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Eclux:.T liq.oe.fi-TO
f^aitairli iSTollege i/ibtats
THE GIFT OF
GINN AND COMPANY
DECEMBER 26, 1923
3 2044 097 005 698
^ kjo btrtr*
e^
//>t^ 7^ -i t.
PROGRESSIVE ARITHMETIC
FIRST BOOK
BY
WILLIAM J. MILNE, Ph.D., LL.D.
PKB8IDBNT OF NEW YORK STATE NORMAL COLLEGE, ALBANY, N.T.
NEW YORK.:. CINCINNATI.:. CHICAGO
AMERICAN BOOK COMPANY
HARVARD CCLi.:3i l\Z SARY
GIFT Uf-
§tNN AND COMPANY
DEC. 26, 1923
Ck>PTKIOHT, 1906, BY
WILLIAM J. MILNE.
Entxbied at Btationkks' Hall, London.
fib8t prog. abith.
E-P 2
PREFACE
This book is designed to cover the first four years of arith-
metic. In many of our largest and best schools the instruction
of the first year and a half or two years of the course is given
orally. In such schools the matter found in Part I may be
omitted, but inasmuch as this is a thorough and complete^
review of the instruction usually given during the first two ^
years, it may be used as a text during the first part of the '
third year, or even earlier. The instruction for the third year -
is given in Part II, and for the fourth year in Part III.
The amount of work that may be accomplished in a half -^^
yftar has been taken as the unit of classification, and within c
that unit the various subjects have been treated topically ("^
though, of course, not exhaustively. With this order of pres-
entation it is believed that the most satisfactory results may
be obtained.
Abundant and varied practice, both oral and written, is
given in order to secure accuracy and facility in computation,
and the method of development is such that the pupil cannot
fail to gain an intelligent comprehension of all the processes
that are presented. The presentation always proceeds by very
easy and progressive steps from the known to the related
unknown.
The large number of exercises and problems will be a wel-
come relief to teachers who have been under the necessity of
3
4 PREFACE
devising and preparing a great amount of supplementary work.
It is generally conceded that supplementary exercises are not
only burdensome for the teacher, but usually unsatisfactory
as to results, because of the great waste of time for both
teacher and pupil.
Yet the book is not merely a book of exercises. Each new
concept is carefully presented by questions designed to bring to
the understanding of the pupil the ideas he should grasp, and
then his knowledge is applied. The formal statement of prin-
ciples and definitions is, however, reserved for a later stage
of the pupil's progress.
The problems have been prepared with much care. They
have been made both rational and practical, and they relate to
a wide range of subjects drawn from modern life and indus-
tries. The several types of problems form a continuous graded
series throughout the book. They have been classified as
scientifically as the abstract work.
It is believed that the book will be found interesting to
children, because the study of numbers is made interesting by
easy progressive steps and by thorough and satisfactory drills.
WILLIAM J. MILNE.
CONTENTS^ ^l\
PART I
pAoa
Reading and Writing Numbers — to 100 7
I Addition 10
Halves and Fourths — of objects only 17
Telling Time — to half hour and quarter hour 20
(Measuring Liquids 22
f Subtraction 24
Thirds and Sixths — of objects only 31
^Measuring Length — inch, foot, yard 33
Parts of Groups — of objects only 36
Numbers TO Fifty— 2's, 3's, 4's, 5's, and inverses .... 37
Review 45
.JdEAsuRiNG Weight — ounce and pound 48
"Terimeter and Area — square inch, square foot, and square yard . 49
Measuring Time — to minutes — calendar 51
Reading and Writing Numbers — to 1000 55
Addition — "carrying" 58
Making Change — upto$l 64
Subtraction — " borrowing " 66
'Multiplication — by 2, 3, 4, and 5 73
Division — by 2, 3, 4, and 5 79
PART II
Reading and Writing Numbers — to 10,000 84
Addition — of 4 -figure numbers 87
Subtraction — of 4-figure numbers 92
Roman Numerals — to C 97
Numbers to Seventy — 6's, 7's, and inverses 99
Multiplication — by 2 to 7 Ill
5
6 CONTENTS
PAOS
Division — by 2 to 7 116
Volume — cubic inch and cubic foot 121
Comparison of Measures 124
Addition and Subtraction — review 126
Numbers to One Hundred — 8's, 9*s, lO's, and inverses . . . 130
Multiplication — by 2 to 10 . . . . . . . . 137
Division — by 2 to 10 140
Review 147
United States Money 151
Addition AND Subtraction — of dollars and cents .... 153
Fractions — halves, fourths, thirds, sixths 157
Reduction, addition, subtraction, finding parts.
Multiplication — by 2-figure numbers 169
Division — by 11, 12, 21, 22, 31, 32, etc • . .175
Review 182
PART III
Reading and Writing Numbers — to 1,000,000 .... 189
Addition AND Subtraction — of 5-figure numbers .... 191
Fractions — business fractions 199
Reduction, addition, subtraction, finding parts and wholes.
Numbers to One Hundred Forty-four — ll's, 12's, and inverses . 214
Measuring — tables, drawing to scale . 218
Multiplication — by 3-figure numbers 229
Division — by 3-figure numbers 235
Review 246
Addition and Subtraction — review 250
Multiplication — review 252
Measuring — tables, reduction 256
Fractions — denominators within multiplication tables . . . 263
More extended informal work with fractions.
Division — more difficult work 277
Decimal Fractions 282
Bills . . . ■^. . • • 287
PROGRESSIVE ARITHMETIC
J- FIRST BOOK
: PART I
"^ READING AND WRITING NUMBERS
- 1. 1. Count the windows in this room. Count the
'^ desks in the first row; the books in this bookcase; the
Q^'^ children in your class.
^ How far can you count ?
2. Write the numbers to ten, using
words and figures.
'-^
One two three four flye six seven eight nine ten
1234567 8 9 10
3. Ten and one are eleven, written 11 ; ten and two are
twelve, written 12 ; ten and three are thirteen, 13 ; ten and
four are fourteen, 14; ten and five are fifteen, 15.
4. Write the word and the figures that stand for ten and
six, the number of books in the case; for ten and seven;
for ten and eight ; for ten and nine.
2. 1. The figure stands for nothing. It is called
naught, or zero. Thus, 10 means one ten and no ones.
2. Two tens are twenty, written 20, which means 2 tens
and ones; three tens, thirty, 30; four tens, forty, 40;
five tens, fifty, 50.
7
8
PROGRESSIVE ARITHMETIC
3. Write the word and the figures that stand for six
. tens ; for seven tens ; for eight tens ; for nine tens.
4. Ten tens are one hundred, written 100.
3. 1. 11 means 1 ten and 1 one; 12 means 1 ten and
2 ones ; 13 means 1 ten and 3 ones.
2. In the same way, tell what 14 means; 15; 16; 17;
18; 19; 20.
3. 21 means 2 tens and 1 one; 22 means 2 tens and
2 ones.
4. In the same way tell what each of these numbers
means: 23, 24, 25, 26, 29, 30, 31, 40, 44, 56, 60, 85.
>r J. , 5. Each of these bundles of sticks contains ten sticks.
^ y\Hn-py TTif^ny stir^ks ^^^ th^^^ in f^a^h group of tens nnd r>npfi?
6. Copy and fill blanks :
FiauBES Mbaminq
46 4 tens and 6 ones
62 and
39 and
50 5 tens and ones
80 and
90 and
99 and
100 10 tens and
Name
Forty-six
Fifty
One hundred
FIRST BOOK
7. Read each number and tell what it means :
27 38 40 56 67 98 53
32
70
57
28
20
63
81
48
100
8. Write in figures, placing ones under ones and tens
under tens :
Three tens and five ones.
Forty-five.
Twenty-two.
Six tens and two ones.
Seventy-nine.
Thirty-six.
Seven tens.
Five tens and nine ones.
Seventy-one.
Ninety-nine.
Sixty.
Eighty-four.
Thirty-three.
Nineteen.
Seventy-two.
Eighty-nine.
9. Observe that the first figure, counting from the right,
stands for ones, and the second figure stands for tens.
4. 1. How many cents is a dime worth? How many
cents are 2 dimes worth ? 3 dimes ? 5 dimes ? 10 dimes ?
10 cents equal 1 dime.
100 cents, or 10 dimes, equal 1 dollar.
2. A dime and a cent are worth how many cents ? 1 dime
and 5 cents ? 2 dimes and 5 cents ? 6 dimes and 3 cents ?
3. The sign f stands for cents; $ for dollars.
Thus, 57^ means 57 cents; $57 means 57 dollars.
4. Read: 45^, 38^, 17^, $6, $25, $88, mt $90.
5. Write : sixteen cents, forty cents, sixty dollars.
v' 10 ^ : V ^ PROGRESSIVE ARITHMETIC
> ^ r p • ^"^
V ^p -" ADDITION
,^ «' &. 1. How many balls are 5 balls and 7 balls?
,. ^'\ \3 2. How many lemons are 9 lemons and 6 lemons?
'i"^"
3. How many are 7 and 5 ? 8 and 3 and 5 ?
4. You have been uniting two or more numbers into one
number.
This process is called addition.
5. Here is a short way of writing " 4 and 2 are 6 " :
4 + 2 = 6.
6. The sign + means and. It is called plus.
The sign = means are or equal (sometimes is or equals).
It is called the sign of equality.
7. Copy, complete, and read :
4+5= 9+5= 6+6= 3+2+4=
7+3= 8+4= 4+5= 1+5+3=
8. Numbers to be added are usually written hke this 4
with the result below : - 2
The result is called the sum. 6
EXERCISES
6. Add quickly, naming only the sxun :
1. 1
7
3
7
4
8
2
5
3
1
4
2
5
6
9
8
6
9
2. 3
2
5
6
2
6
4
8
7
3
1
5
9
4
8
1
7
9
FIRST BOOK
11
3. 8
3
2
1
4
6
1
7
9
8
5
2
3
4.
6
5
7
2
4. 6
8
5
8
3
4
7
6
5
3
4
2
1
7
9
2
1
9
5. 1
7
8
5
1 .
2
4
5
9
9
6
3
4
7
6
3
8
9
These boys and girls are adding 2 to each number around
the ring.
6. Begin at 1 and
see how quickly you can
go around the ring in
either direction, adding
2 to each number with-
out making a mistake.
Begin at 3 and go in
either direction. Begin
at 2 ; at other numbers.
7. Instead of 2 put
3 in the ring and add as before ; put 4 in the ring and add ;
then 5; 6; 7; 8; 9.
8. Clara picked 9 yellow asters and 8 red ones. How
many asters did she pick?
9. Guy had 9 melons in his school garden. Paul had 7
more than Guy. How many had Paul ?
10. Sarah pressed 6 autunm leaves and Julia pressed 9
more than Sarah did. How many leaves did Julia press?
12 PROGRESSIVE ARITHMETIC
1.
EXERCISES
7. Add, giving results instantly :
1 11 21 31 41 51
61
71
81
91
6 6 6 6 6 6
6
6
6
6
Add 1 instead of 6; then add 2; 3;
4; 5
- 7;
8.
2 12 22 32 42 52
62
72
82
92
4 4 4 4 4 4
4
4
4
4
2.
Add 2 instead of 4 ; then add 1 ; 3 ; 5 ; 6 ; 7.
3. 3 13 23 33 43 44 54 64 74 84
2222222222
Add 3 instead of 2; then add 1; 4; 5; 6; 7; 8; 9.
4. 5 15 25 35 45 46 56 66 76 86
55555 55555
Add 6 instead of 5; then add 1; 2; 3; 4; 7; 8; 9.
5. 7 17 27 37 47 48 58 68 78 88
4444444444
Add 2 instead of 4; then add 1; 3; 5; 6; 7; 8; 9.
6. 9 19 29 39 49 59 69 79 89 49
88888888 88
Add 1 instead of 8; then add 2; 3; 4; 5; 6; 7; 9.
FIRST BOOK
13 i
EXERCISES
8. 1. In this diagram, add the three num-
bers in each of three columns, or vertical
rows; in each of three horizontal rows; in
each of two slanting rows.
2. See how rapidly you can find these eight sums vrithout
making a mistake.
Practice with the numbers changed about.
1
6
7
8
5
2
4
9
3
(o-
Add rapidly :
-^ J-
3. 4
8
7
5
2
5
8
8 "^ "^
7
4
5
8
8
9
7
^ ^'\
3
6
5
2
6
6
8
si.^
Add upward and
test your
• result by adding downward
i: '^..:
4. 1
1
2
3
5
6
8
7 -; ^
5
4
3
6
8
9
3
6 •;, '■
3
6
4
7
3
9
7 '^ ■
2
8
5
4
7
9
1
9 ^
c
5. 5
4
4
7
9
4
5
9 .-' :"
1
1
3
8
3
7
3
9 ^^ •
2
5
5
8
9
9 •? .
1
2
9
3
8
5
7
9)"/
2
8
6
8
2
8
9
9 -
6. On Halloween a boy paid 4^ for a mask, 8^ for a
wig, and 5^ for a horn. How much did he pay for all ?
