
2. Tell which of the following fractions are in lowest
terms :
h h 4> 6> 4> 9? 9> 9> "9> TIT' DT> TT> A> T2> T2 #
3. Change £ to lowest terms :
4 4 + 4 1 A
8 = 8+l = 2- An8wer -
4. Change £ to lowest terms :
6 = 6^2 = ? AmW6r -
Change
to lowest terms:
5.
3
6
6. f 7. | 8. ^
9- A
10.
1
ii.
A
12.
A
13. f 14. T 8 e 15. &
16. ^
17.
A
18.
6
TIT
19.
&
20 - A 21 - A 22 - A
ADDITION
23. if
24.
if
25.
M
l.
f+
4 4 ±# * ^ 8 8 *
4 i 1_
?
2.
1+
.2 i 3_8_0 2 i 1 i 2 .
4+4-4- Z - 5 + 5 + 5-
=*=?
i +
i+l
+ 1
^2
= ?
3.
1+
4=? A i 1 = ? 3.2,
W i
+ i
= ?
4.
2|
+ 3i = 5§ = 6. 6J + 8f =
14|=?
5.
3|
+ 2i = ? 4| + 5f = ? 6i
+i-?
6.
llj
Ki = ? 9f + 2J = ? 7j
+2f-i
i
WHOLE AND MIXED NUMBERS 149
WHOLE AND MIXED NUMBERS
A number that is not a fraction is a whole number.
Thus, 5, 8, 10, 11, 15, are whole numbers. Name others.
A ivhole number and a fraction, taken together, make a
mixed number. Thus, 21, 7§, 8f , are mixed numbers.
The value of a fraction whose numerator is larger than
its denominator is a whole or a mixed number.
Thus, | = 3, i = 3i ^-=4, ¥ = 2 |.
How is the value of a fraction found ?
"Find tVip vfllnp nf LP- 2_5 3 9 725 43 2 483
Tina me vaiue oi -% -, -§--, -y-, -25-5 jpf-j "XT*
Written *
i. Add 341 2 . Add 43f
42f 581
56 62-g-
132f = 133 Sum 163-11= 164f Sum
3. 361 4 . 39| 5 . 48f 6 . 961 7 . 235£
41f 91f 62 781 342|
59 85J t 81f 82J 998_
8. 345| 9. 99J io. 83f 11. 12i 12. 892|
2961 12| 491 191 485 4
4081 151- 87 388 207 3
3
4
3
_A J ^!l ^L!_ ouu ^ v, 4
13. 49| 14. 81| 15. 92| is. 2371 17. 324f
-26| -25| -861 -1951 -197f
* Note. — Tn the answer, when the numerator of a fraction is equal to, or
larger than, the denominator, always find the value of the fraction as a
whole or a mixed number. Change the fraction part to lowest terms.
150 FRACTIONS Written
Note. — Many of these exercises may be illustrated by means of
objects and drawings.
l. Add | and £. f = |
W
£ >SWra.
2.
Add f and f .
*•
-4
\-
=1
Jgi- = If /Swra.
3.
Add 12| and 21|.
12f =
= 12|
21f =
= 21f
33f = 34£ Sum.
4.
From 18| take 6J.
18*'
-18*.
H-
12f Remainder.
5.
Add \ and £.
is. 29f + 48i
6.
Add \ and -§-.
16. 37£ + 81£.
7.
Add f and -£.
17. 57| + 93f.
8.
Add J and J.
is. 44f + 65f
9.
From £ take ^.
19. 64J + 23}.
10.
From \ take -|-.
20. 91|-42i
11.
From ^ take J.
21 . 46f-34J.
12.
From | take f .
22. 83£ + 21£.
13.
From £ take J.
23. 42| + 48i
14.
From f take J.
24. 89i + 40|.
25. Alice bought 9| yd. of silk and 4J- yd. of muslin.
How many yards did she buy ?
Oral FRACTIONS 151
I .1 I ." . § |
_i_ jl l_ _L i i.
m.I 2 1 S 1 2 1 2 ^_* h 2 U
1. How many halves in the line MN ?
2. How many sw^As in the line MN ?
3. How many sixths in -| of the line ? J = -g-.
4. Find jr more than \ of the line. How many sixths
of the line have you found ? \ + \ = § -f -J- = J.
5. Find f of the line, f of the line is how much more
than i of the line? f ~i = f -| = f
6. When we ivish to find the differences or sums of
halves and sixths, we change the halves to what ?
7. Draw on the blackboard a picture of a pie cut into
6 pieces. Erase \ of it. How many halves are left ?
How many sixths are left? Add f to the part that is left.
What part have you ? -f + f = ?
q 1x1-? l_l__3=? ij.2 = ? 5._1 = ? 4__1 = ?
8 -2^6^~~* 2^6 • 2^6 * 6 2* 6 2 *
M>
i
\
1
"3"
9. \ = how many 6ths ? f = how many 6ths ?
10. Find I and \ of the line. How many 6ths of the
line have you found ?
11 1_1 — 2._JL — 1 1 J- 3 _ 2 1 3. = 5.
J " L ' 3 6~~ 6 6 ~ 6* 3 ^ 6 ~~ 6 ^ 6 6*
i, lil-? 2. i 1_? 5_1_? 5_2. = ? 3.-1=?
12 '3 + F~- 3^6 * 6 3 — * 6 3 ' 6 3
152 FRACTIONS Oral
M.
1 x x x 4
t . 6 . 6 6 . 6
1 4.
3 ' 3
i
XT.
1. By what part of the line MN can you measure both
thirds and halves f J = how many sixths ? ^ = how many
sixths ?
2. Tb what shall we change halves and thirds when we
wish to find their sums or differences f
3. Find: £ + *; t+ii i-1'5 W-
4. 6-2 = ? C + 3 = ? 6 is what of 2 and 3 ?
s. T|
6.
3*
- 4J
3.
81
9. 6|
1
3
§
J
J.
Subtract :
io. 2f
11.
8*
12. 91
13.
6f
14. 18f
J:
!i
2*
J
Jk
TFnWen
i^'nd results :
i. 4|
2.
15f
3- 41
4.
8f
s. 47f
+ 81
+n
+i
+ 2J
+i«i
6. 13f
7.
49£
s. 99|
9.
4321;
io. 467^
-101
-16f
-151
-129*
-288|
ritten
FRACTIONS
153
Add:
i. 181
16|
2. 161
191
3.
231
98|
4. 54J
16*
5. 351
42|
6. 17|
lof
7. 39£
89$
8.
72$
811
9. 46i
m
10. 83f
10|
ii. 241
12|
12. 35f
19i
13,
41i ;
181
u. 70f
18J
15. 63§
12J
is. 39f
12|
17. 89f
29i
18.
30f i9. 841
19i 19|
20. 97|
16|
Find results
;
2i. 481 22 . 57|
-16i +81|
23.
80f 24. 483f
21| +239|
25. 130f
-21i
26. 231|
+ 498|
27. 437J
+ 49£
28.
380£
-18|
29. 421
-39i
30. 46f
+ 85|
Oral
l. 9-1
2. 7-
*
3. 6-
"i *
H-i
5. 14-|
6. 15-
_3.
4
7. 12
-I 8.
16-|
9. 12 -2£
io. 14-
-3*
ii. 15
-31 12.
18-11
is. 6-2i
14. 5 —
if
15 8-
5f 16.
9-2f
17. 7-1$
18. 12-
-31
19. 14
-8f 20.
12-H|
154
FRACTIONS
Oral
M.
i
f
*
"9 I 9
N.
1. ^ = how many ninths ?
2. Find f more than J. Can you express it in thirds ?
How can you express it ?
3. Express 1 more than f. In order to add thirds
and ninths, toe change the thirds to what f
4. 9-3 = ? 9 is what of 3?
•• t+i-
10.
*+f-
15.
*+i- —
a 2.J-*
11.
*+*-
16.
*-*- —
6 - S+9-
'• i+i
12.
*+!=
17.
8 2 _
9 3-
8- i + i-
13.
*+*-
18.
8 • | _
9 ^ 3 ~"
Q 2 1 1 -
14.
1+1=
19.
9^3
9 - f ^9
Subtract :
20. 1 21. J 22
1 i
• 1
i
23. J
i
24.
f 25. | 26. |
i i i
Written
i. 181 + 171*
2.
661 + 14*
3.
75f + 43f
4. 38f + 41*
5.
341f + 23i
6.
861 + 61*
7. 191 + 321
8.
75f + 46f
9.
73f + 18|
10. lll* + 211f
11.
421$+
161
12.
39| + 16i
13. 88f-43* "
14.
241-141
15.
47$ -19$
16. 97^-18J
17.
125$-
42*
18.
120i-16|
is. 216$ -19*
20.
42|-13i
21.
34$ -13*
Oral REVIEW 155
1. Give the factors of 6 ; 8 ; 9 ; 15 ; 21 ; 33 ; 35 ; 39.
2. Name the multiples of 7 to 84.
3. What three factors, multiplied together, will pro-
duce 30 ? 18? 40? 42?
4. Give four numbers that are factors of 12.
5. A conductor took up $1.00 in 5-cent fares. He
collected from how many people ?
6. 8 oz. is what part of 2 lb. ? *
7. 200-10 = ? s. 56x10 = ? 9. 4300-100 = ?
10. 3 pk. 3 qt. are how many qt. ?
li. What must be paid for 2 \ qt. of berries at 12^ per
quart ?
12. Even numbers are multiples of what ?
Written
1. Add up,
then down.
Time
yourself:
a. 461
b.
$32.15
c.
. 9342
d. 931
350
14.63
8675
49
98
2.75
4038
867
233
3.81
5216
423
57
54.29
7879
78
476
6.38
4632
961
92
7.93
184
28
2. 436x251 3. 429x807 4. 906x583
5. 638x246 6. 1132x406 7. 9381x305
8. Divide 4725 by 63 and test your work.
156 PROBLEMS Oral
1. Find the cost of H lb. of candy at 2 f an ounce.
2. Find the cost of 1J- lb. of ginger at 2^ an ounce.
3. Five boys share equally 1 lb. 9 oz. of candy. What
is each boy's share ?
4. 6 f t. -}- 2 ft. + 4 ft. = how many yards ?
5. How many square inches in a rectangle 6 in. by
21 in.? In a rectangle 8 in. by 3 J in.?
6. Leah bought f yd. of muslin and used f yd. for her
doll. How much remained ?
7. Wallace gave J of his candy to Charles and J- of it
to Harold. What part of his candy did he give away ?
What part did he keep ?