14 PROGRESSIVE ARITHMETIC
7. Draw on paper 6 horizontal lines, 8 vertical lines, 6
slanting lines, and 7 more vertical lines. How many lines
have you drawn altogether ?
8. A postman left 4 letters at Mr. Brown's house, 4 at
Mr. Ward's, 8 at Mr. Joy's, 5 at Mr. Clark's, and 6 at Mr.
Boyd's. How many did he deliver to all ?
. 9. 1. How many ones are 5 ones and 2 ones? How
many tens are 5 tens and 2 tens ? Write 5 tens.
Add rapidly :
2. 4 tens 40 20 30 10 20 50 60
3 tens 30 10 20 40 20 30 20
30
20
60
40
80
40
20
50
40
50
30
40
10
20
70
50
35
43
75
20
40
30
16
27
40
30
20
42
55
65
50
70
4.
WRITTEN EXERCISES
1. Add 24 and 63.
cy. How many ones are 3 ones and 4 ones?
^r. Write the sum of the ones under the ones.
— How many tens are 6 tens and 2 tens ? Write
the sum of the tens under the tens. How do
you read 8 tens and 7 ones? What, then, is the sum of
24 and 63 ? Tell what you did to find the sum.
FIRST BOOK
15
Add:
2. 16
22
3. 33
14
4. 38
11
5. 62
35
6. 45
24
7. 31
46
8. 43
34
9. 15
24
10. 58
20
11. 17
32
Add upward and test your answer by adding downward :
12. 62 13. 41 14. 33 15. 14 16. 22
13 26 32 . 52 23
13 12 33 21 33
17. 10
18. 21
19. 12
20. 22
21. 26
11
23
3
33
40
12
24
50
2
12
13
30
4
30
21
WRITTEN EXERCISES
10. 1. If the Glenwood baseball club played 24 games
at home and 15 away from home, how many games did it
play?
Model Solution
24 games (at home)
15 games (away from home) '
39 games (the number played)
24 games -f 15 games = 39 games.
2. A conductor rang up 22 fares on one trip and 26 on
another. How many did he ring up on both trips ?
3. Charles has 54 cents in his bank, and Edward has 14
cents more than Charles. How much money has Edward ?
16 PROGRESSIVE ARITHMETIC
4. At a party there were 17 boys and 22 girls. How
many children were there at the party ?
5. A boy sold 16 morning papers and 33 evening papers.
How many papers did he sell that day ?
6. Stephen has 44 rare stamps, and Henry has 23 more
than Stephen. How many stamps has Henry ?
7. If 33 boys rode to a picnic in one car and 36 in
another, how many rode in both cars ?
Add and test each result :
8.
9.
10.
11.
12.
16^
72 boys
45 guns
24 balls
4 bats
42^
13 boys
10 guns
40 balls
33 bats
3M
3 boys
32 guns
12 balls
41 bats
13.
14.
15.
16.
17.
$23
35 girls
43 pins
14 dolls
26 bags
14
2 girls
24 pins
13 dolls
30 bags
50
62 girls
11 pins
12 dolls
13 bags
In examples like 13, the sign $ is written only with the first
number and the answer.
18. Mary has ironed 22 towels, 11 napkins, and 5 hand-
kerchiefs. How many pieces has she ironed ?
19. George spent 14^ for a bat, 25^ for a ball, and 40^
for a glove. How much did all cost ?
20. A boy had 35^ left after spending 50^ for a fishing
rod and 11^ for hooks and Unes. How much money had
he at first ?
FIRST BOOK
17
21. Grace spent 20^ for bananas, 12^ for grapes, 22^
for nuts, and 24^ for figs. How much did all cost?
22. On flag day I counted the flags on four buildings.
There were 21, 13, 23, and 20. How many flags did I
count ?
1
•^
23. How much did Ella's party cost, if her expenses ^
were 10^ for lemons, 6^ fgr sugar, 20^ for cake, and 40^ -K^ '
for ice cream ?
a
HALVES AND FOURTHS - :
11. 1. Into how many parts is the apple divided? the r7^
circle ? each square ? the oblong ?
Circle
5?
Square
Square
Oblong
/
2. How do the two parts of the apple compare in size ?
the parts of the circle ? of each square ? of the oblong ?
3. Make a circle, two squares, and an oblong, out of
paper. Fold each paper to find the line that divides it
into tivo equal parts and cut along this line.
4. One of the tivo equal parts of anything is called one
half of it.
5. Show one half of the circle; one half of each square;
one half of the oblong. Show two halves of each.
6. Draw a line and divide it into halves. What do you
do to anything to get one half of it?
FIRST PROG. AR. 2
18
PROGRESSIVE ARITHMETIC
7. What part of each of these circles is shaded ?
part is light?
8. How many halves of a circle
are there in one circle ?
9. To how many circles are
two halves of any circle equal ? four halves of equal circles ?
10. One half is written ^; two halves, f .
ircles is shaded ? What
12. 1. Divide an apple into halves; divide each half
into two equal parts. Do the same with a circle; with two
squares ; with an oblong.
X
i
1
2. Into how many equal parts has each object been
divided ?
3. One of the fowr equal parts of anything is called
one fourth, or one quarter of it.
4. Make a paper oblong, and by folding divide it into
halves and then into quarters.
Do the same with a paper circle.
5. How would you cut a pie into quarters ?
6. What part of a pie is one half of one half of it ?
7. How many fourths of a pie make one half of the pie ?
8. Draw a Une and divide it into fourths. Show one
fourth of it; two fourths; three fourths.
FIRST BOOK
19
9. What part of the first square is shaded? How
many fourths are light?
10. How many fourths of the
second square are shaded? how
many are light?
u. One fourth is written J; two fourths, f.
12. Write three fourths; four fourths.
EXERCISES
13. Using a cent piece, mark and cut out some, paper
circles. Fold and cut some of them into halves, others
into quarters.
1. On a sheet of paper paste 1 whole circle ; then enough
half circles to make 1 whole circle; then enough quarter
circles to make 1 whole circle. Compare them thus :
1 circle = 2 half circles = 4 quarter circles.
1 =2 halves = 4 fourths.
=f
=i-
Using parts of circles as in exercise 1, show that
2. ^ = fourths. ^ = .
3. | + J = fourths. i + i = •
4. Complete and show with circles and parts of circles :
i+*=
i+i-
■+i=
f+i=
20 PROGRESSIVE ARITHMETIC
TELLING TIME
14. 1. Write with figures the numbers from 1 to 12.
2. The Romans used letters for these numbers :
123456 7 8 9 10 11 12
I II III IV V VI VII VIII IX X XI XII
3. We often find these Roman numbers on the face of a
clock, except that there the number four is written IIII,
instead of IV.
Read the numbers on the clock face.
4. To what number is the long hand
of this clock pointing ?
The long hand is called the minute
hand.
5. To what number is the short
hand of the clock pointing? ^ ^ -
The short hand is called the hour hand.
6. By this clock it is nine o'clock.
To what number will the hour hand be pointing at ten
o'clock? at six o'clock? at three o'clock?
7. When the minute hand has passed from XII to III,
it has passed over one quarter of the clock face.
The hour hand has moved a little past IX.
It is then a quarter past nine o'clock.
8. When the minute hand has passed from XII to VI, it
has passed over one half of the clock face.
The hour hand has moved halfway from IX to X.
It is then half past nine o'clock.
FIRST BOOK 21
9. When the minute hand has reached VI, how many
quarter hours have passed since nine o'clock?
When the minute hand has reached IX, how many-
quarter hours have passed since nine o'clock?
The hour hand is then near X.
How many more quarters of the clock face will the min-
ute hand have to move over hefore it gets to XII ?
When the minute hand is at IX and the hour hand is
near X, we say it is " a quarter hefore ten,^' or '' a quarter
to ten,^^ instead of '' three quarters past nine.''
10. When the hour hand is at X and the minute hand is
at XII, what time is it ?
16. 1. How long does it take the minute hand to move
over the face of the clock ?
2. How long does it take the hour hand to move from
IX to X? from X to XI? from XI to XII?
3. How many half hours are there in an hour?
4. How many quarter hours are there in an hour?
5. How many quarter hours are there in a half hour?
6. Read the time shown on each of these clock faces.
7. Draw the face of a clock, the hands showing a quarter
past ten; half past ten; a quarter to eleven; half past one;
a quarter to eight.
i
22
PROGRESSIVE ARITHMETIC
8. Jessie's bedtime is half past eight. One night she sat
up half an hour later. At what time did she go to bed ?
9. Mary starts for school at a quarter to nine. Sarah
lives farther away and starts a quarter of an hour earlier.
At what time does Sarah start for school ?
MEASURING LIQUIDS
16. 1. The smallest measure holds just one pint and is
called a pint measure.
2. Fill it with
water and empty it
into the next larger
measure. Is the
larger measure full?
Do the same thing
again. Is the larger
measure full now ?
3. Tell how many
pints of water there are in it. ^ , 0, ( -^
4. The larger measure holds tioo pints, or one quart, and
is called a quart measure.
^^ 5. How many pints of water equal a quart of water ?
, 6. How many pints of milk equal a quart of milk?
Two pints equal one quart.
2 pt. = 1 qt.
We wjrite pt. ior pint or pints; qt. for quart or quarts.
FIRST BOOK 23
17. 1. Fill the quart measure with water and empty it
into the largest measure.
Do this several times until you have filled the largest
measure.
2. How many quarts of water have you poured into it ?
3. The largest measure holds four quarts, or one gallon^
and is called a gallon measure.
4. How many quarts of water equal a gallon of water ?
Four quarts equal one gallon.
4qt.=l gaL
18. 1. Pour a pint of water into the quart measure.
Notice how far up the water is in the quart measure.
One pint is what part of one quart ?
2. Pour two quarts of water into the gallon measure.
Two quarts are what part of a gallon ?
3. Pour out one quart of the water. What part of a
gallon remains ?
4. How many quarts are there in f of a gallon ?
EXERCISES
19. 1. Roy has poured 2 qt. of water into the pail shown
in the picture, John 1 qt., and Elsie 1 qt.
If each poiu^ in another quart, how many quarts will
there be in the pail? how many quarts more -than a
gallon ? how many quarts less than 2 gallons ? -
2. If each again pours in 1 qt. and this fills the pail,
how many quarts of water does the pail hold?
24 PROGRESSIVE ARITHMETIC
3. Measure any pitchers, basins, jars, or other dishes
that you may have.
4. How many pints are 2 qt. and 1 pt. ? 'How many
quarts are 1 gal. and 3 qt. ? f of a gallon and 2 qt. ?
5. Stella's mother bought 3 pt. of milk one day, 2 pt.
the next, and 4 pt. the next. How much milk did she
buy in the three days ?
6. A woman had a jug containing 2 gal. of vinegar.
After she had put in 3 qt. more, how many quarts were
in it?
SUBTRACTION
20. 1. How many more cars are 9 cars than 4 cars ?
Which is more, 8 or 10 ? 7 is how many more than 5 ?
\ 2. How many cents are 8 cents less 5 cents ?
';^How many are 10 less 4? 9 less 7? 8 less 3?
z' 3. You have been finding the difference between two
numbers, or taking part of a number from it and finding
how many are left.
These processes are called subtraction.
4. Here is a short way of writing " 8 less 3 are 5 '' :
8-3 = 5.
5. The sign — means less. It is called minus.
6. Copy, complete, and read :
9-5= 7-3= 10-5= 8-8 =
6-3= 8-5= 9-3= 7-2=
7. The numbers are often written like this 8
with the result below : , 3
The result is called the difference, or remainder. 5
FIRST BOOK 26
SZERCISBS
21. Subtract quickly ;
1. 6
3
10
15
6
14
5
7
16
3
1
_5
_9
4
_8
1
7
9
2. 5~
4
8
16
2
8
14
18
6
5
2
5
8
2^
4
7
_9
5
3. 2
11
5
4
10
17
3
11
12
1
_4
2
4
_6
9
3
6
9
4. 8
4
10
12
9
15
6
13
12
8
3
_8
_5
2
7
6
_8
6
5. 9
12
7
1
10
13
8
7
14
3
_4
2
1
7
9
7
1
9
6.10
13
9
11
9
8
7
9
11
9
6
1
3
4
6
3
9
2
7. Edward had 14 chickens, but a fox caught 5 of them.
How many chickens were left ?
8. Nora had 10 windows to wash. After she had fin-
ished 3 of them, how many had she to wash ?
9. Twelve things equal a dozen. There were a dozen
lilies in a pond, and Gertrude picked 4 of them. How
many were left?
10. Draw a dozen rings on the board, and rub out 7.
How many are left ?
26 PROGRESSIVE ARITHMETIC
11. Mrs. Case baked a dozen rolls for dinner, and the
family ate all but 3 of them. How many rolls were eaten ?
12. How old are you ? In how many years shall you be
11 years old?
13. Ella has read 9 pages of a story 18 pages long.
How many pages has she yet to read ?
14. Henry counted 17 wild ducks in a pond. When 8 of
them flew away, how many were left ?
15. A farmer had 16 turkeys. If he sold 9 of them at
Thanksgiving time, how many did he have left ?
16. There were 14 persons that took dinner at Frank's
house Thanksgiving Day and 8 at Helen's. How many
more dined at Frank's than at Helen's ?
EXERCISES
22. 1. Subtract, correctly and rapidly, each nimiber
around the ring from the number within,'
beginning with 3 and going in either
direction.
Begin with 8; with 5; with 6; with 5
other numbers.
2. Put 10 in the ring instead of 9 and sub-
tract the numbers outside as in exercise 1.
3. Put 11 in the ring and subtract the numbers outside;
put 12 in the ring and subtract; then 13; 14; 15; 16; 17;
18; 19.
FIRST BOOK 27
Subtract, giving results instantly :
4. 19 29 39 49 59 69 79 89 99
11111111 1
Subtract 2 instead of 1; then 3; 4; 5; 6; 7; 8; 9.
5. 10 20 30 40 50 60 70 80 90
2222222 2 2
Subtract 1 instead of 2; then 3; 4; 5; 6; 7; 8; 9.
6. 17 27 37 47 58 68 78 88 98
7 7 7 7 7. 77 7 7
Subtract 1 instead of 7; then 2; 3; 4; 5; 6; 8; 9.
7. 11 21 31 41 52 62 72 82 92
8 8 8 8 8 8 888
Subtract 1 instead of 8 ; then 2 ; 3 ; 4 ; 5 ; 6 ;
7; 9.
8. 13 23 33 43 54 64 74
84
94
7 7 7 7 7 7 7
7
7
Subtract 1 instead of 7 ; then 2 ; 3 ; 4 ; 5 ; 6 ;
8; 9.
9. 15 25 35 45 56 66 76
86
96
6 6 6 6 6 6 6
6
6
Subtract 1 instead of 6; then 2; 3; 4; 5; 7; 8; 9.
28 PROGRESSIVE ARITHMETIC
23. Subtract rapidly :
1.
2.
5 tens
50
30
60
40
30
70
80
2 tens
20
10
40
10
20
50
40
50
90
80
70
90
60
80
100
30
60
30
20
30
50
10
70
55
65
75
96
36
52
91
87
30
40
50
70
20
40
50
GO
WRITTEN EXERCISES
1. From 97 subtract 52.
gy How many ones are 7 ones less 2 ones ?
Write the difference of the ones under the ones.
— How many tens are 9 tens less 5 tens ?
^^ Write the difference of the tens under the tens.
What, then, is the difference between 97 and 52 ?
Tell what you did to find the difference.
Test. — The answer when added to 52 should give 97.
Subtract, and test each result :
2. 33
3. 63
4,
48
5. 82
6. 66
21
42
35
51
33
7. 46
8. 75
9.
87
10. 98
11. 85
34
53
22
44
24
la. 57
13. 89
14.
44
15. 79
16. 88
25
76
14
27
36
FIRST
BOOK
29
Subtract and test :
17. 45
18.
85
19.
53
20.
99
21.
45
22
33
23
76
34
22. 66
23.
58
24.
68
25.
84
26.
77
34
27
34
31
27
27. 79
28.
91
29.
57
30.
79
31.
63
45
61
45
56
31
32. 37
33.
88
34.
85
35.
67
36.
76
26
45
44
17
43
WRITTEN EXERCISES
24. 1. Mr. Hale had $86 in the bank and drew out $25.
How much money had he left in the bank ?
Model Solution
$86 (in the bank at first)
$25 (drawn out)
$61 (left in the bank)
$86~$25 = $61, for $25-f $61 = $86.
2. There are 34 badges in a box. If 21 belong to John
and the rest to Earl, how many does Earl own ?
3. I have 28 cherries. If I give 14 of them to Clara
and the rest to Grace, how many cherries will Grace have ?
4. There are 43 rooms in the Bayside Hotel. When 30
of them have been swept, how many more are there to
sweep ?
30 PROGRESSIVE ARITHMETIC
5. Frank printed 36 photographs and gave away 22 of
them. How many had he left ?
6. A horse dealer had 64 horses and sold 40 of them.
How many horses had he left ?
7. Mary had 78 cents and spent 25 cents for the
use of a rowboat. How much money had she left ?
8. Frank has 63^ and wishes to buy a wagon costing
75^. How much more money does he need?
9. A man had 32 electric lamps and bought enough
more so that he had 48. How many did he buy ?
10. A girl went to the grocery store with 87^ in her
purse. She spent all but 35^. How much did she
spend?
11. If there are 34 girls and 22 boys in a class, how
many more girls are there than boys ?
12. Harry is 14 years old, and his uncle is 37 years old.
How much older is Harry's uncle than Harry ?
13. If John has 44^ and Beatrice has 67^,' how much less
money has John than Beatrice?
14. If you blow 38 soap bubbles and I blow 23, how
many more soap bubbles do you blow than I ?
15. Mary's mother paid 15^ for cheese and 38^ for butter.
How much less did she pay for cheese than for butter?
16. At a fair a peddler sold 48 red balloons and 26 blue
ones. How many more red balloons did he sell than blue
ones?
FIRST BOOK
31
THIRDS AND SIXTHS
26. 1. Into how many
equal parts has Ruth cut
the cake?
\ 2. One of the t hree equal
parts of anything is called
one third of it.
/ 3. If Ruth cuts each
/ piece into two equal pieces ,
\ into how many equal pieces
\will the cake then be cut?
4. One of the six equal
parts of anything is called one sixth of it.
5. How TTiflnv siyths of a cake are there in one third of
a cake ? What part of a cake is one half of one third of it ?
6. Draw a Une and divide it into thirds ; into sixths.
7. What part of the first oblong is light ? How many
v^
thirds are shaded ?
8. What part of the second oblong is
shaded ? How many sixths are Ught ?
9. How many thirds of an oblong are
there in one oblong? how many sixths?
■
^M
10. How many sixths of this oblong are
shaded ? how many are Ught ?
11. One third is written ^ ; one sixth, ^.
12. Write two thirds ; three sixths ; five sixths ; six sixths.
-iPAr^^y^
\^ 22 ' -\ ^ .^"^ , TROGRESSIVE ARITHMETIC
.'''» ^J^ . *.-.^
:-&y-V-' w ^3" 'acJ
>r".\- 26. 1. How many thirds of a circle are there in one
' .' circle? how many sixths?
■ Q=q 0=$ a:)-$^
2. How many sixths are there in ^? in ^? in f ?
3. If I divide an orange into thirds and give 1 third to
John, how many thirds do I have left? 1 ""i = •
4. If I then give 1 third to William, how many thirds
do I give to both boys ? i + i = — ~-
How many thirds do I have left ? 1 — t = •
5. Floy gave |^ of a pie to Ruth and J to Jane. How
many sixths of it did she give away? i + i== •
How many sixths were left ? l^f^f^e"^ •
To how many thirds are f equal? f ?
6. Floy gave ^ of the pie to George. How many sixths
had she then given away ? i + i + i = •
How many were left ? l""f = t""t=='
To how many halves are f equal?
FIRST BOOK
33
MEASURING LENGTH
27. 1. Examine your rule. Notice the long marks that
are numbered.
Notice the distance between two of these marks.
2. This length is called one inch.
3. Using your rule to measure, draw on the board a line
twelve inches long.
4. This length is called one foot.
5. How many inches are there in one foot ?
Twelve inches equal one foot.
12 in. = 1 ft.
6. Count the inches on your rule. How long is it ?
28. 1. Make a paper rule one foot long, and mark the
inches on it as shown in this drawing, which is made
smaller than a foot rule.
1
2
3
4
6
6
7
8
9
10
11
12
2. Fold the rule, bringing the ends together. How
many inch spaces are there in each half of the rule ?
^ of 1 foot = inches. ^
3. Fold the rule again and find how many inches there
are in one fourth of a foot. " ^
:^ of 1 foot = inches.
4. Count the inches in two fourths of a foot; in three
fourths of a foot.
5. How many fourths of a foot make one half of a foot?
FIB8T PROO. AR. — 3
h
^
34 PROGRESSIVE ARITHMETIC
6. Make another paper rule and fold it at the 4-inch and
8-inch marks.
What part of a foot is 4 inches ? How many thirds of a
foot are 8 inches ?
7. Taking the rule as it is now folded, fold it again in
the middle. What part of a foot is J of ^ of a foot ?
Count the- inches in ^ of a foot; in f of a foot.
How does f of a foot compare with J of a foot ?
We may write "^^ of a foot" in a short way like this: ^ ft.
What does J ft. mean ? ^ ft. ? ^ qt. ? J gal. ?
EXERCISES
29. 1. Without measuring, draw a line as nearly 1 ft.
long as you can. Test it by measuring with a rule. How
many inches too long or too short is your line ?
2. In the same way draw a line ^ ft. long and test your
estimate; ^ ft* long; ^ ft. long; 2 in. long.
3. Estimate the length of your desk. Measure it.
4. Estimate the width of the door; the width of the
window. Test your estimates by measuring.
5. Estimate and measure the length, width, and height
of the table ; the length and width of your pencil box.
6. Estimate how much wider your copy book is than this
book. Test by measuring.
7. Is this book more or less than J ft. wide? ^ ft.?
^ ft. ? How many inches more or less in each case ?
8. W^hich is longer and how much, a 7-inch line or one
I ft. long ? an 8-inch Une or one f ft. long ?
FIRST BOOK 36
30. 1. Draw a line one foot long on the blackboard;
extend it a foot ; extend it another foot.
How many feet long is the whole line now ?
2. This length is called one yard.
3. Hqw many feet are there in a yard ?
Three feet equal one yard.
3 ft. = 1 yd.
4. What things are measured by the yard ?
31. 1. Draw a 1-yard line and mark it off into feet.
What part of 1 yard is 1 foot? 2 feet?
2. Measure and count the inches in ^ yd. ; in f yd.
12 in. + 12 in. = in.
3. Measure and count the inches in f yd., or in 1 yd.
12 in. + 12 in. + 12 in. = in.
4. How many inches are ^ of 36 in. ? | of 36 in. ?
EXERCISES
32. 1. How many yards long do you think the school-
room is ? how wide ? Measure to see.
2. Estimate, in yards, the length of each blackboard in
the room. Test your estimate by measuring.
3. Draw a hne 2^ ft. long and another 1 yd. long.
Which is shorter? how many inches shorter?
4. Take a string 1 yd. long and cut it in the middle.
Measure one piece and compare it with a 2-foot line.
Which is longer, and how many inches longer?
•4
36
PROGRESSIVE ARITHMETIC
,t;
PARTS OF GROUPS
ci
.^ r
^
33. 1. If 6 pears are separated into two equal groups,
how many are in each group ?
2. What part of the pears is
in each group ? How many pears
are | of 6 pears ?
3. Separate 6 pears into three //% (fw^ ii^L%
equal groups. How many pears ^^ Simmm Sjyjpyr
are ^ of 6 pears ? f of 6 pears ?
4. Take 12 splints. Separate them into 2 equal groups.
How many splints are ^ of 12 splints ?
5. Separate them into 3 equal groups. How many
splints are ^ of 12 sphnts ? f of 12 splints ?
6. Separate them into 4 equal groups. How many
splints are ^ of 12 splints? f of 12 splints? | of 12?
7. By properly grouping the splints, find ^ of 12. How
many are f of 12? f of 12? f of 12? f of 12?
INI UN mil Mill III III IN II II II II
8. What is I of 8? J of 10? ^ of 9?
9. What part of a dozen buttons are
3 buttons? 6 buttons? 9 buttons?
10. What part of a dozen buttons are 4
buttons? 8 buttons?
i of 8?
11. How many buttons are there in i of a
dozen buttons? in 1^ dozen? in ^ dozen?
in If dozen?
BIO
FIRST BQt
S TO FIFTY
84 ^^^ounting bytwo g)
1. Count the boys in this procession by twos
%( Count them in such a way as to tell how many time%
you have counted two boys, thus: '' One 2 is 2; two 2's are
4; three 2's are 6;'' and so on.
3. How many boys are two times 2 boys ? three times
2 boys ? Continue to ten times 2 boys.
4. How many pints are there in 1 quart? in 2 qt.?
in 3 qt.?
5. In 4 quarts there are 4 times 2 pints, or 8 pints. Tell
in the same way how many pints there are in 5 qt.; in
6 qt. ; in 7 qt. ; in 8 qt. ; in 9 qt. ; in 10 qt.
6. Instead of the word ''times'' the sign x is used.
7. This is the table of
twos to 10 times 2.
Copy it; then commit it
to memory.
1x2= 2
6x2 = 12
2x2= 4
7x2 = 14
3x2= 6
8 X 2 = 16
4x2= 8
9 X 2 = 18
6x2 = 10
10x2 = 20
38
PROGRESSIVE ARITHMETIC
35. 1. If 4 boys march by twos, how many twos will
there be ? How many 2's are there in 4 ?
2. How many 2's are there in 6? in 8? in 10? in 12?
in 14? in 16? in 18? in 20?
3. How many times can 2 apples be taken
out of this basket, if it contains 12 apples ? if
it contains 14 apples? 16 apples? 18 apples?
20 apples?