Written
1. At $1.55 a yard, what will 64 yd. of carpet cost?
2. Two boys skate in the same direction. One goes
65 yd., the other 3 times as far. How far apart are
they ? (Picture.)
3. How many yards and feet in the perimeter of a floor
20 ft. by 15 ft.? (Picture.)
4. Hubert found 58|- inches of rubber pipe and used
19J inches of it for his air pump. How much remained ?
5. A pine tree measures 39|- in. around. Five years
ago, it measured 28|- inches. How much has the measure
increased ?
6. If 3f yd. of ribbon are cut from 11J yd., how much
remains ?
Oral
FRACTIONS
157
M.
10 I 10 i 10
10
^.u^
10
JJL
1.
4.
first t
5.
8.
11.
14.
16.
18.
How many tenths are there in
v
2. How many tenths in jr
i _ ? .
2 ■" ro >
2 _. ? .
5" ""TO 9
Inf?
9
Inf?
4 _ ?
"5~ — T0~*
Inf?
5 -ro->
7n order to add fifths and halves what must we do
10 + 2 = ? 10 + 5 = ? 10 is what of 5 and 2 ?
1 . 1 _
■F +o- —
+
4 _
6.
9.
.1+2.=
2 + 5
1+1=
TO 4 i
1_
2
10.
13.
4 i 1 _
T + 'fr —
* + f —
4^ + 61 =
is. 3i + 5f =
17.
19.
2 + 5
11^
20. Frank shoveled ^ the sidewalk and Henry J- of it.
What part of the walk was shoveled ? What part of the
walk was not shoveled ?
Written
i. 235f
-1871
2. 307|
-2991
3. 799J
+ 609£
4. 293f
+ 6171
s. 9001f
-8992^
6. 83f
+ 791
7. 4281
-399f
s. 5981
+ 2*
158 REVIEW AND PRACTICE Written
1. Harry took in at his soda fountain on Monday
$6.37, on Tuesday $9.14, on Wednesday $6.84, on
Thursday $9.25, on Friday $5.76, on Saturday $7.28.
a. How much money did he take in during the week ?
b. Harry's best day was how much better than his poorest
day?
2. A merchant bought a case of pencils containing 120
boxes, each box containing 6 dozen pencils, a. How
many dozen were there? b. How many pencils were
there?
3. 296£ 4. 99$ 5. 793f e. 308£
+ 549| +8l| -24l| -2091
7. 435| 8. 895f 9. 973| 10. 43f
+ 79| + 4081 +461 + 98|
n. 784^ i2. 46 T % is. 89| 14. 201£
+ 91f +78^ +43^ -108f
15. Divide and test your work: a. 17,745 by 35;
b. 331,444 by 47; c. 476,834 by 95; d. 32,769 by 46/
16. What number is a multiple of 436 and 987 ?
17. 3233 is a multiple of what number besides 53 ?
18. Find a number that is a multiple of 19, 23, and 41.
19. 65J-14i=? 20. 42f-13i = ? 21. 84|-23£ = ?
22. The ice froze 4J- inches thick last week, and 5f
inches more this week. a. How thick is it? b. If it
should thaw 2J in., how thick would it then be?
Oral FRACTIONS 159
M.
20 l l l 1 I I I l l l 1 I l I 1 I I I I k
i i
J, i 1 l X
1. How many are there of the smallest parts of the
line MN ? Each of them is what fraction of the line?
2. ^=how many twentieths? J = how many twen-
tieths? To what must we change fourths and fifths in
order to find their sums or differences f
3. 4x5 = ? 20-5 = ? 20-4 = ? 20 is what of 4
ana O I J-^O"? J~TG> ~S"~^J5> 4 _ 2(I? 4 — 2TF*
4. i+sW 5. i + ^ = ? 6. | + ^ = ? 7. * + &-?
8- l+i-1 9- * + t = ? 10. i + f = ? 11. | + i = ?
12. f + J-T 13. f + f = ? 14. f+i-T 15. f + | = ?
Written
i. 39J 2. 49f 3. 87ft 4. 92£
+ 46^ +8Lfr + 46£ +71|
s. 42f e. 211ft 7. 149£ s. 21|
+ 89J- -16f +| -14f
9. 71£ 10. 342£ ii. 61f 12. 123£
-26^ -187f +88f -38|
13. 91 5 V 14. 109| 15. 482f is. 821^
+ 88f -491 -157£ -1371
160 PROBLEMS
Answer to yourself these questions about each problem :
a. What is asked f b. What is told f c. What must I find
first?
1. A liveryman bought 8 bu. of oats at $ .40 a bushel
and 2 loads of hay at $12 a load. What did both cost?
2. Horace traveled 37 miles and Joseph five times as
far. How far did both travel ? (Picture.)
3. A farmer sold some butter for $47.85, some eggs
for $5.38, some hams for $11.57, and some apples for
$13.50. He put $53.89 in the bank and spent the
remainder of the money. How much money did he spend?
4. Mrs. Yates bought some coffee for 48 cents, some
sugar for 65 cents, and some eggs for 88 cents. She gave
the clerk a $5 bill. How much change should he give
her?
5. A man earned $392 and used -f- of it. a. How
much did he use ? b. How much had he left ?
6. 8 arithmetics cost $4.48. What will 16 arithmetics
cost?
7. A man earns $15 a week and saves J of it. How
long will it take him to save $96 ?
8. A man born in 1812 died in 1890. How old was
he when he died?
9. Ted had 49 marbles and Ned had four times as
many. How many had both ?
10. Mrs. French bought 38 yards of carpet, and took
back a piece 54 feet long. How many yards did she keep ?
Oral
FRACTIONS
161
1
3
\ — i — i — y
^ — i — i — i — h
i
t
H — I — r
1
5 I
1. The line MN is divided into how many equal parts ?
What is each of these parts ?
2. £ = how many fifteenths ? 1 = how many fifteenths ?
3 * 5^ ~ TW>
5 — 15 9 5 ~ T~5~ > 3" ~ 15-
4. 3 x 5 = ? 15 -+• 3 - ? 15 + 5 = ? 15 is what of
3 and 5 ?
5. To what shall we change thirds and fifths so that ive
may add or subtract them ?
fi 1 4_ 1 —
6 - 3 + T5"-
o 1 1 2 _
in 1 1 2 _
— 8.
11.
14.
1
3
3
5
3
5
i
+ i=
+*=
+*-
1 _
9 - 3 ' 5
19 1 1 4
10 - 5 ' 3 -
13- f + f= —
u 1 2 _
12. 3 1 5 -
,~ 1 1 _
lj - 5 15 -
16 - f 15
J./.
5
Written
i. 31$
-25$
2. 49$ 3.
+ 82$
613f
-127$
4.
412|
-361f
5. 912|
+ 87^
6. 171 7.
+ 21f
84f
+ 84$
8.
490f
-390i|
9. Mr. Ruggles worked 4|- months in Boston and 6§
months in Troy. How many months did he work ?
162 REVIEW AND PRACTICE Oral
1. *+*-* 2- f+i-t 3. i + f = ? 4. $ + *-?
5. f + f = ? 6. 1 + 1 = ? 7. l + |- = ? 8. 1+H?
9. f+i-T 10. 7| + i = ? 11. i + l = ? 12. i-i=?
is. f-^-t «. A-i-» is- A-*=? is- *-*-»
1. When 36 barrels of flour cost $140, what will 12
barrels cost ?
2. A farmer received $240 for grain, potatoes, apples,
and chickens. \ of the money was for potatoes, \ for
apples, J for grain, and the remainder for chickens.
a. How much did he receive for grain ? b. For potatoes ?
c. For apples ? d. For chickens ?
3. A trader bought a horse for $150, and sold it so as
to gain \ of the cost. a. What did he gain ? b. For how
much did he sell the horse ?
4. At $39 a head, how many head of cattle can be
bought for $4173?
5. Mr. Shepherd sold 132 sheep to one man for $ 528,
to another man 156 sheep for $468, to another man 25
sheep for $ 90, to another 35 sheep for $ 140. a. How
many sheep were sold ? b. How much was received for
them ?
6. When $7490 are paid for 214 cows, what is the
cost of one ?
7. 306f s. 223f 9. 150f 10. 17f 11. 238|
+ 98f -161 _1391 +18| -197|
Oral
FRACTIONS
163
' - A 4 1
t 3
jA|A|-A-|A|A|A|A|ife
1
3
12 1 12 | 12 1
1
1
1 1
12 j
m i i i i i i i i i
1 .* I i 1 i
1 1 1
1
1
1
1. J of the line MN is how many twelfths of it ?
2. \ of the line MN is how many twelfths of it ?
3. Can you find how many twelfths in \ of the line ?
In i of the line ?
4.
_ ? . 3_ ? .5_ ?.jl— '. i— t
"~ 12? 4~T2> 6" — T2 > 2~T2> ¥ _ T2 '
5. ^o wAa£ sAaZZ we change fourths and thirds in order
to find their sums or differences f
6. 12-^4 = ? 12-*-3 = ? 12 is what of 4 and 3 ?
7.12^-2 = ? 12 + 6 = ? 12 is what of 6 and 2 ?
8. Of what four numbers is 12 a multiple ?
10. | = I V 11. i +A = ? 12. | + ^ = ?
9. *-
_ ?
Tf
13. i+ 1 =? 14. |+ 1 -? 15. f + J =? 16. f + f =?
»• l+A"* 18. 4 + ^ = ? 19. ^ + f -? 20. & + | =?
21. i"^ = ? 22. i~^=? 23. i - 1 =? 24. | - £ =?
25. |- i =? 26. |- | =? 27. f -£ = ? 28. f - &=?
i. 16}
6. 14|
+ 93}
25|
3.
43J
+ 17& -16^
4. 84f
+ 18?
s. 415^
-247|
. 67|
+ 88J
i. 395f
-1971
9. 59^1 lo. 135^
+ 296|
-41|
164 REVIEW AND PRACTICE Oral
i. James gave J of his marbles to one boy and \ to
another. What part of his marbles did he give away?
What part did he keep ?
2. If Harry ate |- of a melon and George \ of a melon,
how many melons did both eat ?
3. I planted \ of my garden to corn and \ to potatoes.
What part of my garden is planted to corn and potatoes ?
Which crop occupies more of the garden and how much
more?
4. 10x4 = 20x? 8x3=4x? 3x4=2x?
5. If Harry has \ of a dollar, how much more must he
obtain before he can buy a $ 2 sled ?
Written
l. Add :
a.