4. Count by twos to 20, and as you name each num-
ber tell how many times it contains 2, thus: ''2 contains 2
once ; 4 contains 2 two times;'' etc.
5. Another way to say *'12 contains 2 six times" is to
say ''12 divided by 2 is «qual to 6."
In writing we use the sign -^ for ''divided by." ^
Thus, 12 -J- 2 = 6 means " 12 contains 2, 6 times," or « 12 divided
by 2 is equal to 6."
6. Read, fiUing blanks :
4 times 2=8
5 times 2 = 10
6 times 2=12
10 times 2 = 20
2;^2= 6-2 =
4-^-2= 8-^-2 =
8 contains 2 times.
10 contains 2 times.
12 contains 2 times.
20 contains 2 -^ — times.
10^2= 14^2= 18-i-2 =
12^2= 16-*-2= 20-*-2 =
7. 6 = 3 twos, II II II; ^ of 6 is .
8 = 4 twos, II II II II; i of 8 is .
8. Find ^ of 4; ^ of 3; f of6; f of 8; ^ of 12.
FIRST BOOK
39
SXERCISES
Here are ten columns of 2's. The number of 2's in
V7
rt?
each colunm is written at the top. Copy on the blackboard, q
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
. 2
2
2
2
2
2
c2
1. Add the colunms in this way: ''One 2 is 2, two 2's C
are 4," etc. Also add in this way: "Once 2 is 2, two l^
times 2 are 4/' etc. Do this rapidly. ^
2. Name the sums only, as rapidly as you can, as the
teacher points to various columns.
3. Beneath each column writ6 its sum. Which column
shows 6 divided into 3 equal parts ?
Tell about the column thus :
"3 times 2 are 6; ^ of 6 is 2; 6 contains 2, 3 times."
4. Tell about the column whose sum is 4 ; 8 ; 12 ; 20.
5. Which column shows 8 divided into 4 equal parts?
How many 2's are there in J of 8 ? in f of 8 ? f of 8 = .
6. In the same way find | of 6 ; f of 12 ; f of 12.
40
PROGRESSIVE ARITHMETIC
<')
fl"
7. Count the parts of this oblong. How do they compare ?
8. One of the/i;6 equal parts of any-
thing is called one fifth of it.
One fifth is written i.
9.
II II II
10 = —
II II
-2's.
^oflO =
14 + 2 =
iof 4 =
18 + 2 =
f of6 =
iof8 =
ioflO =
|of8 =
f ofl2 =
The grocer is putting them
)
10. Answer quickly :
2+2+2= 5x2=
2is Jof— 2 is ^ of —
4x2= ^ofl2 =
2 is i of— 12-5-2 =
37. Counting by threes.
1. Albert is buying 30 eggs,
into the basket three
at a time. Count for
Albert by threes to 30.
2. Count to 30 thus :
''One 3 is 3; two 3's
are 6;'' and so on.
3. How many eggs
are 2 times 3 eggs?
3x3 eggs? 4x3 eggs?
5x3 eggs ? Continue
to 10 X 3 eggs.
4. How many feet are there in 1 yard ? in 2 yd. ? in 3 yd. ?
5. In 4 yards there are 4 times 3 feet, or feet. Tell
in this way how many feet there are in 5 yd. ; in 6 yd. ; etc.
FIRST BOOK
41
6. Memorize this table of threes.
7. How many times 3 is
6? Answer in this way: "6
is 2 times 3.''
How many times 3 is 9?
12? 15? 18? 21?
8. Read, filling blanks :
8 times 3 = 24 ; 24 contaiAs 3
9 times 3 = 27 ; 27 contains 3
10 times 3 = 30 ; 30 contains 3
3-5-3= 9-3= 15-3= 21-3 =
6-«-3= 12-^3= 18-3= 24^3 =
1x3= 3
6x3 = 18
2x3= 6
7x3 = 21
3x3= 9
8x3 = 24
4x3 = 12
9x3 = 27
5x3 = 16
10x3 = 30
9. 6 = 2 threes,
I ; i of 6 is
10. Find i of 8; i of 12; ^ of 6; J of 6; i of 9; ^ of
10; Jof 15; ^of 12; i of 18.
11. Compare 2x3 with 3x2
38. Counting by fours. - ^ ~^
1. Write these columns of 4's and others, X 4
increasing in height until the tallest con- ' 4 4
tains ten 4's. Under each column write its - 4 4 4
sum. (4444
"' 2. Read the sums in this way: V
'' One 4 is 4; two 4's are 8;'' and so on to ten 4^s.'
3. Suppose that each 4 stands for 4 quarts, or 1 gallon.
How many quarts are there in 3 gallons? in 4 gal.? in
5 gal. ? in 6 gal. ? in 7 gal. ? in 8 gal ? in 9 gal. ? in 10 gal. ?
^
42
PROGRESSIVE ARITHMETIC
1x4= 4
6x4 = 24
2x4= 8
7x4 = 28
3x4=12
8x4 = 32
4x4 = 16
9x4 = 36
6x4 = 20
10x4 = 40
4. Memorize this table of fours
5. How many 4's are
there in 8? in 12? in 16?
in 20? in 24? in 28? in 32?
in 36? in 40?
6. Copy, complete, and
read:
4-^4= 12^4= 20-4= 28 + 4= 36-^4 =
8-5-4= 16-^4= 24 + 4= 32 + 4= 40 + 4 =
7. Look at your columns of 4's, and their sums, and
tell what part 4 is of 8; of 12; of 16; of 20; of 24.
8. Find f of 12; | of 16; ^ of 20; i of 24; f of 24.
9. What part of a gallon is 1 quart? 2 qt.? 3 qt.?
10. What part of a dozen is 4 ? How do you know ?
11. Compare 2x4 with 4x2; 3x4 with 4x3.
EX£RCISES
39. 1.
Tell quickly the value of each of the following :
4x3
7x2
14 + 2
30+ 3
iofl5
5x2
8x4
15 + 3
32+ 4
iof 12
4x4
6x3
16 + 2
40+ 4
iof 20
6x2
10x2
18 + 2
iof 6
iof 8
5x4
8x3
18 + 3
iof 8
fofl2
7x3
9x4
24 + 3
iofl2
f ofl2
8x2
10x4
24 + 4
iof 12
iof 18
5x3
8-»-4
27 + 3
ioflO
|of 9
6x4
12 + 2
28 + 4
iof 16
|ofl6
FIRST BOOK
43
2. Compare 8 and 2 thus : 8 is 4 times 2; 2 is J of 8.
Compare in the same two ways :
3. 6 and 2.
6. 12 and 3.
9. $16 and $4.
4. 6 and 3.
7. 12 and 2.
10. 10^ and 2^.
5. 12 and 4.
8. 15 and 3.
11. 18 hr. and 3 hr
^9
40, <^ounting by fiv e
-^J^
1. Let us keep tally-
while the coal man car-
ries in the coal.
We will make one
mark for each bag
emptied, drawing every
fifth mark across the pre-
ceding four, thus: ttl|.
2. When the tally is
\Hl nil, how many bags
have been emptied ? How many are two 5's, or 2 x 5 ?
3. Show the tally for three 5's, for four 5's, and so on
to ten 5's, telling each time how many bags it stands for.
4. WTiat is the value of 2 five-cent coins? of 3 such
coins? of 4? of 5? of 6? of 7? of 8? of 9? of 10?
5. Memorize this table of fives.
6. How many 5's are there
in 10? in 15? in 20?
Tell how many times each
of these numbers contains 5 :
25, 30, 35, 40, 45, 50.
v^
1X5= 5
6 X 5 = 30
2 X 5 = 10
7x5 = 35
3 X 6 = 15
8 X 5 = 40
4x5 = 20
9 X 6 = 45
6x5 = 25
10 X 5 = 60
44 PROGRESSIVE ARITHMETIC
7. Copy, complete, and read :
5 + 5= 15 + 5= 25 + 5= 35 + 5= 45 + 5 =
10 + 5= 20 + 5= 30 + 5= 40 + 5= 50 + 5 =
8. A half dollar is worth 50 cents, and a quarter dollar
25 cents. How many five-cent pieces is each worth ?
9. What part of 20^ is 5^? Find J of 20^; f of 20 ^.
10. Find ^ of 25; f of 25; f of 15; ^ of 30; f of 30.
11. Compare 2x5 with 5 x 2 ; 3 x 5 with 5x3; 4x5
with 5x4.
EXERCISES
41. 1. The first circle is for drill on the table of 5's.
Give the results rapidly, beginning with 2 5's and going in
either direction. Begin with other numbers around the circle.
2. How rapidly can you go around the first circle when
the number inside is 2 ? 3 ? 4 ?
3. How many 3's are there in each number around the
second circle? Give the results rapidly.
4. How many 4's are there in each of these numbers :
4, 12, 20, 8, 40, 36, 28, 16, 12, 24?
5. How many times do these numbers contain 5 :
5, 15, 35, 45, 25, 10, 20, 30, 40, 50?
J
REVIEW
EXERCISES : . I
42. 1. Count these dots ••••• ••••• •••••^
by 4's; by 2's; by 5's; by \^^^
lO's. You should get the • • • • • • • • • • • • • • • ^ ^^
same answer each time. * ^ %
2. Count by 2's from to 50, thus : 0, 2, 4, 6. etc. ^
3. Count by 3's from to 60; by 4's from to 80; by
5's from to 100; by lO's from to 100.
4. Count by 2's from 1 to 49, thus: 1, 3, 5, 7, etc.
5. Count by 3's from 1 to 58 ; from 2 to 59.
6. Count by 4's from 1 to 77; from 2 to 78; from 3
to 79.
7. Count by 5's from 1 to 96 ; from 2 to 97 ; from 3 to
98; from 4 to 99.
8. Count by lO's from 1 to 91 ; from 2 to 92 ; etc.
9. Carrie bought 7 cents' worth of plums at 3 for a cent.
How many plums did she buy ?
10. At 3 plums for a cent, how many cents would she
have needed to buy 30 plums? 24 plums?
11. When milk costs 4 cents a quart, how much must be
paid for a gallon at the same rate ? for 6 qt. ?
How many quarts can you buy for 20 cents ? for 32
cents? for 28 cents? for 36 cents?
12. When you have read 4 pages more, what will be
your page niunber ?
46 PROGRESSIVE ARITHMETIC
Add or subtract as the signs indicate :
13. 21+8 14. 39-6 15. 72 + 5 i6. 58-5
17. 42 18. 58 19. 81 20. 64
+ 7 -3 +8 +5
>^
21. 77 22. 61 23. 29 24. 99
-20 +30 +50 -60
•a
25. When lemons cost 2 cents each, how much will 3
lemons cost ? half a dozen lemons ? 5 lemons ? 8 lemons ?
10 lemons?
26. When Ella had set 10 toy cups and saucers on her
table, how many dishes were there on it ?
27. How many lemons costing 2 cents each can you buy
for 10 cents ? for 14 cents ? for 8 cents ? for 18 cents ?
28. When milk costs 5 cents a quart, how much will
3 quarts of milk cost? a gallon? ^ gal.? 2 gal.? How
many quarts can you buy for 20 cents ? for 35 cents ?
29. Jennie has 20 cents. How many 5-cent m easures of
peanuts can she buyj^^^l^many 4-cent measures^
30. How much money do you need to buy 5 3-cent bags
of pop com ? 4 bags ? 7 bags ? 9 bags ?
31. Three boys sold lemonade and earned $9, which they
divided equally. How much money did each receive ?
32. How much do 3 roses cost at i^i^finifi^eacb.? 4 roses ?
6 roses ? 10 roses ? At this price, how many roses can you
buy for 20 cents? for 32 cents? for 28 cents?
FIRST BOOK 47
33. Find the sum of 50 cents and 25 cents.
34. How many inches are there in 1 foot and 6 inches ?
35. Robert picked 9 chestnut burs and found 2 chest-
nuts in each. How many chestnuts did he find in all ?
36. Eva made 45 penwipers for a fair but only 25 were
sold. How many were left ?
37. In a game of prisoner's base there were 12 children
free on one side and 10 on the 'other, and 7 were prisoners
om the bases. How many children were playing ? -
38. Ralph caught 9 fish, 3 of which were trout. What
part of Ralph's fish were trout?
39. What part of a dozen fish did Ralph catch ?
40. John has 72 cents in his bank. If he puts in 5 cents
and then 2 cents, how much money will then be in the
bank?
41. On election night there were 16 bonfires on Main St.
and 12 on Maple St. How many bonfires were there on
both streets ?
42. When oil costs 12 cents a gallon, how much will a
quart of oil cost ?
A quart is J of a gallon.
A quart of oil will cost \ of 12 cents, or cents.
43. When tarts cost 20 cents a dozen, how much will
3 tarts cost at the same rate ?
44. When molasses costs 14 cents a quart, how much
will a pint of molasses cost ?
48
FBOGRESSIVE ARITHMETIC
MEASURING WEIGHT
48. 1. What are these children doing? For what are
i\;lli
to the smallest weight.
the weights used?
It is called an
ounce weight, for it
weighs one ounce.
2. Point to the
largest weight.
It weighs as much
as sixteen of the
ounce weights, or one
pound, and is called
a pound weight.