61 b. 16&
c. 13J-
d. 4J
«• 91f /. 12i
7* 15*
19J
H
14| 8&
6^ n
15i
2&
8A 7i
2. A garden 75f ft. long and 421 ft. wide will require
how many feet of fence to inclose it ? (Picture.)
3. A farm of 108 acres was sold for $5940. What
was the selling price of an acre ?
4. The battleship Kansas is 456 feet long. a. How
many yards long is she ? b. How many inches ?
5. 36 bushels of apples at 75 cents a bushel will exactly
pay for 25 yards of cloth at cents a yard.
6. 10 tons of hay at $9 a ton will pay for 18 tons of
coal at $ per ton.
Oral
FRACTIONS
165
i
i
M.
u
-Ik
-f
1. Into how many equal parts is the line MN divided ?
What is each of those parts called ?
2. 7 — 14>2~~14>7~Tl~> T — Ti~> T~~ TT> T~ T4> T~~T4*
3. To w;7ia£ shall ive change halves and sevenths to find
their sums or differences f
4. 14-2 = ? 14-7 = ?. 14 is what of 2 and 7 ?
5. W=? W=? *-*-» i+W *+*«>
2^7
i + f =
2^7
2^7
* 2^14 * 2 ^ 14 * 7^14 '
*+*+&=*
15}
28^
1401
139f
64
23&
259f
1641
d. 131J| e.
87^
63f
981$
49^
88&
2. Subtract :
a. 4011
359|
&. 71£
36f
c. 731
15f
d. 391f
' 1581
e. 81$
291
3. Add :
a. 13^ b
16f
_4f
76f
19|
5f
c. 43|
15|
71
'6
d. 120-iJ
96}
14i
e. 12f
L 4 L
166 REVIEW AND PRACTICE Oral
i. Genevieve had f of an orange and Edith -| of an
orange. Which had the greater part and how much
greater ? (Illustrate.)
2. Four quarts of berries at 9 cents a quart will pay
for how many pineapples at 12 cents apiece ?
3. A page is 8 in. long and contains 40 sq. in. How
wide is it ? (Draw it the exact size.)
4. Which is greater, f of a dollar or J of a dollar ?
How much greater ? (Show by picture.)
5. 3 five-cent packs of firecrackers and one ten-cent
pack cost how much ?
Written
1. a. If it takes $512 to pay the hands in a certain
factory for one day, what will it take to pay them for one
week ? b. For 52 weeks ?
2. If \ lb. of tea costs 22 cents, what will 5 lb. cost ?
3. Take 37^ from the sum of 15 J and 24J.
4. a. A half peck and a half bushel of peanuts are how
many quarts ? b. How much are they worth at 3 cents a
pint?
5. Divide the sum of 21684f and 169421 by 19.
6. On the first day of January, Kate had $ 8.52 in the
bank and deposited $3.15. On the first of March she
drew out $4.84, and on the first of April deposited $5.86.
She then had how much money in the bank ?
7. How many pound cakes of sugar in 17 boxes, each
containing 240 cakes ?
FRACTIONS 167
1. Before we find the sums or differences of fourths
and halves, we change the halves to . 4 is a
of 2.
2. Before we find the sums or differences of fourths and
eighths, we change the fourths to . 8 is a of 4.
3. Before we find the sums or differences of halves
and eighths or fourths and eighths, we change the halves
and fourths to . 8 is a of 2 and 4.
4. Before we find the sums or differences of halves
and thirds, we change them to . 6 is a of 3 and 2.
5. Before we find the sums or differences of fifths and
thirds, we change them to . 15 is a of 5 and 3.
6. Before we add halves, thirds, fourths, and sixths, we
change them all to . 12 is a multiple of ,
7. If you wish to subtract or add sevenths and thirds
you change them to . is a multiple of 7 and 3.
21 + 8-t *-£ 21 + 7=? i = a-
s- f=<n: $—A f=2T f=2T 4=2T f=3rr
9 - ■5T=3' 2T~^ 2T-T ST~T 5I - T 2T - V
Test: + + & = & + &-&-*
Written
Subtract and test your work :
1.
i-f
2.
3 _ 1
T 3
3.
1-4
6.
t-i
7.
5 _ 2
T 3
8.
1-1
4. W 5. f-i
9- f-J 10- l-l
L68 REVIEW AND PKACTICE Oral
i. If an 8-cent tablet lasts you 4 weeks, what is the
cost of your tablets for a term of 20 weeks ?
2. What must be paid for a knife at 30 cents and a
pair of skates at 65 cents ?
3. Change to loivest terms : £ ; f ; f ; f ; T 2 ^ ; § ; ^ ;
6.2.3.4. 8.10. 2. 7. 6. 4. 8.12
T2 > T2 » T2 > T2 9 12 > 12' 14 9 T4 > 14 > 14 > 14 > 1"4 *
4. Find the value of J£; |; ^; ^; ^; ^-; ^; ^.
5. What is the second multiple of 12 ? The third ?
6. \ of my trees are apple trees and \ are cherry trees.
What part of all my trees are apple and cherry ?
7. What is the fourth multiple of 5? The seventh
multiple of 9 ? The eleventh multiple of 12 ?
8. What is the smallest number that is a multiple of
2, 3, 4, and 5? Of 2, 4, 8, and 16 ? Of 3, 2, and 5?
Written
Add:
i. 42^ 2. 83} 3. 291 4. 49f 5. 196f
6_5J 41^ 68f 84| 25-if
6. 421| 7 . 93| 8 . 576 9 18 i ia 6 i
89* 86f 82/ T 14| 41
51 7f
11. 481 12 . 161 13 . 851 14 . 311 15 . 91
13| 12| 161 53| lOf
3. ' L 4 I l!i 67| 12|
16. The rent of a store is $840 a year. How much
rent must be paid for the store for 3 \ years ?
Oral FRACTIONS 169
1. Name a number which is a multiple of 8 and 3.
2. If we wish to add or subtract eighths and thirds, to
what shall we. change them?
3. Name all the numbers of which 24 is a multiple.
What fractions other than eighths and thirds can you add
or subtract by changing them to 24ths?
*• 1=2*4 3=-h 4 = 2T 6 = A T2 = A*
- 1_ ? 3_ ? 2— ? 3_ ? 5__L_ 5 — ?
5 - 2 - 2~4 ¥-24 "3-21" 4 ~ 24 6"~24 12~2¥'
6 - ¥~24 T2 _ 24 12-24 3 + 8~- 8 12 "" •
*• *+W i-i=? i+A=? |-.*-t *+&-»
Written .
i. 35£ 2. 81£ 3. 24J 4. 52J 5. 29| '
+ 42| -37j +99j + 49| -16&
6. 48^ 7. 405ft s. 48f 9. 479£ 10. 405f
-29| -98| +91| -379| -399f
11. 43^ 12. 72f 13. 85f 14. 213| 15. 315f
+ 89* -16£ +88| -164| -143|-
«. 43*
17. 16JJ
is. 99f 19. 71f
20. 63^-
64*
19*
63* 99|
47^
ISA
22*
71J 161
sift
ISA
si*
81 T V 141
*k
21. 3£+4| + 5} = ? 22. 6f + 3^+14* = ?
23. 3i + 3£ + 6*=?
170 REVIEW AND PRACTICE Written
i. From the sum of 4| and 6J take the sum of 2^ and
3*.
2. Ben rode his wheel 5f miles on Monday and 6|
miles on Tuesday. How many miles did he ride in the
two days ?
c. One bale of hay weighs 175J lb., another, 186f lb.,
and another 199^ lb. How many pounds do all three
weigh ?
4. A collector received $2f at one house, $5f at
another, $6J at another, and $8J at another. How
much did he receive ?
5. Change to lowest terms Jt> ft* it> A' tt> H
6. Find the value of ^ ; ±6^ ; ^^ ; l||A.
7. a. Find the cost of 35 bushels of potatoes at 58
cents a bushel.
b. Find the cost of 19 bushels of apples at 87 cents
a bushel.
c. Find the cost of 15 boxes of peaches at 35 cents
a box.
d. Find the cost of all three of the above items.
8. Eugene ran 26^- rods while Charles ran 25^ rods.
Which was ahead and how much, if they started together ?
9. a. How man) pounds of cotton in 100 bales, each
weighing 480 lb. ? b. How many tons ?
10. 1000 lb. is what part of a ton ? At $ 18 a ton what
is the cost of 1000 lb. of hay?
Oral FRACTIONS 171
i. To what would you change ninths and halves if
you wished to add or subtract them ?
2. What other fractions than ninths and halves could
be added or subtracted by making the same change ?
3. What is the smallest number that exactly contains
2, 3, 6, and 9 ?
» 1— ! 1__ f 1-^ ? 1 __ t 2_ ? 2 __ ? 5— ?
*• 2 ■ T8> 3 ~ T8> 6 "" TO? "9 ~~ TF> 3 ~ TS> 9 ~ I~8> 6 !¥'
m 4_? 5 _ ? 7 _. ? 8 _. ?
s * ¥ 1T8"> 9 — TB~> 9 ~" T85 9 ~~ T8 *
«• i+A=? £+&=? i+H=? i+H=?
7. i+i=? j-i-? |+|=? i+|=? i+i-?
a- #-§-« *+i= ? W=? &+W
i. 39J 2. 316f 3. 45§ 4. 88} s. 486^
+ 42^ -2151 -27f +98| + 3971
6. 32^ 7. 99£ s. 304| 9. 392| io. 83J
-28$ +991 -108^ -186& -47|
a. 203f 12. 84f 13. 45J 14. 79f is. 239}
-107j +171 -13J -16f -175|
16. 43^ 17. 39£ is. 991 19. 43^ 20. 8^
66H 25^ 251 51* 21
23A 41| 42| 17| 6|_
21. ll| + 6-| + 7i + 3 T \ = ? 22. 4f + H + 2 T V + 3i = ?
23. 5| + 2i + 8i + 4^ = ? 24. 3i + 4i + 5i + 2 i = ?
172 REVIEW AND PRACTICE Oral
1. \ pk. + -§- pk. is how many quarts ?
2. Which is greater, § of a foot or f of a foot, and how
much greater ?
3. Which is greater and how much, J- of a day or -| of
a day?
4. A milk man sold a customer 5 quart tickets and 8
pint tickets. How many quarts of milk must he give for
all the tickets ? How much is it worth at seven cents a
quart?
5. When 2 lb. of sugar are sold for 9 cents, what must
be paid for 8 lb.? 8 lb. is how many times 2 lb.?
Written
i. A young man earns $575 a year. What has he left
after paying his board at $ 15 a month ?
2. % 8820 was divided equally among 84 Indians. How
much money did each receive ?
3. 18 boys received each 38 cents for distributing hand-
bills on Saturday. How much did they all receive ?
4. Multiply the difference between 6008 and 2119 by 69.
5. John earned $21, William $1|, and Henry $5f.
How much did all earn ?
6. A boy ate \ of a cocoanut. What part of the cocoa-
nut was left if he had \ of it at first ?
7. The four sides of a field are 33^ rods, 16f rods, 38f
rods, and 41 rods. How many rods of fence will inclose
the field ?
FRACTIONS
173
1. Here are how many pies ? Take away 2 pies. How
many are left ? If you take away 2^ pies, what must you
do to one of the pies ? Make a picture of the 2^ pies that
you take away. Make a picture of the pies that are left.
5 pies less 3 J pies are how many pies ? 5 apples less 3J
apples = ?
2. Make a picture of 5 pies less 1 J pies ; 5 pies less
If pies ; 9 pies less 3 J pies ; 4 pies less 1 J pies ; 5 pies
less 2-| pies.
3. Froir
t 5 take 2$.
5 =4f
2J-2J
2| Remainder.
4. 83
-17*
s. 48
-19J
6. 631 7. 7
-29| -2|
8. 431
-231|-
9. 423 10. 69 11. 29
-1921
-58f
-9f
14. 61 is. 46 16. 28
-A -if
-14&
19. 1 20. 61 2i. 832
-H -15f -731|f
12.
401
- 300f
17.
13
22.
39
°9
-18*
18. 16
15*t
23. 4-87^,
-48fe )
174 REVIEW AND PRACTICE Oral
1. How many pounds in 5 tons of coal ?
2. A man bought a wheelbarrow for $3.75 and paid
for it with a $5 bill. What change should he receive ?
3. Minnie had 5 apples and gave If apples to her sis-
ter. How many had she left ?
4. 15^- barrels of water were drawn out of a cistern
containing 19^ barrels. How many barrels were left?
5. A boy was four feet tall on his ninth birthday.
He had grown If inches in a year. How many inches
tall was he on his eighth birthday ?
Written
1. Write in words 410,004 ; 203,416 ; 3,000,015.
2. Express in figures seven hundred six thousand
iwenty-nine.
3. Write in Roman, 451. Write in figures, CCXI.
4. Add $10.06, $15.72, $60.87, $1.59, $3.45.
Add:
s. 63
6. 87
7. 42
s. 96
9. 54
10. 83
n. 28
59
64
35
42
96
73
18
17
65
49
28
16
94
31
64
82
39
50
26
45
17
23
72
18
25
16
25
29
36
28
65
32
44
46
38
Multiply :
12. 896 is. 897 14. 598 is. 384 ie. 999 17. 894
94 63 76 65 106 200
OrU ONXTED STATES MONEY 175
We have learned that cents make one dime and
that dimes make one dollar.
The smallest piece of money used in our country is the
cent, but in making calculations we sometimes have to
speak of smaller amounts than one cent.
One tenth of a cent is called a mill ; ^ of a cent are
three mills ; ^ of a cent are seven mills, etc. ^ of a
cent are how many mills ? What part of a cent are 9
mills ? Since a mill is ^ of a cent, mills make one
cent.
A ten-dollar gold piece is called an eagle.
TABLE OF UNITED STATES MONEY
mills make 1 -
cents make 1 -
dimes make 1 -
dollars make 1
1. A 5-cent piece is what part of a dime ?
2. A dime is what part of a dollar ?
3. A 50-cent piece is how many dimes ?
4. A 2 5-cent piece is how many dimes ?
5. How many 2 5-cent pieces are worth as much as a
silver dollar ?
6. Express $ 1\ as dollars and cents.
7. Express 4^ dimes as cents.
8. A half dime, 2 dimes, a quarter, and a 50-cent piece
are how many cents ? How many dollars ?
176 REVIEW AND PRACTICE Written
l. A dairyman sold 459 lb. of cheese at $.11 per pound.
How much did he receive for it ?
459
He received as many cents as the product of 459 and
11, or 5049 cents, which equals $ 50.49. Answer.
$50.49
2. 1423 bu. of peaches at $1.25 per bushel cost how
much?
1423
flIJ -J op*
■ 71 ^ $ 1.25 = 125 cents. 1423 bu. of peaches at 125 cents
QQin a bushel cost as many cents as the product of 1423 and
1423 125 ' 0r 177875 cents, which equals $ 1778.75. Answer.
$1778.75
3. What must be paid for 7 dozen handkerchiefs at
$ 1.85 per dozen ?
$ 1.85 At $ 1.85 per dozen, 7 dozen handkerchiefs will cost
7 as many cents as the product of 185 and 7, or 1295 cents,
$12.95 which equals $12.95. Answer.
Note. — From the above examples, it is seen that when either the
multiplicand or multiplier contains cents, the product also contains
cents. We may use either factor for the multiplier, pointing off
two places, for cents, in the product.
4. A man bought a bushel of berries for $2.88 and
sold them for $3.15. At that rate, how much would he
gain on 123 bushels ?
5. Find the cost of 19 lb. of coffee at $.33 a pound
and 134 lb. of tea at $.56 per pound.
Make problems and multiply :
6. $4.15 7. 247 s. $9.36 9. 3456 10. 438
39 $.05 42 $.98 $.25
Written UNITED STATES MONEY 177
i. Find the sums and time yourself:
a. $41.36
6. $34.63
c. $12.98
d. $46.89
52.81
8.47
6.32
4.37
8.46
92.45
4.28
90.19
79.38
3.06
7.91
7.81
8.92
93.57
5.16
6.29
4.05
.69
70.80
4.38
2. Find ivhat I must pay for all of these articles :
5 boxes of note paper at $.25 per box.
5 dozen tablets at .50 per dozen.
12 paper weights at .19 apiece.
7 ink wells at .29 apiece.
3 bottles of mucilage at .05 per bottle.
1 pair of scissors at .62 per pair.
3. A merchant bought 56 yd. of silk for $43.68.
a. What did one yard cost? b. What did 11 yd. cost?
4. A farmer bought 12 sheep at $3.75 apiece. If he
sold them at $4.75 apiece, what was his entire gain?
5. Mr. Taylor went to Boston. His railroad fare was
$8.22 each way. He paid a hotel bill of $3.50 per day
for 6 days. His other expenses were $7. If he started
with $ 50, how much had he left ?
6. A man worked a week for $2.75 per day. How
much more did he earn than enough to buy a coat for
$9.75, a vest for $1.90, and a hat for $2.00 ?
7. From the sum of $4.75 and $3.74 take the sum of
$2.38 and $4.25.
178 REVIEW AND PRACTICE Oral
1. Frank's mother made 4 pies. They were cut into
quarters, and to each of seven boys was given a quarter.
How many pies were left ? (Picture.)
2. Susan found 7 apples under the pippin tree. After
she had given away 4 apples, and eaten |- of an apple, how
many were left ?
3. What is the 7th multiple of 12 ? 56 is the 8th mul-
tiple of what ? 150 is the 10th multiple of what ?
4. Give three factors of 20 ; four factors of 16.
5. Name three numbers that will exactly divide 28.
6. Name three numbers that will exactly contain 5.
Written
1. From the sum of $12.15 and $16.48 subtract the
sum of $10.18 and $9.50.
2. Add six hundred four thousand five hundred eight
to ninety-four thousand fifty-six, and from the sum sub-
tract five hundred six thousand ten.
3. A farmer had 25 acres of corn which yielded 55
bushels per acre. a. How many bushels of corn did the
farmer have? b. How many pounds did it weigh if a
bushel weighed 56 pounds ?
4. a. Find the cost of 5 chickens at 37 cents apiece
and 8 ducks at 42 cents each.
b. How much more do the ducks cost than the chickens?
5. a. 6f + 4f + 7f = ? b. 9ii-7f = ? (Problems.)
6. Express in Roman 696 ; in figures DCXCIV.
LIQUID MEASURE 179
One fourth of a pint is a gill. It is sometimes used in
measuring small quantities of liquids. A common teacup
holds a little less than two gills.
TABLE OF LIQUID MEASUKE
gills (gi.) make 1 ■
pints (pt.) make 1
quarts (qt.) make 1 (gal.)
1. There are how many pints in a gallon ?
2. There are how many gills in a gallon ?
3. Three quarts are what part of a gallon ?
4. Seven pints are what part of a gallon ?
5. Five gills are what part of a gallon ?
Written
1. A milkman sold 19 gal. of cream in bottles, each
holding 2 gi. How many bottles of cream did he sell ?
2. One customer bought 2 gal. 1 qt. of milk, another
7 qt., and another 20 pint bottles. How many quarts of
milk did they all buy ?
3. How many gallons and quarts of vinegar are needed
for 138 cans of pickles, using 1 pt. of vinegar for each can "
4. Change to pints : a. 17 gal. 3 qt. o. 51 gal. 1 pt.
c. 144 gi. d. 4325 gal.
5. Change to gallons : a. 128 qt. b. 112 pt. c. 352 gi.
6. How many days will 5 gal. of oil last an engineer
who uses 1 gi. every day ?
180 REVIEW AND PRACTICE Oral
i. When a gallon of molasses is worth 48 cents, what
is a pint worth ? Two quarts ? One gill ?
2. At 24 ^ a dozen what must be paid for 18 eggs ?
3. If 6 plums cost a cent, how many can be bought for
12 cents?
4. 3 £ lb. of beefsteak cost how much at $ .12 per lb. ?
5. How many dollars must be paid for 15 spelling books
at $ J apiece ?
6. What is the smallest number that contains the factors
3, 2, and 5 ? 2, 3, and 4 ? 5, 4, 10, and 2 ?
Written
i. A merchant sold 3J yd. of velvet to one lady, 4-| yd.
to another, 1^ yd. to another, and 1^ yd. to another.
How many yards of velvet did he sell to all ?
2. Irene bought a handkerchief for $ J-, bead trimming
for $f, and a sailor hat for $1. a. What was the entire
cost ? h. What change did she receive for a $ 5 bill ?
3 3 9 7 8
d - 3 9
_ 9 11704.
56
_? 8 9 3 2 _ ?
29
148_tl _ f
19
24644 _ 9
61
4. Add:
a. 2\
b. 3£
c. 92f
£
46£
«. 481
%
^
m
79A
82|
5f
n
79f
48ft
66i|
3.
8*
641
80*
991
5. Subtract and test
your work :
a. 39
b. 401
c. 98f
d.
78f
e. 435!