3. How many ounces are there in a pound
Sixteen ounces equal one pound.
16oz. = llb.
4. The weight that just balances the box is half a pound.
How many ounces does the box weigh ?
5. If George puts the quarter pound weight on the
scales with the half pound weight, what part of a pound
of sand will he have to pour into the box to make the
scales balance again ? how many ounces of sand ?
How many ounces do box and sand together weigh ?
6. What part of a pound are 8 ounces ? 4 ounces ?
7. 1 pound less 9 ounces = ? 9. 14 oz. less J lb. = ?
8. 7 ounces and \ pound = ? lo. f lb. plus 3 oz. = ?
' FIRST BOOK 49
PERIMETER AND AREA
44. 1. Draw an oblong 5 inches long and 2 inches wide.
How many inches is it around the oblong ?
2. This distance is called the perimeter of the oblong.
3. Cut out of paper an oblong 6 in. long and 3 in. wide,
or '' 6 in. by 3 in." Find its perimeter.
4. Find the perimeter of an oblong 5 in. by 4 in.
5. What is the perimeter of a triangle whose sides are
each 4 in. long? 5 in. long?
45. 1. ' Measure the sides of this square. How long is
it ? How wide is it ?
2. A square whose sides are each 1 inch
long is called a square inch.
3. Take a piece of paper 2 in. by 1 in.
and fold it into square inches. How many
square inches of paper are there ?
One
Square Inch
1 sq. in.
4. Cut three strips of paper each 3 in. by 1 in. How
many square inches does each contain ?
5. Arrange two of the strips to form an oblong 2 in.
wide. How long is the oblong ?
How many square inches does it contain ?
2 X 3 sq. in. are sq. in.
6. Use the three strips to make a square.
How long is the square ? How wide is it ?
How many square inches does it contain ?
3 X 3 sq. in. are sq. in.
A square 3 in. by 3 in. is called a 3-inch square.
FIRST PROO. AR. — 4
60
PROGRESSIVE ARITHMETIC
7. This picture represents an oblong
5 in. by 3 in. divided into square inches.
How many square inches are there in
1 row? in 2 rows? in 3 rows?
How many square inches does the oblong contain?
3 X 5 sq. in. are sq. in.
8. Draw an oblong 4 in. by 2 in. Find its area.
In one ro.w of square inches there are 4 sq. in.
In two rows there are 2 x 4 sq. in., or sq. in.
9. This is called the area of the oblong.
10. A square whose sides are each one foot long is called
a square foot ; a square whose sides are each one yard long
is called a square yard.
11. How long and how wide is a 5-inch square? a
3-foot square ? a 10-yard square ?
12. How many square feet are there in a 3-foot square ?
in a yard square ?
13. How many square feet are there in a square yard?
Nine square feet equal one square yard.
9 sq. ft. = 1 sq. yd.
46. Find the perimeter and area of :
1. A 4-inch square.
2. A 5-foot square.
3. An oblong 4 in. by 3 in.
4. A card 7 in. by 5 in.
6. A rug 3 yd. square.
7. A table top 4 ft. square.
8. A floor 5 yd. by 4 yd.
9. A desk top 3 ft. by 5 ft.
5. A blotter 8 in. by 4 in. lo. An envelope 6 in. by 3 in.
FIRST BOOK
61
MEASURING TIME
47. 1. Read the letters on the clock face. Tell what
they mean.
2. Observe the little spaces marked
on the rim just outside of the letters.
These are minute spaces,
3. Count the number of minute
spaces between XII and I; I and II;
X and XL
How many minute spaces does the minute hand pass
over in moving from XII around to XII again ?
4. What time is it when both hands point toward XII ?
Where will the hands be pointing one hour later?
How many minute spaces will the minute hand move
over during that time ?
5. How many minutes are there in an hour?
^
Sixty minutes equal one hour.
60 min. = 1 hr.
6. How many minutes are there in half an hour ? in a
quarter of an hour? in three quarters of an hour?
7. Draw a clock face to show a quarter past four
o'clock; a quarter to b\ 20 mm. past 7; 25 min. to 8.
When the time is more than half past an hour, we may
tell it by giving the number of minutes to the next hour.
8. What time is it when the minute hand is at III, and
the hour hand is a Uttle past X? when the min-
ute hand is at VIII and the hour hand nearer VI than V ?
PROGRESSIVE ARITHMETIC
9. For ''20 minutes past 1^' we often say ^'one twenty,^*
and write 1:20; for ''20 minutes to 2/' ''one forty, '^ and
write 1 : 40.
10. Read in two ways: 11:20; 2:50; 3:15; 10:35;
4:05; 6:10; 8:40; 2:45.
11. What time is it when the minute hand points to I,
and the hour hand is near VI? when the minute hand
points to X, and the hour hand is near XII?
12. Where do the hands of a clock point when it is 25
min. past 4? a quarter to 12? ten fifty? six thirty?
Wten? 5:50? 7:10? 3:48? 6:05? 1:55?
48. 1. Count on the clock face the number of hours
from 9 o'clock to 9 o'clock again.
2. At what time in the morning does school begin?
To what number does the hour hand point at that time?
3. WTiat time of day will it be the next time the hour
hand points toward IX? How many hours will that be
from the time school began in the morning ?
4. How many hours will it be from 9 o'clock at night
until school begins the next morning?
5. How many hours is it from school time one morning
until school time the next morning? how many days?
6. How many hours are there in a day ?
Twenty-four hours equal one day.
24 hr. = 1 da.
This means both the day time and the night time.
FIRST BOOK
53
7. For telling time the day is divided into two parts.
The time from midnight to noon is called forenoon^ and
the time from noon to midnight is called afternoon.
We write a.m. for forenoon and p.m. for afternoon.
Thus, " ten minutes after 9 in the morning " is written 9 : 10 a.m.,
and " ten minutes after 9 in the evening " is written 9 : 10 p.m.
8. If you start for school at 8:20 a.m. and arrive at
8:50a.m., how long are you on the way?
9. How long a time is it from 11 : 25 a.m. to noon?
10. How many hours is it from 9 a.m. to 4 p.m. ?
49. 1. What day of the week is this? Name all the
days of the week. How many are there ?
Seven days equal one week.
7 da. = 1 wk.
1907 DECEMBER 1907
2. Find on this calendar
the short ways of writing the
names of the days.
3. How many days are
there in December? how
many weeks and how many
days over?
4. December is the last
month in the year. January is the first month in the year.
Can you name all the months ? How many are there ?
The names of the months are often written in this way : Jan.,
Feb., Mar., Apr., May, June, July, Aug., Sept., Oct., Nov., Dec.
Sun.
Mon.
Tne.
Wed
Thu.
Frl.
Sat.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
64 PROGRESSIVE ARITHMETIC
5. On what day of December does Christmas come ?
The date of Christmas Day, 1907, is written,
Wednesday, Dec. 25, 1907.
6. Write the date for New Year's Day in 1908; the
date of to-day ; of to-morrow ; of a week from to-day.
7. Write the date of your next birthday; of the next
holiday ; of other holidays.
8. If you leave home at 7 : 40 p.m. on Friday and are
gone 20 hours, at what time do you return?
WRITTEN EXERCISES
60. Here are two problems about an oblong 4 inches by
2 inches.
1. What is the area of an oblong
4 in. by 2 in.?
Area = 2x4 sq. in. = 8 sq. in.
2. What is the perimeier of an oblong 4 in. by 2 in. ?
Perimeter = 4 in. + 2 in. -h 4 in. -h 2 in. = — in. = — ft.
Make and solve as many problems as you can about :
3. A window 5 ft. by 3 ft., with panes 1 foot square.
4. A room the floor of which is 6 yd. by 5 yd.
5. A week less 2 days (Saturday and Sunday).
6. The number of days in 4 weeks.
7. An hour less 20 minutes.
8. Two books, one weighing 12 oz., the other 24 oz.
9. The number of days in December after Dec. 11.
10. The number of hours from 8 p.m. to 7 a.m.
FIRST BOOK 55
READING AND WRITING NUMBERS
51. 1. Count by ones from 1 to 10, thus: "1 one,
2 ones," etc. Write each number as you name it.
2. What is the largest number of ones that can be
written with one figure? How many figures are needed to
write ten ones?
3. 10 means either ten owes or 1 -axr ^^^^^^^^>b^ I
ten (and ones). In what place, ^^^ ten ones
counting from the right, does 1 stand when it means 1 tenf-^
Show this with other numbers than 10, as 11, 12, etc. p
4. Calling 10 "1 ten," count by tens from 10 to 100. ^
Write each number as you name it.
5. What is the largest number of tens written with two
figures? How many figures are needed to write ten tens? '
6. 100 means either ten tens or 1 hundred (and tens
and ones). In what place, counting from the right, does
1 stand when it means 1 hundred f
7. What does 1 mean when it stands in ones' place ? in
tens' place? in hundreds' place? What does 2 mean in
ones' place? in tens' place? in hundreds' place?
8. Write in figures :
3 ones. Four hundred. Seven hundred.
3 tens. Five hundred. Eight hundred.
3 hundreds. Six hundred. Nine hundred.
9. Ten hundred, written 1000, is called one thousand.
)
66
PROGRESSIVE ARITHMETIC
10. Read: 10, 30, 60, 90, 100, 200, 500, 700, 900, 1000.
52. 1. The number that is 1 greater than 100 is 101,
read "one hundred one.'' The number that is 2 greater
than 100 is 102, read "one hundred two."
2. Count from 100 to 109, writing the numbers in a
column as you name them, with hundreds under hundreds,
tens under tens, and ones under ones.
3. 110 is read " one hundred ten." Name the numbers
from 110 to 119 and write them in a column by the side of
your first column of numbers.
4. Continue naming numbers until you reach 149, writ-
ing them in coliunns of ten numbers each.
2 hundreds 3 tens 5 ones
5. What number is shown in this picture? Write the
number and tell what each figure means.
6. Tell what each figure means in these numbers :
10 100 112 167 266 307 990
25 110 240 384 502 222 1000
7. In numbers that are written with three figures, the
first figure^ counting from right to leftj stands for ones, the
second figure for tens, and the third figure for hundreds.
FIRST BOOK 67
EXERCISES
53. 1. Read these numbers :
375 822 610 160 300 202
462 555 106 601 251 909
2. Write in figures, placing hundreds under hundreds,
tens under tens, and ones under ones :
Four hundred sixty-five. Nine hundred.
Two hundred forty-eight. Eight hundred one.
Six hundred sixty-one. One hundred twelve.
One hundred ninety-six. Six hundred thirty.
Three hundred forty-four. Ninety-nine.
Five hundred eighty-eight. Nine hundred nine.
One hundred seventy-two. Eight hundred five.
Three hundred forty-three. Eight hundred fifty.
Seven hundred seventy-six. One thousand.
3. 463 means hundreds tens and ones.
4. Tell in the same way what these numbers mean :
756, 242, 403, 250, 632, 190, 333, 444, 206.
5. What number is 1 less than 10? than 100? than
200? than 550? than 910? than 1000?
6. What number is 10 greater than 100? 10 less than
100? 10 less than 550? 20 greater than 760 ?
7. Name and write the numbers that are 100 greater
than the following ; also the numbers that are 100 less :
300, 325, 684, 522, 736, 109, 204, 900, 777.
8. What is the smallest 3-figure number? the largest?
68 PROGRESSIVE ARITHMETIC
ADDITION
54. Express each sum as tens or as tens and ones :
I. 9
5
6
7
8
8
8
1
5
4
3
2
3
4
2. 40
45
46
47
48
48
48
30
35
34
33
32
33
34
WRITTEN EXERCISES
1. Find the sum of 48 and 34.
48 How many ones are 4 ones and 8 ones?
g^ In 12 ones there are 1 ten and 2 ones.
— Write the 2 ones under the ones, and keep
^^ the 1 ten to add to the 3 tens and 4 tens.
How many tens are 1 ten and 3 tens and 4 tens?
Write the number of tens under the tens.
What, then, is the sum of 48 and 34 ?
Tell all you did to find the sum.
Add the following :
2. 57
3. 49
4.
46
5.
69
6.
36
15
14
37
26
64
7. 46
8. 32
9.
19
10.
29
11.
78
26
29
45
47
22
12. 65
13. 43
14.
47
15.
59
16.
36
17
38
47
39
24
FIRST BOOK 69
Add upward and test your answer by adding downward :
17. 33 18. 28 19. 65 20. 28 21. 17
24 41 4 10 2
33 22 25 44- 53
22. 44
23.
37
24.
29
25.
17
26.
14
16
4
15
65
24
23
42
21
3
47
27. 22
28.
16
29.
37
30.
24
31.
18
35
13
6
37
19
18
48
42
16
18
7
16
9
19
22
32. 18
33.
26
34.
37
35.
19
36.
18
27
8
18
17
18
19
38
9
29
18
28
19
28
29
18
WRITTEN £X£RCIS£S
55. 1. Ruth weighs 48 pounds and Edith 45 pounds.
How much do both weigh?
2. Isabel picked 17 poppies and 28 pinks. How many
flowers did she pick ?