19f
36i
21f
291
2411
DRY MEASURE 181
TABLE OF DKY MEASURE
— pints (pt.) make 1
— quarts (qt.) make 1
pecks (pk.) make 1 (bu.)
Note. — One quart, dry measure, is nearly equal to 1| quarts, liquid
measure.
i. 1 bu. = pk. = qt. = pt.
2. How many quarts in 1 bu. ? In 1 bu. ? In ^ bu. ?
3. Seed corn at 2 cents a pint is how much a quart ?
4. 3 quarts are what part of a peck ?
5. A man bought a bushel of beans, sold 3 pk., and
gave away 4 qt. How many pints did he keep ?
Written
1. A boy bought 3 bu. of peanuts at $1.75 per bushel.
a. What did they cost ? b. He roasted them and sold
them at the rate of 5 cents for a pint cupful. What did
he receive ? c. How much did he gain ?
2. a. In 205 bushels there are how many pecks ?
b. How many quarts ? c. How many pints ?
3. In 435 pt. there are : a. How many quarts and
pints? b. How many pecks, quarts, and pints ? c. How
many bushels, pecks, quarts, and pints ?
4. \ bu. and \ bu. are how many pints ?
5. If 8 bu. of sweet potatoes cost $6.72, what will 1
peck cost at the same rate ?
6. If my horse eats 6 quarts of oats a day, how many
days will 12 bushels of oats last him ?
182 REVIEW AND PRACTICE Oral
i. An orchard has 600 trees in 20 rows. How many
trees in a row ?
2. To how many girls could 6 apples be given if each
girl receives \ of an apple ? (Illustrate.)
3. 40 + 30 = ? 43 + 34 = ? 35 + 27 = ? 24 + 29 = ?
4. 93-33 = ? 93-37 = ? 42-26 = ? 84-45 = ?
5. \ and \ of a pound of sugar are what part of a
pound ?
6. If there are ten brown eggs in 9 dozen and the rest
are white, how many are white ?
7. One eleventh of a class of 55 pupils are absent.
How many are present?
Written
1. A man received $2.40 for eight hours' work. How
much did he receive for three hours' work ?
2. 800 qt. are how many bushels ?
3. Where are the hour and minute hands of a clock at
half past 12 ? (Picture.)
4. Express in Roman three hundred fifty-four.
5. How many quart boxes can be filled from 38 bushels
of peaches ?
Add:
6. Sf
7. 4|
8. 4|
9. 8f
10. %ts
H
11J
H
7A
H
H
H
H
5J
n
4A
8A
§t
3|
8*
TIME 183
TABLE OF TIME
seconds (sec.) make 1 -
minutes (min.) make 1
hours (hr.) make 1
days (da.) make 1 (wk.)
months (mo.) make 1 (yr.)
Learn :
" Thirty days have September,
April, June, and November."
1. How many months have 30 days each ?
2. February has 28 days in all years but leap years.
How often does leap year come ?
3. How many days has February in leap year ?
4. How many months have 31 days each ?
5. a. Write the names of the months in order with
the number of days in each. b. Which long months are
not separated by short months ?
6. How many seconds in 1 hour ?
7. How many minutes in 1^ hr. ?
8. 15 min. is what part of an hour ? 30 min. ? 45 min. ?
9. There are 180 minutes in a certain number of hours.
180 is the product of 60 and .
10. 2 hours is what part of a day? 3 hr.? 8 hr.? 12 hr.?
li. How many hours in -| of a day ? In f of a day ?
In |- of a day ? In f of a day ? In % of a day ?
12. Twelve boys went to a fire and were 15 min. late at
school. How many minutes were lost ? How many hours ?
184 TIME Written
i. In the month of September there are how many
(a) hours, (b) minutes, (c) seconds?
2. a. If a clock pendulum swings once every second,
in how many minutes will it swing 1,814,400 times?
b. In how many hours ? c. In how many days ? d. In
how many weeks ?
3. The Spanish War was fought in 1898. That was
how many years ago ?
4. In four years, February has how many days less than
January has during the same years ? Hours ? Minutes ?
5. If you are idle one fourth of the time during eight
hours of every day, how many hours do you lose during a
year of 307 working days ?
6. $ 1296 a year is how many dollars a month ?
7. If there are 300 working days in a year, how
much would it cost to hire a man for 5 years at $3|
per day?
8. The President of the United States receives a salary
of $ 50,000 per year. If his expenses are $ 35,000 per year,
how much a month can he save from his salary ?
9. If a boy sells an average of 1 paper a minute for half
an hour every day, at 2 cents apiece, how much money
will he take in during a week ?
10. From noon until midnight is how many minutes?
li.. March, April, and May are the spring months.
September, October, and November are the fall months.
Which is longer, spring or fall, and how much ?
PROBLEMS
185
From photograph by A. P. Yates.
i. This train is called the " 20th Century Limited."
It runs from New York to Chicago, a distance of 980
miles, in 18 hours, a. That is an average rate of how
many miles an hour ? b. What part of a day is required
for the trip ? c. How many minutes are required for the
trip ? d. If the five cars are each 73 feet long and the
locomotive and tender together are 58 ft. long, how long
is the train ?
2. When this picture was taken, the train was running
at the rate of 90 miles an hour. a. It was running at
what rate per minute? b. How far would it go in 20
min. at that rate?
3. a. Find the cost of a ticket from New York to
Chicago at 2^ per mile. b. From New York to Buffalo
is 440 miles. From Buffalo to Chicago is how far ?
186
DIVISiOJN
Written
WjlBf?
1. Divide 4693 by 100.
46^ Quotient 4693 = 4600 + 93
4600-100 = 46
93-*- 100 = ^5- 46 T 9 ^ Quotient
Divide 3687 by 40.
92 ¥ 7 - Quotient 3687 = 3680 + 7
4PJ368; 3580-40 = 92
40 = A
»2A
Quotient
3. Divide 54,763 by 500.
109ff£ Quotient 54,763 = 54,700 + 63
5PP)5470?
54,700-*- 500 = 109 and 200 over
4. 149-10
7. 5638-1000
io. 9747-50
263^500 = fff
5. 3462-10
8. 2420-20
ii. 98,924-40
is. 947,612-3000 14. 29*305-600
is. 98,370-5-90 17. 73,462-90
109fff Quotient
6. 84,763-1000
9. 3742-200
12. 6807-340
is. 6350-50
is. 742,491-6000
19 14030
19 - 4 6
21.
79808
22.
1 62400
35
on 17464
20. 74 * A . 58
23. In examples 19 to 22, tell which numbers are prod-
ucts and which are factors. When a product and one of
its two factors are given, how can the other factor be
found? 70,196 = 92 x?
24. A rifle range is 625 yards long and 98 yards wide.
How many square yards does it contain ? The area is
what of 98 and 625 ? Find the perimeter.
AVOIRDUPOIS WEIGHT 187
TABLE OF AVOIRDUPOIS WEIGHT
ounces (oz.) make 1 pound
pounds (lb.) make 1 ton (T.)
1. Give the number of ounces in J lb. ; f lb. ; f lb.
2. How many ounces in 1 T. ?
3. How many pounds in J T. ? In \ T. ?
4. 100 pounds is what part of a ton ?
5. 100 pounds is sometimes called a hundredweight.
Cwt. stands for hundredweight. How many hundred-
weight make a ton ? \ T. ? \%\ f T. ?
6. What must be paid for 1 T. of hay at $ 1 per hun-
dredweight ?
7. If a ton of coal cost $4.00, what will 5 cwt. cost?
8. At $ 2 per hundredweight, what will 1 T. cost ?
Written
1. How many 4-ounce bags can I fill from a box con-
taining 7 J? lb. of candy ?
2. I had 12 T. of coal delivered in bags holding 100 lb.
apiece. How many bags of coal were there ?
3. A wagon contained a ton of coal. J- of it was de-
livered to Mr. A. and 450 lb. to Mr. B. a. How many
pounds did Mr. A. receive ? b. How many pounds re-
mained in the wagon?
4. If there are 80 pieces of baggage in the baggage car
(p. 185), weighing an average of 50 lb. apiece, how many
tons does the baggage weigh ?
188 LINEAR MEASURE
THE TABLE OF LINEAR MEASURE
12 inches (in. ) make 1 foot.
3 feet (ft. ) make 1 yard.
5| yards (yd.) 1
or > make 1 rod.
16| feet J
320 rods (rd.) make 1 mile (mi.).
Oral
1. The longest boards commonly used for floors, siding,
etc., are 16 feet long. They are how much less than a
rod long ? They are how many yards and feet long ?
2. Measure a rod on the floor with a foot rule, and
then with a yardstick. Draw on the blackboard a line that
you think is 1 rod long. Measure and correct it. Esti-
mate and measure various distances, as the length and
breadth of the school lot, the distance to the nearest
corner, etc.
3. A city lot 3 rods wide is how many feet wide ? A
city lot 4 rods wide is how many feet wide ?
4. A city lot 8 rods long is how many feet long ?
5. Knowing that 5^ yd. make 1 rod, how could you
prove that 16^ feet make one rod ?
6. A short city block is about 20 rd. long. How many
such blocks would make a mile ? If the blocks were twice
as long, how many blocks would make a walk of 1 mile ?
7. How many feet of moulding will make a picture
frame 36 in. by 24 in? Make a drawing.
Written LINEAR MEASURE 189
i. Find the number of feet in
one mileo
2. How many ties are needed for
a mile of railroad track, if they are
laid two feet apart, from center to
center ?
3. If a man's steps are each three
feet long, how many steps will he take in walking 1±
miles ?
4. A field is in the shape of a rectangle 44 rods by 68
rods. How many rods of fence are needed to inclose it ?
(Picture.)
5.
a.
How
many
feet in J
mi.?
6.
In
1
mi.?
c.
In
l
mi.?
d.
Inl
mi.?
e. In £
mi. ?
/•
In
7
H
mi.?
9*
In
5
G
mi.?
h.
Inf
mi. ?
i. In 6|
mi.?
6. A 16-foot wire could be cut into how many 1-inch
pieces ?
7. How many yards of matting would be needed to
reach the length of a hall that is 87 ft. long ?
8. A man bought a rope 66 ft. long. He cut off and
used \ of it ? How many inches of rope were left ?
9. A race track, shaped like a zero, is 80 rods around.
a. How many times must a runner go around the track to
run 2 miles? b. How many miles does he run in going
around the track 32 times ?
10. How many yards make a mile ?
11. How many inches in a mile ?
12. How many inches in -| of a mile ?
190 REVIEW AND PRACTICE Written
i. What is the cost of 42 yd. of carpet at $.75 a
yard ?
2. A peach orchard contains 625 trees in 25 equal
rows.
a. How many trees in each row ?
b. If each tree bears 168 peaches, how many peaches
do all the trees bear?
c. How many baskets, each holding 28 peaches, will
contain the crop ?
d. If they are shipped in crates, each holding 6 baskets,
how many crates are needed ?
e. What are the peaches worth at 95 cents a crate ?
3. Mr. Blank earns $ 96 a month and his expenses are
$ 58 a month, a. How much can he save in 1 year ?
b. How much can he save in 25 years ?
4. How many hundredweight of coal in 25 tons ?
5. John was born in 1888 and Ethel in 1897. a. How
old is each now ? b. John is how much older than Ethel ?
6. If a clock gains 2 min. every day, in how many
days will it gain 1 \ hours ?
7. How many hundredweight in 27 tons ?
8. a. How many feet in 48 rods? b. How many
yards ?
J " L '2^5^10^2lT- iZ '20 5 *
13. 136-19f-=? 14. f-f=?
_ 803 + 796 9 647-256 9 72 x 54 ,
15. = i 16. = i 17. = i
39 23 12
Written DIVISION 191
i. Divide 495,018 by 534.
927 Quotient.
534)495018
4806
1441 We get the quotient figures by saying, "How
1068 many 5's in 49, in 14, in 37 ? "
3738
3738
Test every example by multiplication.
2. Divide 84,148 by 193. What will be your guide
figure ?
3. Divide 410,032 by 523.
4. Divide 18,432 by 512.
5. Divide 183,513 by 913.
Find the value :
io. *£fta 11. A^J. 12- W 13. *u^
14. *m & «• "^gii^ «• ^We 41 "■ ^fF
.Fmd quotients and remainders :
is. 12,324 + 213 19.32,634 + 111 20. 22,724-*- 437
21.23,919 + 119 22.18,647 + 29 23. 11,502 + 309
24.53,261 + 205 25. 4,312 + 99 26. 8,432 + 761
27. 31,845 + 301 28. 29,631 + 405 29. 293,476 + 310
30. 82,437 + 3100 31. 23,976,124 + 51,000 32. 487,500 + 500
33. One factor of 5328 is 144. Find the other. (Problem.)
34. 4™^ = 35. 13824^576 36> 132 x?= 121,836
192 REVIEW AND PRACTICE Written
i. How many pints are there in 568 gallons ?
2. A grocer buys cinnamon at $.50 a pound and sells it
at 5 cents an ounce, a. How much does he gain on a
pound? b. On 53 pounds?
3. 60,000 lb. of coal at $ 5 per ton cost how much ?
4. I work 28 days at $2.50 a day and take 14 tons
of coal for my pay. a. How much is my labor worth ?
b. How much a ton do I pay for the coal ?
5. Subtract the sum of 5 J and 7 \ from the sum of 8f
and 9^-.
6. A man bought 3 sacks of flour at $ 1.65 per sack,
and 4 bu. of corn at $ .75 per bushel. How much change
should he receive from a ten-dollar bill?
Quick Test
1. How many gills in 5 quarts ?
2. In how many hours can you walk 12 miles if it takes
you 15 minutes to walk one mile ?
3. What is the cost of 24 quarts of clover seed at $ 1 a
peck?
4. Theodore picked 15 quarts of berries and sold | of
them at 10 cents a quart. How much did he receive ?
5. What is the smallest number that exactly contains
either 3, 4, or 6 ?
6. What is the difference between -| and ^ ?
7. Two and one half quarts of milk taken from a can
containing 2 gal. leaves how many quarts ?
s. 4800 ^ 20 = ? 9. 25 x 20 = ? 10. 12 + 3£ = ?
Oral and Written SURFACE MEASURE 193
1. A square foot is how many inches long ? Wide ? It
contains how many square inches ?
2. Draw a square foot on the blackboard, cut it into
square inches. How many are there ?
3. A square yard is how many feet long ? Wide ? How
many square feet does it contain ? Show it by a drawing
on the blackboard.
4. A square rod is how many yards long? Wide?
What would you do to find how many square yards there
are in 1 square rod ? 5 J x 5 J- = 30 \. How many square
yards in one square rod ?
5. About how many square rods are there in the floor
of your schoolroom ?
6. A piece of land 8 rods wide and 20 rods long con-
tains an acre of ground. How many square rods does it
contain ? How many square rods make an acre ? Make on
the blackboard a drawing of this piece of land, using 1 inch
for 1 rod. Make it into lots 4 rd. wide and 8 rd. long.
These are good-sized city lots. How many are there ?
7. If your school ground is 132 feet from front to rear
and 165 feet along the street, it contains a half acre. How
many square feet does it contain ?
8. Draw a picture of a field 28 rods long and 24 rods
wide, using \ inch for a rod. How many square rods does
it contain ?
9. Draw a picture of a floor 35 feet long, containing
1050 square feet. Use \ inch for 1 foot. How wide
is the floor?
194 SURFACE MEASURE
THE TABLE OF SURFACE MEASURE
144 square inches (sq. in.) make 1 square foot
9 square feet (sq. ft.) make 1 square yard
30] square yards (sq. yd.) make 1 square rod
160 square rods (sq. rd.) make 1 acre (A.)
Note. — In working the following examples, first answer to yourself
these questions about each one : a. What is given ? b. What am I asked tc
Jindt c. Will the answer be greater or less than the number given?
Oral
1. How many square inches in 12 sq. ft. ?
2. How many square rods in \ A. ?
3. A floor 4 yd. long and 3 yd. wide contains how
many square yards ? How many square feet ?
4. The front of a desk drawer is 20 in. long and 5 in.
wide. It contains how many square inches ?
Written
1. How many square feet in 437 sq. yd. ?
2. How many square inches in 94 sq. ft.?
3. How many square yards in 48 sq. rd. ?
4. How many square rods in 26 A. ?
5. How many square yards in 3933 sq. ft.?
6. How many square feet in 13536 sq. in. ?
7. How many acres in 4160 sq. rd. ?
8. Change : a. 124 A. to square rods ; b. 36 sq. rd. to
square yards ; c. 523 sq. yd. to square feet ; d. 12 sq. ft.
to square inches ; e. 1 A. to square rods, to square yards,
to square feet, to square inches.
Oral SURFACE MEASURE 195
i. The area of a rectangle is always the product of
what two factors f
2. The number of square inches in a rectangle is the
product of ivhat two numbers f
3. The number of square yards in a rectangle is the
product of what two numbers ?
4. When a product and one of its factors are given,
how can you find the other factor f
5. The length of a map is 8 feet. Its width is 5J ft.
What is its area ?
6. A piece of pasteboard 20 inches long must be how
wide to contain 120 square inches ?
7. A rug 3 yd. wide and 4 yd. long covers how many
square yards of floor ? How many square feet ?
8. A flag is 3 yd. long and 2 yd. wide. It is how
many feet long ? Wide ? Find in two ways the number
of square feet in it. Make pictures to prove your work.
9. A door mat is 20 inches by 30 inches. Find its area.
10. Mrs. Smith's rose bed is 2 yd. wide and covers 48
sq. yd. of ground. How long is it ? Find its perimeter.
li. Mr. English has a lawn 3 rd. by 5 rd. In one cor-
ner is a summer house covering 1\ sq. rd. and in another
corner a fern bed covering \ sq. rd. How much surface
is left for grass ? (Picture, using 1 in. for 1 rd.)
12. Herbert has a pansy bed 4 ft. by 12. There are
2 plants in every square foot of ground. How many
plants in the bed?
196 SURFACE MEASURE Written
Change :
l. 96000 sq. rd. to acres. 2. 5616 sq. in. to square feet.
3. 3429 sq. in. to square feet and square inches.
4. 1683 sq. ft. to square yards.
5. 4346 sq. ft. to square yards and square feet.
6. 1837 sq. rd. to acres and square rodso
7. 13 sq. ft. 72 sq. in. to square inches.
8. 43 sq. yd. 7 sq. ft. to square feet.
9. 48 sq. rd. 13 sq. yd. to square yards.
10. 12 sq. yd. 4 sq. ft. to square inches.
u. 14256 sq. in. to square feet ; to square yards.
12. Find the area of a door mat 25 in. by 36 in.
13. Mr. Welton's cornfield is 25 rd. by 32 rd. a. How
many square rods of land in the field ? b. How many
acres ? c. How much corn does it yield at the rate of 46
bu. per acre ? d. How much is the corn worth at $ .60
per bushel ?
14. A rectangular farm which is half a mile long must
be how wide to contain 100 acres ?
Hint. — The farm must contain how many square rods ? It is how many
rods long?
is. How many square inches in the top of a table that
is 4 ft. long and 3 ft. wide ?
16. At 45 cents a square yard; what would be the cost
of matting to cover a floor 15 ft. by 18 ft.? (This may
be found in three ways.)
17. 6 A. is how many square rods more than 4 J A. ?
Written SURFACE MEASURE 197
i. Mr. Hadley owned a piece of land 39 rd. by 24 rd.
How many square rods had lie left after selling % of an
acre?
2. A square mile is how many rods long ? Wide ?
a. It contains how many square rods ?
b. It contains how many acres ?
3. A rectangular church floor is 84 ft. long and 48 ft.
wide. It covers how many square yards of land ?
4. A square park is \ mi. on a side. a. How many
square rods does it contain ? b. How many square yards ?
c. How many acres ? d. How much is it worth at $ 200
per acre ?
132 ft,
48 ft.
S
House.
Grass.
5. a. How many square feet
are there in this entire lot ?
b. How many square feet of
ground are occupied by the
house? c. How many square
feet of grass are there ?
6. A man cut an acre of land into 5 building lots and
sold four of them. The first contained 27f sq. rd., the
second 36 sq. rd., the third 30^ sq. rd., the fourth 29f
sq. rd. The fifth one he kept. a. How many square rods
of land did the man sell ? b. How much land did he keep?
7. Mrs. Rich bought a rug 12 ft. by 18 ft., and another
15 ft. by 21 ft. How many square yards of floor will
both rugs cover ?
8. What is the cost of a sidewalk 6 ft. wide in front of
three fifty-foot lots if it costs 14 cents a square foot ?
198 REVIEW AND PRACTICE Written
Add:
1. 397
2. $138.49
3. 768
4. $12.99
5.
4086
498
6.52
546
6.28
9798
684
8.79
987
143.72
8469
963
7.56
645
24.08
3578
589
109.84
867
16.49
5946
786
3.58
988
4.45
9894
999
17.75
789
9.78
87.65
6. 5£
4f
3&
7. 9f 8.