3. If 26 days since the term began have been sunny
and 18 cloudy, how many days have passed ?
f^^.,£^ciysi\ telephone^ 34 times in May, 29 times in
iphone^
in July.
le, and 25 times in July. How many times did he tele-
lone in the three months ? , _. .
C.'-
60 PROGRESSIVE ARITHMETIC
5. John and Ira went nutting. John got 12 pounds of
nuts and Ira 18 pounds. How many pounds did both get ?
6. John had 37 wabiuts and 48 butternuts. Ira had
54 wabiuts -and 49 butternuts. How many walnuts had
both boys ? how many butternuts ?
7. The next time they went nutting they got 56 pounds
of wabiuts, 18 pounds of hickory nuts, and 25 pounds of
hazelnuts. How many pounds of nuts did they get in all ?
8. Into a dish of nuts they put 26 walnuts, 17
hazelnuts, 25 hickory nuts, and 8 butternuts. How many
nuts were there in the dish? •-:^r&-
9. How many yards is it around
this croquet ground?
10. What is the perimeter of an
oblong lot that is 36 yards long and
13 yards wide?
11. What is the perimeter of a 25-foot square?
12. Measure the length and width of your schoolroom
and find its perimeter.
13. It is 29 miles from Albion to Berne, and Canton is
i I I
18 miles farther on than Berne. How far is it from Albion
to Canton ?
14. If you ride on the train from Albion to Canton and
back again, how many miles do you ride ?
n
n n n
rfi
n n n
n
T °
l4-YAr\0&
FIRST BOOK
61
.Add and test:
15.
16.
17.
18.
19.
16 weeks
24 dayi
3
18
min.
27 1b.
18 oz.
13 "
19
((
17
i{
7 " ■
16 "
7 "
8
II
16
i<
28 "
9 "
18 "
10
II
27
«
12 "
14 "
26 "
19
11
46
((
9 "
15 "
20.
21.
22.
23.
24.
25.
$15
$18
$16
$17
$19
$18
7
4
39
7
19
18
8
7
9
18
9
19
9
28
6
8
19
9
14
9
8
29
9
8
17
16
7
9
19
9
26. Mrs. Chase went to do her Christmas shopping.
She spent $14 for books, $28 for other useful articles, $5
for toys, $1 for a Christmas tree, and $2 for decorations.
How much did she spend?
27. This is a picture of Ella's garden.
How many feet is it around the garden ?
28. My bookcase contains 18 books on
the top shelf; 16 on the next; and 21, 15,
14, 12, in order to the bottom. How
many books are there in the bookcase?
29. A milkman had five cans of milk on his wagon, con-
taining 24 qt., 16 qt., 20 qt., 17 qt., and 19 qt., respectively.
How many quarts of milk were there in the five cans?
62 PROGRESSIVE ARITHMETIC
66. 1. Express as hundreds: 50 + 50; 40 + 60; 70 + 30.
2. Express as hundreds and tens: 70 + 40; 70+50;
70 + 80.
3. How many hundreds are 5 hundreds + 2 hundreds ?
500 + 200 and 50 + 50? 500 + 200 and 40 + 60?
4. Add 500 + 70 and 200 + 30 ; or add 570 and 230.
5. Add: 550 540 570 570 570 570
250 260 230 240 250 280
WRITTEN EXERCISES
1. Find the sum of 574 and 289.
574 Add the ones. What is their sum?
289 13 = 1 ten + 3 ones. Write only the 3 ones.
Z7Z Add the tens, beginning with the 1 ten not
yet written. 1 ten + 8 tens + 7 tens = .
16 tens = 1 hundred + 6 tens. Write only the 6 tens.
Add the himdreds, beginning with the 1 hundred not yet
written. 1 hundred + 2 hundreds + 5 himdreds = .
Read the sum. Tell all you did to obtain it.
Add the following :
2. 435 3. 243 4. 625 5. 367 6. 573
128 581 299 484 369
7. 508
294
8. 627
275
9. 486
314
10. 548
252
11. 281
719
12. 324
249
13. 518
173
14. 489
256
15. 269
347
16. 587
166
FIRST
' BOOK
63
Add and test
:
17. 127
18.
489
19.
287
20.
777
21.
685
366
98
269
77
99
208
366
97
7
129
22. 364
23.
188.
24.
406
25.
265
26.
388
247
243
308
93
277
87
562
16
64
66
196
38
94
256
222
27. 376
28.
492
29.
209
30.
199
31.
178
89
39
89
99
279
235
48
38
88
177
144
253
419
457
276
32. 124
33.
218
34.
156
35.
139
36.
499
60
43
185
68
98
208
75
96
29
77
43
302
278
387
89
112
391
149
179
237
37. 288
38.
162
39.
296
40.
239
41.
199
23
83
69
99
88
37
29
86
78
98
40
37
178
68
89
92
62
99
49
67
101
289
167
379
459
N
\-
PROGRESSIVE ARITHMETIC
MAKING CHANGE
Bill of Fare
Oysters
Ham Sandwich
Sdwicli V r 'g"t< goiis, each .
Chicken Sandwich 10
Eggs, each ... 5
g^ggrftoas t . . 'f^ offee^ith Cream
'^ta1
jtatDea. . .
^» I Hanlv^Eg^^
Ci^ beefsteak .
. 6
.20
Pork Chops .
Laml9 Chops
.16
,16
20
67. For the exercises below, each pupil who orders a
lunch should have a half
ULSTER LUNCH dollar and two quarter
dollars, or something to
represent these coins.
The teacher appoints
a waiter and a cashier.
The cashier has red
slips of paper marked 1
for 1-cent coins, white
slips marked 5 for 5-
cent coins, and blue
slips marked 10 for
dimes.
Z3>
Baked Beans . .16
Coffee .... 6
Tea . .
Chocolate
26 Tjffi . r . . ..^
Pie or Cake .
Ice Cream .
. 6
.10
EXERCISES
1. This is Edith's order: "Beefsteak, 2 rolls, coffee/'
The waiter announces the cost, " 34 cents. " Is he right?
- Edith gives the cashier 50 cents.
_j^ / The cashier says "J4 cents"; then gives Edith 1 cent,
I and says " 35 " ; then 5 cents, and says " 40 " ; then a
\dime, and says "50."
^ Has Edith received the right change?
In the following exercises the cashier should count out change as
he did in exercise 1. If the waiter or the cashier makes an error,
hfe should be discharged and another employed in his place.
2. Alfred orders 2 ham sandwiches; he pays with 25^.
3. Roy orders coffee with cream; he pays with 25^.
FIRST BOOK 65
Order other lunches. Here are some specimen orders,
each with the amount given to the cashier in payment:
4. Egg on toast; 25^. 9. Egg on toast, tea; 25^.
5. Ham and eggs; 50^. lo. Oysters, tea, pie; 50^.
6. Beefsteak, pie; 50^. ii. Ice cream, cake; 50^.
7. Chicken sandwich; 25^. 12. Oysters, beans; 50^.
8. Chocolate, 3 rolls; 25^. 13. Pork chops, 1 roll; 25^.
14. Ham sandwich, milk; 25^.
15. Milk, 3 rolls; 25^.
16. Egg sandwich, coffee with cream; 25^.
17. Milk, pie, ice cream; 25^.
18. Beefsteak, potatoes, milk; 50^.
19. Ham and eggs, 3 rolls, coffee with cream; 50^.
20. Oysters, 2 rolls, chocolate; 50^.
21. Beefsteak, egg on toast; 50^.
22. Beans, pork chops, fried potatoes, 1 roll; 50^.
23. Lamb chops, 3 rolls, chocolate, apple pie; 50^.
24. Egg on toast, beefsteak, oysters; 75^.
25. Oysters, beefsteak, coffee with cream, cake; 75^.
26. Pork chops, potatoes, beans, ice cream; $1.
27. Baked beans, 3 rolls, coffee with cream; 50^.
28. Beefsteak, egg on toast, potatoes, coffee with cream,
cranberry pie, cake, ice cream; $1.
29. For 4 boys: 8 eggs, 8 rolls, 4 glasses of milk; 75^.
30. For 2 persons: 6 rolls, 2 eggs, 2 beefsteaks, 1 cup
of coffee with cream, 1 glass of milk ; $ 1 .
FIRST PKOO. AR. — 5
c
r 66
1 ./'
PROGRESSIVE MUTHMETIC
SUBTRACTION
68. Subtract: 8 tens 80 15
2 tens 20 7
^^0 + 15 = 95.
\20+ 7 = 27;
WRITTEN EXERCISES
1. From 95 subtract 27.
Can you subtract 7 ones from 5 ones ?
95 Then take 1 ten from the 9 tens to unite
?i with the 5 ones.
"^ How many ones are 1 ten and 5 ones ?
Now subtract 7 ones from 15 ones. How many ones are
left ? Write the difference imder the ones.
How many tens have you already taken from the 9 tens ?
How many tens are left ?
Then subtract the 2 tens from 8 tens. How many tens
are left ? Write the difference under the tens.
What, then, is the difference between 95 and 27 ?
Tell all you did to find the difference.
Subtract, and test each result as on page 28 :
2.
47
3. 70
4. 92
5. 43
6. 33
28
33
79
26
15
7.
61
8. 64
9. 56
10. 82
11. 58
43
48
17
37
29
12.
25
13. 98
14. 60
15. 55
16. 83
19
79
26
36
48
67
17. 76 18. 83 19. 21 20. 86 zi. 96^1 ^^
FIRST
BOOK
Subtract and test :
. 76
18. 83
19.
21
20.
86
38
68
16
48
, 62
23. 67
24.
82
25.
71
48
49
37
H
78
28. 56
29.
93
30.
41
69
38
66
19
54
33. 45
34.
74
35.
80
15
28
35
17
96^ "
28
22. 62 23. 67 24. 82 25. 71 26. 54 '^ (f
27. 78 28. 56 29. 93 30. 41 31. 61 j; 'h
46 ^.
1/
WRITTEN EXERCISES
32. 54 33. 45 34. 74 35. 80 36. 72 4 'I
^ c
59. 1. Eliza has 50^. If she were to spend 35^ for a ^ 5
doll, how much money would she have left? - j J
2. If instead of the doll she were to buy a set of dishes ^^ S
costing 32^, how much money would she have left? j 1
3. Suppose she gave 28^ to John to buy a knife worth ^
half a dollar. How much more money would he need ? ^ J;
4. How much more than 28^ would he need to buy a ; ;
knife worth 75^? 60^? 40iz^? ^- f
5. Roy can jump 50 inches and Clarence 38 inches. ^^ ^
How much farther can Roy jump than Clarence ? *% ]-:
6. How many days are there in December ? How many ^ 1
days of December are left after Dec. 15? ^"^
7. How many minutes is it from 9 :15 a.m. to\0 a.m.?) '(J;
8. Lucy has 90 picture post cards, and Sarah has 75.
How many more has Lucy than Sarah ?
68 PROGRESSIVE ARITHMETIC
9. Cut a foot of string from a piece 30 inches long.
How many inches of string are left ?
10. When Frank went to visit his uncle, he had to ride
40 niiles in an automobile. When he had ridden 25 miles,
how far had he yet to ride ?
11. How far had Frank ridden when he had only 12
miles farther to ride ?
12. George can throw a ball 36 yards, and Paul can
throw it 60 yards. How much farther can Paul throw tbe
ball than George ?
Subtract and test :
13. 14.
15.
16.
17.
18.
$53 $40
$27 $18
$81
$14
$96
$77
$37
$19
$86
$68
19. 20.
21.
22.
23.
24.
55^ 42^
28^ 25^
50^
62^
m
36^
17/
98/
69/
25. Henry bought 90 eggs for hatching, but 18 of them
failed to hatch. How many chickens did he get from the
whole number of eggs ?
26. Fifteen of the chickens died before three months.
How many chickens were left at the end of the three
months?
27. Of the chickens that were left, all except 18 were
sold. How many were sold?
FIRST BOOK 69
28. Speckle ate 52 grains of com and Fluffy ate 36.
How many more grains did Speckle eat than Fluffy ?
29. Fluffy laid 54 eggs while Speckle laid 49. How
many more eggs did Fluffy lay than Speckle ?
60.
Subtract :
1.
5 hundreds
500
800
460 150 180
G-
2 hundreds
200
600
300 70 90
r
2.
700
140
9
700 + 140 + 9 = 849
+'
>
300
80
5
300+ 80 + 5 = 385
3.
800
110
8
800 + 110 + 8 = 918
^
500
40
2
500+ 40 + 2 = 542
WRITTEN EXERCISES
Subtract and test :
1. 849 2. 918 3. 239 4. 556 5. 827
385 542 72 283 562
6. 580 7. 636 8. 453 9. 145 lo. 769
257 84 428 75 288
12. 865 13. 648 14. 452 is. 860
507 70 239 528
11.
646
339
16.
888
79
17. 918 18. 243 19. 487 20. 365
640 91 395 84
70
PROGRESSIVE ARITHMETIC
61. Subtract
:
1. 600
400
150
70
13
5
600 + 150 + 13 = 763
400+ 70+ 5 = 475
2. 800
200
120
50
14
6
800 + 120 + 14 = 934
200+ 50+ 6 = 256
WRITTEN EXERCISES
1. From 934 subtract 256.
® ^^ " Can you subtract 6 ones from 4 ones?