5|
13f
15f
H
9. 13|
H
4&
10.
1»A
16*
12 i
Subtract :
u. 14$
12. 7f
13. 17f
14. 18
15.
24
H
ii
Jk
14|
Zi T8
Multiply :
is. 729
17. 897
is. 976
19. 298
20
. 365
38
89
76
49
Jl
i^n<f the values :
21 * 3 6 8
22 19 ° 8
££. 18
23. Iff*
24. Iff*
25.
2625
2 5
26. Add the difference between 9835 and 4768 to the
difference between 694 and 138.
27. Divide the product of 96 and 55 by the product of
11 and 12.
Oral PRIME AND COMPOSITE NUMBERS 199
i. What is a factor ? Name all the factors of 4 ; 6 ;
8; 10; 9; 18.
2. 3 = 3x1. 3 and 1 are what of 3 ? What other
factors has 3 ?
3. 7 = 7 x 1. 7 and 1 are what of 7 ? What other
factors has 7 ?
4. 13 = 13 x 1. 13 and 1 are what of 13? What
other factors has 13 ?
5. What factor is found in 3, 7, 13? How does the
other factor of each of these numbers compare with the
number itself? Without naming the factors, tell what
are the factors of each of the numbers, 3, 7, and 13.
Name another number that has no other factor than itself
and one. Name several such numbers.
6. A number that has no other factors than itself and
one is a prime number.
Name all the prime numbers smaller than 20.
7. What is true of 4, 6, 8, 10, 9, and 18 that is not
true of 2, 3, 5, 11, and 17?
8. A number that has other factors than itself and one is
a composite number.
Name all the composite numbers to 20.
Tell which of the following numbers are prime and ichich
are composite :
9. a. 8; 5; 9; 12; 24; 19; 33; 41; 17; 28; 37;
29; 32; 15; 16; 18; 11; 23; 31; 40; 45.
b. The number of hours in a day ; quarts in a gallon ;
cents in a half dime ; cents in a quarter ; feet in a yard
200 PRIME FACTORS
1. 2 x 3 x 5 = ? 2, 3, and 5 are what of 30 ? The\
are what kind of numbers ?
2. 7 x 5 = ? 7 and 5 are what of 35 ? They
are what kind of numbers ?
3. 2 x 5 x 11 = ? 2, 5, and 11 are what of 110 ?
They are what kind of numbers ?
4. What two things have you found true of each of
the numbers 2, 3, 5, 7, and 11 in the above questions ?
5. A prime number used as a factor is a prime factor.
What are the prime factors of 30? Of 35? Of 110?
Of 10? Of 14? Of 12? Of 8? Of 21? Of 25?
6. 2 and 3 are the prime factors of what number?
2 and 5? 5 and 3 ? 7 and 2 ? 2 and 11? 2, 3, and 5 ?
2, 3, and 7 ? 2, 3, and 11 ? 11, 2, and 7 ?
7. Find the prime factors of 210 ; of 540.
We divide the given number
by the smallest prime number
that will divide it, using the
same divisor as many times as
possible. We then divide the
quotient by the next larger
prime number that will divide
it, and so on till the quotient
becomes a prime number. Each quotient becomes the dividend for
the next division. The last quotient and all the divisors are the
prime factors of the given number.
Find the prime factors of the following numbers:
8. 50 9. 45 io. 56 n. 72 12. 125 13. 75
14. 96 15. 330 is. 420 17. 231 is. 385 19. 154
2
S
5
210
105
35
7
2
2
3
3
540
270
135
45
2.3.5.7 Arts.
3
15
5
2
.2.3.3.3.5 Ana,
Written FACTORS AND MULTIPLES 201
Find the prime factors of:
1. 81 2. 400 3. 441 4. 294 s. 264
6. 273 7. 595 s. 456 9. 184 10. 882
11. Of what number are 2, 2, 3, and 11 the prime
factors ?
12. 5, 7, 13, and 19 are the prime factors of what
number Sf
13. 41 is a prime factor of 1763. What is the other ?
14. Tell which of the following numbers are prime and
which are composite: 50; 64; 71; 59; 52; 61; 63; 55.
15. Find the number whose prime factors are 11, 7,
and 17.
16. The product of three prime numbers is 805. Two
of the numbers are 7 and 5. What is the other ?
17. The product of three numbers is 2233. The product
of two of them is 77. What is the third ?
is §M = ? 385_x_3 = ? 385 + 7 «
'35 35x3 * 35+7
442 + 2 = 9 442x3 = 9 442 + 17 »
34 + 2 ' 34x3 ' 34 + 17
20. Dividing both dividend and divisor by the same
number affects the quotient how ?
21. Multiplying both dividend and divisor by the same
uumber affects the quotient how ?
22. 2x3x5x7x11 = ? 2x3x5x7 = ? 2310 + 210=?
2x3x5x7x11 a 3x11x17x19 a
23.
2x3x5x7 11x19
202 CANCELLATION
i. Taking a factor out of a number divides the number
by the factor taken out, thus:
210 = 2x3x5x7
2x3x5 = 30 ^= 30
2. 2730 = 2x3x7x13x5 65 = 5x13
2730 = 2x3x7x X ^ = 2x3x7 = 42 Quotient
65 0xj£
3. Taking the same factor from both dividend and divisor
is cancellation. In example 2 what factors were taken from
both dividend and divisor ?
4. Find the quotients by cancellation :
2x5x11x13 ,3x17x19x2
o.
d.
f.
7 x 6 x 21 J
12x16x3x45x19 ,
g. - h.
s:
5x13
4x
:8x9x 11x14
14 x 9 x 8
21
x7x3x5x6
7 x 6 x 21
12
x 16x3x45x19
19x3x12
2310 2x£x5x7x
n
3:
xl9
8
x8x
12 x
13x15
15
x8 x
:13
4
x31
x 50x6x9
50
x 6 x
:4
8
xl7
x 5 >
:6x7
5x8x7
5x7 = 70 Quotient
33 ?x/J
Find the quotients by factoring the dividend and the
divisor and canceling :
390 , '770 1925 , 900 2736
"•To" & -"35" C -~25" d "W ""W
f 462 2310 , 2x7x13x17 . 1932 . 2520
7 * "14 9 ' 70 119 *' 23 x 2 3 \ 24
CANCELLATION 203
We take the factor 2 out of 12
and 18; the factor 7 out of 7 and 49;
x ffx?X^X^ a210 the factor 5 out of 5 and 25 . and
j x ;g x cancel the factor 9 from both divi
dend and divisor. The factors re-
maining in the dividend are 6, 7, and 5. 6x7x5 = 210 Quotient
7
q* We take the factors 3 and 11 out oi
2 » o£ = 7 Quotient both dividend and divisor.
»
9£ 9 79 11 70 ^ e * a ^ e ^ e factor
3. ?x9xl2Q ~W = 7i Quotient 12 out of 72 and 120,
^ **jL then the factor 5 out
™ of 25 and 10.
36x27x49x50 ^ 9 7x4x24x2 ,
4.
70x18x15 2x7x12x2
6. (2x5x54) + (10x6) = 2 * 5 * 54 = ?
10 x 6
7. (36 x 48 x 16) + (27 x 24x8) = ?
8. Divide 25x2x72x14 by 6x9x120.
9. (Ilx3xl5xl4) + (21xllx3) = ?
4x6xl0x20 ^ 9 8xl4x22xl8 __ 9
10 * 12x25 ' ""2x11x7x3
12. What is the quotient of 4 x 9 x 17 x 80 divided bj
17x90?
13. (16x24x33x34)^(11x4x8x17) = ?
204 PROBLEMS SOLVED BY CANCELLATION
i. How many pineapples at 8 cents apiece will pay for
10 hours' work at 12 cents an hour ?
The work is worth (12 x 10) cents.
One pineapple is worth 8 cents.
(12 x 10) cents will buy -^— — pineapples.
o
3 5
= 15 pineapples Answer.
2. A farmer exchanged 45 cabbages at 9 cents apiece
for sugar at 5 cents a pound. How many pounds did he
receive ?
3. A milkman sold 280 quarts of milk at 6 cents a
quart and bought corn at 40 cents a bushel. The milk
paid for how many bushels of corn ?
4. William traded 6 bushels of hickory nuts at 96 cents
a bushel for hens at 48 cents apiece. How many hens
did he get ?
5. A college student worked 72 days in vacation at $ 3
a day. If all his expenses in college amounted to $2 a
day, how long did his money last ?
6. How many bricks 8 inches long and 4 inches wide
are required to cover a hearth 64 inches long and 32
inches wide ? (Picture.)
7. How many baskets of peaches, each containing 10
quarts worth 6 cents a quart, must be given for 18 bushels
of sweet potatoes at 60 cents a bushel ?
Oral REVIEW 205
i. What is the cost of 30 tons of hay at $15 a ton ?
2. If 7 acres of land cost $200, what will 14 acres*
cost?
3. 3200 ounces make how many pounds ?
4. When 1 lb. of tea costs 20^, what must be paid for
J of a pound ? For J of a pound ?
5. A owns | of a farm and B f of it. What part of
the farm do both own ? If C owns the remainder, what
part of the farm does C own ?
6. Will has $ 2 \ and James $ 3 J. How many dollars
have both ? How much less than $10 ?
7. What is the smallest multiple of 5, 2, 10, and 4 ?
Written
i. 8 bu. of cranberries were put in quart boxes and sold
at 14 cents a box. a. How many boxes were there ?
b. How much did they bring ?
2. How many pints in 5 bu. of birdseed ?
3. How many ounce weights will just balance 8 lb. ?
4. What will it cost at 18 9 a square yard to pave a
cellar 54 ft. by 33 ft. ?
5. How many hundredweight in 5 sacks of feed, each
containing 120 lb. ? Solve by cancellation.
6. How many square feet in 246 sq. yd. of paper?
7. Change 24 rods to yards and then to feet.
8. A farmer sold J of his flock of 640 sheep, a. How
many did he sell ? b. How many did he keep ?
206 REVIEW Oral
i. £ is how many 24ths?
2. ^ is how many 18ths ?
3. Add \ and \. Subtract |- from J.
4. Multiply 12 by 4J. (Problem.)
5. A rectangle 3 ft. wide, containing 24 sq ft., is how
long ? What is its perimeter ?
6. How many square inches in a 5-inch square ?
7. How many rods of fence will inclose a field 10^
rods square ?
8. A cask holds 48| gal. of water. If 20 J gallons
leak away, how many gallons remain ?
Written
1. What must be paid for 12 tons of grate coal at
$5.35 a ton and 4 tons of chestnut coal at $5.50 a ton?
2. If 10 men earn $ 120 a week, what will 6 men earn
at the same rate ?
3. Elsie spent J of $5 for a book and the remainder
for a pair of shoes. What did the shoes cost ?
4. At $ .80 a gallon, what is the cost of 10 qt. of ice
cream ?
5. A clock that ticks twice every second ticks how
many times in an hour ?
6. If a bushel of corn weighs 56 lb., how many bushels
of corn in a car load weighing 14 tons ?
7. 1568 oz. = how many pounds ?
Oral REVIEW 207
1. If \ of a pound of coffee costs 9 cents, what will
2 lb. cost?
2. 240 bu„ of oats at $.48 per bushel will pay for 16
barrels of flour at what price per barrel ?
3. How many square yards in 4 sq. rd. ?
4. Read DCCXXVIII.
5. How many square feet in 100 square yards ?
6. 3 qt. are what part of a peck ?
7. How many days in July and August t
Written
1. A merchant bought 44 yd. of silk for $ 39.16 and
sold it so as to gain $16.72. a. For how much did he
sell it ? b. At what price per yard did he sell it ? c. At
what price per yard did he buy it? d. What did he gain
on a yard ?
2. How many half-bushel baskets will hold 400 qt. of
cranberries ?
3. Mr. Rich sold his horse for $275 and his carriage
for $125. He then bought an automobile for 5 times as
much as he received for the horse and carriage. What
did the automobile cost ?
4. A farmer shipped to the city 32 cans of milk, each
can containing 40 quarts, a. How many gallons did he
ship ? b. What was it worth at 2| cents a quart ?
5. How many yards of cloth in 3 remnants containing
\ yd., 2 1 yd., and h\ yd. respectively ?
208 REVIEW Oral
i. Name 5 factors of 30. 2. 5 x ? x 7 = 70.
3. At 6 cents an ounce, what must be paid for a pound
of cloves ?
4. Of what numbers is 77 a multiple ?
5. At 10 cents a day, what is the cost of milk for a
family during the month of May ? April ?
6. Read 3,050,120.
7. Name the letters used in Roman Notation and give
the value of each.
Written
1. If 12 men earn $2880 in a certain time, how much
could 6 men earn in the same time ?
2. Add nine dollars five cents, fourteen dollars sixteen
cents, forty-eight cents, two dollars five cents, and seven-
teen dollars fifteen cents.
3. a. How many rods in \ of a mile ? 6. How many
feet?
4. Express in words 5,003,016.
5. The divisor is 234 and the quotient 108. What is
the dividend ?
6. What must be added to $63.75 to make $178.13?
7. Find quotients and remainders and test your work :
a.
49 7 6 7, 426 95 n 3 9 7 518 J &3 \$ 1
18 6 °* 26 8 C - 13 7 °" 6l4
P 4 25639 / 129675 n 683912 l "">
t " ~"2 5 3 /• 4 31 if* 9~T5 f( "
19
8. Make a problem for 6375 -i- 25.
THE MULTIPLICATION TABLE
209
2x 1= 2
3x 1= 3
4x 1= 4
5X1=5
2x 2= 4
3x 2= 6
4x2=8
ox 2 = 10
2x 3= 6
3x3=9
4x 3 = 12
5x 3 = 15
2x 4= 8
3 x 4 = 12
4 x 4 = 16
5x 4 = 20
2x 5 = 10
3 x 5 = 15
4x 5 = 20
5x 5 = 25
2x 6 = 12
3x 6 = 18
4 x 6 = 24
5x 6 = 30
2x 7 = 14
3 x 7 = 21
4x 7 = 28
5x 7 = 35
2x 8 = 16
3x 8 = 24
4 x 8 = 32
5x 8 = 40
2x 9 = 18
3 x 9 = 27
4x 9=36
5x 9 = 45
2 x 10 = 20
3 x 10 = 30
4 x 10 = 40
5 x 10 = 50
2 x 11 = 22
3 x 11 = 33
4 x 11 = 44
5 x 11 = 55
2 x 12 = 24
3 x 12 = 36
4 X 12 = 48
5 x 12 = 60
6x 1= 6
7x 1= 7
8x 1= 8
9x 1= 9
6x 2 = 12
7x 2 = 14
8x 2 = 16
9x 2= 18
6x 3 = 18
7 x 3 = 21
8x 3 = 24
9x 3= 27
6x 4 = 24
7 x 4 = 28
8x 4 = 32
9 x 4 = 36
6x 5 = 30
7x 5 = 35
8 x 5 = 40
9x 5= 45
6 x 6 = 36
7 x 6 = 42
8x 6 = 48
9x 6= 54
6x 7 = 42
7 x 7 = 49
8x 7 = 56
9x 7= 63
6 x 8 = 48
7x 8 = 56
8x 8 = 64
9x 8= 72
6 x 9 = 54 *
7 x 9 = 63
8x 9 = 72
9x 9= 81
6 x 10 = 60
7 x 10 = 70
8 x 10 = 80
9x10= 90
6 x 11 = 66
7 X 11 = 77
8x11 = 88
9x11= 99
6x12 = 72
7 x 12 = 84
8 x 12 = 96
9 x 12 = 108
10 x 1= 10
11 X 1= 11
12 x 1= 12
Roman
10 x 2= 20
11 X 2 = 22
12 x 2= 24
Numerals
10 x 3= 30
11 x 3 = 33
12 x 3= 36
10 x 4= 40
11 x 4 = 44
12 x 4= 48
I =1
10 x 5 = 50
11 X 5 = 55
12 x 5= 60
V=5
10 x 6 = 60
11 X 6 = 66
12 x 6 = 72
X = 10
10 x 7= 70
11 x 7 = 77
12 x 7= 84
L =50
10 x 8= 80
11 X 8 = 88
12 x 8 = 96
C =100
10 x 9= 90
11 x 9 = 99
12 x 9 = 108
D=500
10 x 10 = 100
11 X 10 = 110
12 x 10 = 120
10 x 11 = 110
11 x 11 = 121
12 x 11 = 132
M = 1000
10 x 12 = 120
11 x 12 = 132
12 x 12 = 144
M = 1,000,000
210
TABLES
LIQUID MEASURE
4 gills (gi. ) = 1 pint (pt. )
2 pints = 1 quart (qt.)
4 quarts = 1 gallon (gal.)
DRY MEASURE
2 pints (pt.) = 1 quart (qt.)
8 quarts = 1 peck (pk.)
4 pecks = 1 bushel (bu.)
UNITED STATES MONEY
10 mills = 1 cent
10 cents = 1 dime
10 dimes = 1 dollar
10 dollars = 1 eagle
AVOIRDUPOIS WEIGHT
16 ounces (oz.) = 1 pound (lb.)
2000 pounds = 1 ton (T.)
100 pounds = 1 hundredweight
(cwt.)
LINEAR MEASURE
12 inches (in.) = 1 foot (ft.)
3 feet = 1 yard (yd.)
5} jr f d M=i^ ( rd.)
or 16 1 feet J '
320 rods = 1 mile (mi.)
TIME
60 seconds (sec) — 1 minute
(min.)
60 minutes = 1 hour (hr.)
24 hours = 1 day (da.)
7 days = 1 week (wk.)
365 days = 1 common year
366 days = 1 leap year
SQUARE MEASURE
144 square inches (sq. in.) = 1 square foot (sq. ft.)
9 square feet = 1 square yard (sq. yd
square feet
30 | square yards
160 square rods
1 square yard (sq. yd.)
= 1 square rod (sq. rd.)
= 1 acre (A.)
Addition, 33-40, 43, 44.
Of dollars and cents, 41.
Addition and subtraction, 47, 53, 86.
Of fractions, 157, 159, 161, 163, 165,
167, 169, 171, 173.
Area, 131.
Avoirdupois weight, 103, 187.
Bushel, 72.
Cancellation, 202, 203.
Counting, 1, 2.
Days in different months, 92.
Days of the week, 7.
Division, 65, 75, 76, 105, 115, 129, 132,
186, 191.
Drill tables,
Addition, 31.
Multiplication, 73, 77.
Subtraction, 31.
Dry measure, 181.
Factors, 142, 144.
Factors and multiples, 201.
Finding any part of a number, 93.
Foot, 15, 122.
Fractions,
Addition and subtraction of, 126,
150-154, 157, 159, 161, 163, 165,
167, 169, 171, 173.
Halves, fourths, and eighths, 122,
146.
Lowest terms, 148.
One half, 9.
One third, 17.
One fourth, 20.
Terms of, 147.
INDEX
Gallon, 18.
Inch, 22.
Linear measure, 188, 189.
Liquid measure, 179.
Making change, 116.
Making questions, 110.
Miscellaneous problems, 92, 94, 98, 99,
117, 118, 120, 121, 123.
Money, 41.
Multiples, 145.
Multiplication, 61, 62, 69, 72, 89, 90,
102, 119.
Multiplication and division, 59, 60, 68,
70, 71, 77, 78, 80, 100, 106, 109 ;
114, 126, 128, 130.
Odd and even numbers, 141.
Peck, 72.
Perimeter, 127.
Pint, 5.
Prime and composite numbers, 199.
Prime factors, 200.
Problems,
In addition, 43.
In fractions, 156.
In temperature, 54.
In time, 185.
Of two steps, 160.
Solved by cancellation, 204.
Quart, 5, 72.
Quick tests, 91, 95, 107, 143.
Reading numbers, 3, 32, 84, 124
211
212
INDEX
Rectangles, 112, 113.
Review, 56-58, 63, 66, 67, 73, 79, 81,
82, 88, 91, 97, 101, 104, 108, 111,
125, 133-138, 155, 158, 162, 164,
166, 168, 170, 172, 174, 178, 180,
182, 190, 192, 198, 205, 208.
Roman numerals,
To five, 8.
To twelve, 11.
To twenty, 20.
To twenty-four, 28.
To one hundred, 64.
To one thousand, 1 16.
Subtraction, 45, 46, 48-62, 87.
Surface measure, 193-197.
Tables,
Of addition, 31, 66.
Of denominate numbers, 210.
Of multiplication, 73, 74, 77, !
United States money, 175-177.
Whole and mixed numbers, 149.
Writing numbers, 3, 32, 84, 124.
Of dollars and cents, 41.
Yard, 16.
M305881
THE UNIVERSITY OF CALIFORNIA LIBRARY
GENERAL LIBRARY
UNIVERSITY OF CALIFORNIA— BERKELEY
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