9 3 4
2 r /> Then take 1 ten from 3 tens to unite
with the 4 ones. To how many ones is 1
ten equal? 1 ten and 4 ones?
How many ones, then, are 14 ones — 6 ones?
Write 8 under the ones.
How many tens have you already taken from the 3 tens ?
How many tens are left?
Can you subtract 5 tens from 2 tens ?
Then take 1 hundred from the 9 hundreds to unite with
the 2 tens. To how many tens is 1 hundred equal? 10
tens and 2 tens ?
How many tens are 12 tens — 5 tens?
Write 7 under the tens.
How many hundreds have you taken from the 9 hun-
dreds? How many hundreds are left?
How many hundreds are 8 hundreds — 2 himdreds?
Write 6 under the hundreds.
You have subtracted 256 from 934.
Read the difference. Tell all you did to find it.
FIRST BOOK
71
Subtract and test :
2. 432 3. 578 4. 342
5. 861
6. 426
154 299 85
476
348
7-. 564 8. 777 9. 838 lo. 675 ii. 381
365 88 549 96 193
12. 234 13. 586 14. 344 is. 735 16. 626
75 297 69 486 27
400 + 90 + 14 = 504
200 + 20+ 6=226
600 + 90 + 12 = 702
500 + 30+ 8 = 538
62. Subtract:
1. 400
90
14
200
20
6
2. 600
90
12
500
30
8
wrii;ten exercises
1. From 702 subtract 538.
t ^ ^^ Can you subtract 8 ones from 2 ones?
7 2
Can you take 1 ten from tens?
^A^ Then take 1 hundred from the 7
^ ^ ^ hundreds, change it to 10 tens, and
take 1 of these tens to unite with the 2 units; that is,
change 7 hundreds tens and 2 units to 6 hundreds 9 tens
and 12 units, and subtract.
72 PUOGRESSIVE ARITHMETIC
Subtract and test :
2. 307
169
3. 806
248
4.
400
91
a. 504
346
6.
902
705
7. 701
426
8. 208
79
9.
803
466
10. 105
47
11.
600
579
12. 900
101
13. 707
278
14.
306
99
15. 505
268
16.
807
629
WRITTEN EXERCISES
63. Subtract and test :
1. 758 2. 596 3. 465 4. 581 a. 600
324 206 98 257 463
6.
947
7.
405
8.
708
9.
198
10.
314
684
83
640
79
128
11.
666
12.
700
13.
111
14.
876
15.
644
99
637
35
345
67
16.
406
17.
513
18.
263
19.
300
20.
765
•
348
45
249
31
208
21.
375
22.
808
23.
633
24.
263
25.
500
243
709
38
184
372
26.
740
27.
403
28.
987
29.
800
30.
585
309
272
832
508
396
FIRST BOOK
78
■
i;
MULTIPLICATION
64. 1. In this oblong, how many squares are there in
each horizontal row?
Count the squares by 4's.
2. How many squares are there in
each vertical row, or colimm?
Count the squares by 3's.
3. Compare 3 times 4 squares with 4 times 3 squares. '
4. In what two ways have you found the niraiber of \,
squares ? Compare three 4's with four 3's in this way :
Three 4's = four 3's, or 12. . )
3x4 = 4x3, or 12.
5. Count these dots by 5's. Count them by 3's.
Compare three 5's with five 3's, and write the result
as in exercise 4.
6. Using squares, or dots, or buttons, etc., com-
pare three 2's with two 3's as in exercise 4.
7.' Add three 6's. Add six 3's. Compare the sums, and
write the result as above. Also compare three 7's with
seven 3's.
8.
Copy and complete as in the first column :
2x 6=6x2=
2x 7=7x2=
2x 8 = =
2x 9= =
2x10 = =
3x 6 =
3x 7 =
3x 8 =
3x 9 =
3x10 =
4x 6 =
4x 7 =
4x 8 =
4x 9 =
4x10 =
5x 6 =
5x 7 =
5x 8 =
5x 9 =
5x10 =
74 PROGRESSIVE ARITHMETIC
BXBRCISES
V 65. 1. Give the table of 2's, from 1 x 2 to 10 x 2.
2. In the same way give the tables of 3's, 4's, and 5's.
3. Besides these you have learned the 6's to 5 x 6, the
7'8 to 5 X 7, the 8's to 5x8, the 9's to 5 x 9, and the lO's
to <5 X 10. Give these tables as far as you can.
4. Tell quickly the value of each of the following :
5x3 3x7 2x7 9x4 4x10 5x6
4x7 4x6 4x5 2x6 4x 8 2x9
6x4 3x6 2x8 7x3 4x 9 9x5
WRITTEN EXERCISES
66. 1. How many are four 32's, or 4 times 32?
22 The sum of four 32's is 128.
^2 Four 32's may be added also in
^2 this way :
r.^ Four 2's are 8, the number of
ones; four 3's are 12, the number of
128, sum ^^ . j2 tens H- 8 ones = 120 + 8 = 128.
Here is a shorter process for finding 4 times 32.
Write 4 under the last figure of 32.
32
. 4 times 2 ones = 8 ones.
4
"TT J . 4 times 3 tens =12 tens.
128, product
12 tens + 8 ones = 120 + 8 = 128.
You have multiplied 32 by 4.
The answer, 128, is the product of 32 and 4.
FIRST BOOK 75
Here are two short ways of writing 32 + 32 + 32 + 32 :
First loay. 4 x 32, read " 4 times 32."
Second way. 32 x 4, read ^' 32 multiplied by 4."
This shows that x is read " times " when it is before the
number to be multiplied, and ^'multiplied by" when it
follows the number to be multipUed.
32
. means " multiply 32 by 4 "; or, " find 4 times 32."
2. Find the value of 23 + 23 + 23 by addition and then
by multiplication.
3. Find in two ways the value of 41+41+41+41+41.
Which is the shorter way ?
Find results and compare them :
4.
5.
12
62
6.
24
24
+ 12
12
+ 62
62
+ 24
x2
+ 12
x3
+ 62
x3
7.
8.
9.
10.
11.
Multiply
By
14
2
31
2
92
2
21
3
40
3
12.
13.
14.
15.
16.
Multiply
By
53
3
82
3
91
2
80
2
71
3 -
76
PROGRESSIVE ARITHMETIC
17.
18.
19.
20.
21.
Multiply
40
22
31
50
81
By
4
4
4
5
5
22. Multiply 47 by 5.
47 5 times 7 = 35, or 3 tens and 5 ones.
5 Write 5 in the product, under the ones,
235 and keep the 3 tens to add to 5 times 4 tens.
5 times 4 tens = 20 tens, and 20 tens 4- 3 tens = 23 tens.
Write 23 in the product, before 5.
The product is 23 tens and 5 ones, or 235.
Tell all you did to find the product.
Multiply, testing each result by addition :
23. 48 24.
54
2S. 66
26.
75
27. 95
2
3
3
3
2
28. 86 29.
37
30. 63
31.
26
32. 44
2
3
4
4
4
33. 53 34.
24
3s. 92
36.
64
37. 16
5
5
5
5
4
Multiply :
38. 22 by 5
42. 53 by 5
46.
76 by 5
39. 29 by 2
43. 99 by 2
47.
86 by 3
40. 77 by 4
44. 49 by 3
48.
99 by 4
41. 36 by 3
45. 88 by 4
49.
78 by 4
FIRST BOOK 77
50. Find the product of 75 and 4 ; of 3 and 66.
Suggestion. — Multiply the larger number by the smaller.
Find the product of :
SI.
48 and 2
57.
2 and 65
63.
85 and 4
92.
61 and 5
58.
5 and 52
64.
5 and 38
53.
38 and 3
59.
3 and 97
65.
95 and 5
54.
82 and 5
60.
4 and 85
661
2 and 89
55.
89 and 4
61.
4 and 57
67.
87 and 4
56.
96 and 3
62.
2 and 99
68.
5 and 99
WRITTEN EXERCISES
67. 1. How much will 2 quarts of ice cream cost at
35 cents a quart ?
or J
cy 2 quarts of ice cream will cost 2 times 35^,
w """■
2. How much money does a boy need to buy 4 collars
at 15 cents each ?
Find the cost of the following :
3. 2 quarts of oysters at 45 cents a quart.
4. 5 pineapples at 15 cents each.
5. 2 boxes of honey at 14 cents a box.
6. 5 bmiches of celery at 16 cents a bunch.
7. 3 pounds of nuts at 18 cents a pomid.
8. 4 gallons of sirup at 33 cents a gallon.
9. 5 pounds of figs at 18 cents a pound.
78 PROGRESSIVE ARITHMETIC
10. How many inches are there in 4 feet ?
11. Charles planted 5 rows of tulip bulbs, 56 in each row.
How many tulip bulbs did he plant ?
12. How many ounces are there in 2 pounds ?
13. Mary's bed of pansies is 18 feet long and 4 feet wide.
What is the area of the bed ?
Multiply
14-
15.
16.
17.
18.
$25
12 pens
36 stars
24 trees
39 ft.
5
4
3
4
5
19.
20.
21.
22.
23.
$75
22 days
54 boys
88 books
981b.
3
5
4
5
4
24. How many minutes are there in 5 hours ?
25. Twenty things equal a score. Mabel's grandfather
is fourscore years old. How many years old is he ?
26. John's cousins number twoscore. How many cousins
has he ?
27. How many hours are there in 3 days ?
28. A square garden 95 feet on each side is inclosed by
a fence. How long is the fence ?
29. How many tomato plants are there in 4 rows, if there
are 13 in each row ?
30. Find the number of cabbages in 3 rows, if there are
38 cabbages in each row.
31. Find the area of a turnip bed 87 feet by 5 feet.
FIKST BOOK
79
DIVISION
68. 1. Four 3's are
Three 4's are
What
is the product of 4 and 3 ?
2.. How many times does the product of 4 and 3 contain
3? How many times does the same product contain 4?
4x3=? 12-i-3=? 12-5-4=?
3. Count these squares by 2's ; by 4's.
How many times does the product of 4
and 2 contain 2 ? How many times does
it contain 4 ?
4x2=?
8-5-2=?
8-5-4=?
4. How many times does 5x3 contain 3 ? How many
times does 5x3 contain 5 ? How do you know ? ^
5. How many times does 8x2 contain 2 ? How many
times does 8x2 contain 8? How do you know?
EXERCISES
69. Answer quickly :
1.
6x2 =
12-!-2 =
12-!- 6 =
9.
27-!- 3 =
2.
7x2 =
14-h2 =
14-!- 7 =
10.
27-!- 9 =
3.
8x2 =
16-!-2 =
16-i- 8 =
11.
30-!- 3 =
4.
9x2 =
18 + 2 =
18-!- 9 =
12.
30-!- 10 =
5.
10x2 =
20-!-2 =
20 -J- 10 =
13.
24-!- 4 =
6.
6x3 =
18-^3 =
18-!- 6 =
14.
24-!- 6 =
7.
7x3 =
21-!-3 =
21-!- 7 =
IS.
28-!- 4 =
8.
8x3 =
24-i-3 =
24-!- 8 =
16.
28-!- 7 =
80 PROGRESSIVE ARITHMETIC
Answer quickly :
17. 32-8-8= 20. 50-s-10= 23. 35-!-7 =
18. 36-s-9= 21. 30-i-10= 24. 45-8-9 =
19. 30-8-6= 22. 40-5-10= 25. 40-5-8 =
26. How many boxes of Christmas candles costing 6
cents a box can be bought for 24 cents ?
27. Riith has 32 lily bulbs to plant. If she plants 8 in
a row, how many rows will she have ?
28. A man wishes to plant 45 trees in 5 equal rows.
How many trees shall he plant in each row?
29. Last summer Louise spent 21 days at her uncle's.
How many weeks did she yisit him ?
30. A large milk can holds 32 quarts. How many gal-
lons does it hold ?
31. Clara's father gave her 50 cents in dimes. How
many dimes did he give her?
32. How many yards of ribbon costing 9 cents a yard
can be bought for 27 cents ?
70. 1. Find ^ of 8. Find how many times 8 contains
2. How do your answers compare ?
2. 8^2, read ''8 divided by 2," means either ''Find |
o/8/' or ''Fbid how many times 8 contains 2."
Another way to write 8 -»- 2 is 2)8.
3. 12 -s- 3, or 3)12, means either ''Find \ of 12,'' or
"Find how many times 12 contains 3."
What two meanings may 6-^2 have? 4}12? 5)10?
FIRST
BOOK
81
Give results quickly :
4. J of 6
6H-2
iof6
6 + 3
5. J of 15
3}15
^of20
5}20
6. 3]9
3)9 tens
3}90
3)90 + 3
7. 2}8
2)8 hundreds
2)800
2)800 + 60+4
WRITTEN EXERCISES
1. Find J of 64.
How many tens are J of 6 tens ?
2 )64 Write the number of tens imder the tens.
32 How many ones are ^ of 4 ones ?
Write the number of ones under the ones.
The answer is 3 tens and 2 ones, or 32.
Test. — 32 + 32, or 32 multiplied by 2, is equal to 64.
Find:
2. ^of42 3. ^of39 4. J of 88
6. How many times is 2 contained in 864?
2 is contained in 8 hundreds, 4 hun-
2 )864 dreds times.
432 Write 4 under the hundreds.
2 is contained in 6 tens, 3 tens times.
Write 3 under the tens.
2 is contained in 4, 2 times. Write 2 under the units.
You have divided 864 by 2, and found that 2 is contained
432 times in 864.
The result, 432, is called the quotient.
Test. — 432 multiplied by 2 gives 864, the number divided.
FIRST PROO. AR. — «
82 PROGRESSIVE ARITHMETIC
Copy, divide, and test the quotient by multiplication :
9. 10.
2)48
2)26
2)84
2)68
2)680
11.
12.
13.
14.
IS.
2)440
2)626
2)842
2)406
2)208
16.
17.
18.
19.
20.
2)804
2)202
3)69
3)36
3)66
21.
22.
23.
24.
25.
3)33
3)360
3)963
3)609
3)396
Find the value of each of the following :
26. ^ of 86 30. 44 + 4 34. 1 of 622
27. J of 63 31. 84-^-4 35. ^ of 366
28. J of 48 32. 55-J-5 36. J of 844
29. ^ of 99 33. 505-8-5 37. ^ of 550
WRITTEN EXERCISES
71. 1. If 63 pens are divided equally among 3 classes,
how many pens will each class receive ?
3 )63 pens Each class will receive ^ of 63 pens, or
21 pens 21 pens.
2. If 48 picture cards are divided equally between 2
children, how many will each receive ?
FIRST BOOK 83
3. Four boys made a bobsled. It cost them 84^, and
they shared the expense equally. How much did each
pay?
4. If 42 children choose sides for a game of prisoner's
base, how many children will there be on each side ?
5. A log 64 feet long was sawed into two parts of equal
length. How long was each part ?
6. Mr. Giles has 96 apricot trees growing in 3 rows,
each containing the same number of trees. How many
apricot trees are there in each row ?
7. If a caddie earns $2 a week, how many weeks will
it take him to earn $46?
The number of weeks it will take
^—- him is the same as the number of times
that $2 is contained in $46.
$2 is contained 23 times in $46.
Therefore it will take him 23 weeks to earn $46.
8. How many 2-cent stamps can be bought for 66^?
9. If 48 boys march ''four abreast," or in 4 columns,
how many boys will there be in each colunm ?
10. How many 5-cent stamps can be bought for 55/2^?
11. Tell how many quarts there are in 28 pints.
12. How many gallons are there in 40 quarts ?
13. Anna's mother made 39 glasses of jelly. One third
of it was quince jelly. How many glasses of quince jelly
had she?
14. How many yards wide is a road that is 66 feet wide ?
PART II
READING AND WRITING NUMBERS
72. 1. Count by ones, or units, to 10; by tens to 100;
by hundreds to 1000; by thousands to 10,000 (10 thousand).
2. How many units are there in 1 ten? tens in 100?
hundreds in 1000? thousands in 10,000?
3. Read: 100 400 700 500 . 900 1000
What is the largest number of hundreds that can be
written with three figures?
In what place, counting from the right, does 1 stand
when it means 1 thousand?
4. Read: 2000 5000 7000 9000 10,000
What is the largest number of thousands that can be
written with four figures?
5. Read: 1000 1100 1110 1111
What does 1 mean when it stands in thousands' place ?
in hundreds' place ? in tens' place ? in units' place ?
6. Read: 3000 3300 3330 3333
What does 3 mean when it stands in thousands' place?
in hundreds' place ? in tens' place ? in units' place ?
7. Tell what each figure means in these numbers :
40 126 2742 7420 3009
65 304 6037 4600 2704
32 790 3491 8000 9085
84
FIRST BOOK 85
8. In four-figure numbers, the^rs^, counting from right
to left, stands for units ; the second, for tens ; the third, for
hundreds; and the fourth, for thousands.
73. 1. The number that is 1 greater than 1000 is 1001,
read " one thousand one.''
2. Count from 1000 to 1009 and write the numbers in a
column as you name them, placing thousands under thou-
sands, hundreds under hundreds, etc.
3. One thousand ten is written 1010.
Name the numbers from 1010 to 1020 and write them
in a column as you did the other numbers.
4. Name and write in a column ten numbers in order,
beginning with 1095.
£X£RCIS£S
74. 1. Read:
5839 3246 2000 5007 3960
4444 5438 4100 9024 7500
3621 4187 8360 2050 6006
8295 7352 5942 6703 3080
Write in figures :
2. Four hundred twenty-four.
3. Eight thousand two hundred sixty-one.
4. Three thousand nine hundred seventy-six.
5. Five thousand seven hundred fifty-eight.
6. Nine thousand three hundred twenty-seven.
7. Four thousand eight hundred seventy-three.
86 PROGRESSIVE ARITHMETIC
8. Read:
1374
604
2400
869
6030
4209
7008
920
5555
8742
9. Write in figures, placing thousands under thousands,
hundreds under hundreds, etc. :
Ten thousand. Three thousand ten.
Two thousand nine. Eight thousand sixteen.
Five hundred forty. Six thousand fifty-two.
Six thousand sixty. Two thousand thirty-six.
Nine thousand one. One thousand eighty-six.
Four thousand two hundred one.
Six thousand one hundred ten.
Eight hundred seventy-three.
Two thousand five hundred six.
75. Sometimes in reading four-figure numbers the thou-
sands and hundreds are read together as hundreds; thus,
2460 may be read, '^ twenty-four hundred sixty."
BXBRCISBS
1. Read the following in. two ways :
6152 2066 1732 1898
1905
3720 1492 1620 1776
1864
2. Write in figures :
Nineteen hundred. Sixteen hundred seven.
Sixty hundred fifty. Fifty-six hundred sixty-one.
Fifteen hundred four. Eighteen hundred eighty-two.
8 5 6
7 9 5
nRST BOOK
87
ADDITION
'
BXEKCISBS
ts instantly :
9 5
8
7
9
8 7
4
6
9
2. 52
74
5
63
7
3
92
34
6
3
24
5
42
86
5
4
3. 5
43
9
74
57
78
3
6
75
7
32
6
4
2
49
67
4. Count by 2's from to 20; from 1 to 31.
5. Count by 3's from to 30 ; from 1 to 43 ; from 2 to 50.
6. Count by 4's from to 40 ; from 1 to 49 ; from 2 to
58; from 3 to 63.
7. Count by 5's from to 50; from 1 to 56; from 2 to
67 ; from 3 to 73 ; from 4 to 79.
8. Add rapidly and test results :
3
2
5
4
8
9
7
1
7
1
3
2
5
3
7
4
6
2
3
8
6
9
6
6
9
1
7
5
7
8
5
2
7
9
8
5
9
8
5
7
8
1
5
8
4
9
88 PROGRESSIVE ARITHMETIC
£X£RCIS£S
77. 1. How many snowballs did Elmer make if he had
7 in one pile, 8 in another, and 6 in another?
2. A farmer sold a calf for $9 and 3 sheep for $4 each.
How much did he receive for all ?
3. A lady bought 5 Christmas cards at 3^ each and paid
8^ for envelopes for them. How much did all cost?
4. Edith fed 4 nuts to each of 5 squirrels, and 8 to a
chipmunk. How many nuts did she use ?
5. There were 14 boys and 8 girls skating on the pond.
When 9 of the children went home, how many were left ?
6. One caddie carried 8 golf sticks, another carried 5,
and 3 others carried 3 each. How many did they all
carry?
EXERCISES
78. Add, giving answers at sight :
1. 64 20 48 13 30 56 24 40
10 52 40 70 17 10 30 23
2.
35
16
30
71
60
26
50
49
30
40
56
20
37
60
44
30
3.
21
42
36
44
23
61
11
22
23
41
32
44
23
12
33
22
4.
14
55
41
66
32
22
74
44
11
22
21
33
21
44
12
33
FIRST BOOK 89
WRITTEN EXERCISES
79. 1. Find the sum of 2495, 3983, and 1678.
In adding do not think, ''8 and 3 are 11
and 5 are 16, '' but add the units rapidly
Jg^g Uke this: ^'8,11, 16/'
^yr^ Write 6 under the units and add the 1
ten to the tens, thus: '' 1, 8, 16, 25/'
Write 5 under the tens and add 2 with the hundreds :
'^2, 8, 17, 21.''
Write 1 under the hundreds and add 2 with the thou-
sands: ''2, 3, 6, 8." Write 8 under the thousands.
Read the sum. Tell how you found it..
Add upward and test by adding downward :
2. 1234 3. 4375 4. 5209 5. 2481
5678 2986 1872 4667
1109 3467 2369 3986
6. 7999 7. 4567 8. 6472 9. 5316
1888 3879 2328 4684
10. 2384
11. 7621
12. 4636
13. 5426
1246
978
2534
2809
2968
1346
856
1765
14. 3427
15. 6286
16. 4578
17. 3888
1902
940
726
1222
2345
1122
1967
1777
1063
657
2648
2345
90 PROGRESSIVE ARITHMETIC
Add and test
:
18. 346
19.
999
20.
562
21.
727
22.
473
791
888
875
908
189
588
123
88
649
694
699
456
769
878
780
247
789
373
999
876
23. 98
24.
45
25.
71
26.
56
27.
99
75
9
36
92
88
46
76
28
6
47
87
88
42
80
76
49
7
97
8
85
66
37
86
87
78
28. 2368 + 74 + 318 + 4092
29. 3491 + 2350 + 1634 + 2396
30. 136 + 934 + 673 + 549 + 732
WRITTEN EXERCISES
80. 1. What was the value of a farmer's crop, if his
com was worth $325, oats $298, and potatoes $663?
Model Solution
$325, corn
298, oats
663, potatoes
$1286, value of crop
2. How many books are there in three bookcases, if one
contains 241 books, another 196, and the third 275 ?
FIRST BOOK 91
3. A milk dealer's sales for a day were 152 quarts from
one wagon, 136 from another, and 148 from another. How
many quarts of milk did he sell that day ?
4. A fire engine cost $4625 and a chemical wagon $2075.
How much did both cost ?
5. A school has 269 pupils in the primary department,
198 in the grammar department, and 152 in the high school.
How many pupils are there in the whole school?
6. If one of Mr. Fay's horses weighs 1473 pounds and
the other 1514 pounds, how much does the team weigh?
7. A fruit dealer bought four crates of oranges. There
were 150 oranges in one, 172 in another, 126 in the third,
and 128 in the fourth. How many oranges did he buy ?
8. A railway station is 186 feet long and 112 feet wide.
What is the distance around it ?
9. There are 31 days in March, 30 in April, 31 in May,
30 in June, 31 in July, and 31 in August. How many days
are there in these six months ?
10. A grocer's wagon carried a barrel of flour, 196 pounds,
and a barrel of potatoes, 180 pounds. The barrels weighed
36 pounds and the driver 155 pounds. What was the
weight of the load?
11. Mr. Hall bought a city lot for $1345 and built a
house on it for $6739. How much did the property cost?
12. In a political parade there were 234 men from the
tenth ward, 142 from the eleventh, 287 from the fourteenth,
and 358 from the sixteenth. How many men were there
from these four wards?
92 PROGRESSIVE ARITHMETIC
SUBTRACTION
EXERCISES
81. Subtract, giving results instantly :
1. 11 10 12 16 12 13 12 14
_2_7 4 8_5_8_9_8
2. 10 11 14 12 15 11 15 18
3. 30 44 16 13 90 52 11 64
58969438
4. 13
72
25
40
84
17
33
14
9
5
7
8
6
9
4
9
5. 36
53
74
81
47
23
62
93
8
7
9
7
8
9
7
6
6. Count backward by 2's from 20 to like this: "20,
18, 16, 14, 12, 10, 8, 6, 4, 2, 0/'
Count backward by 2's from 31 to 1.
7. Count backward by 3's from 30 to ; from 43 to 1 ;
from 50 to 2.
8. Count backward by 4's from 40 to 0; from 49 to 1;
from 58 to 2 ; from 63 to .3.
9. Count backward by 5's from 50 to ; from 56 to 1 ;
from 67 to 2; from 73 to 3; from 79 to 4.
FIRST BOOK 93
£X£RCIS£S
82. 1. Clyde has 16 jackstones and Ruth has 9. How
many more jackstones has Clyde than Ruth ?
2. I bought some sugar and gave the grocer 25^. If he
gave me 7^ in change, how much did the sugar cost?
3. If a man buys pens at 8 ^ a dozen and sells them for
1 ^ each, how much does he gain on a dozen ?
4. A boy had 18^. He bought some peanuts for 5^ and
some candy for 4^. How many cents had he left?
5. Oliver had 14 tin soldiers. He broke 5, and his mother
bought him 8 more. How many had he then ?
6. Eveline had two kinds of ribbon, 20 yd. in all. She
used all but 4 yd. of the white and 3 yd. of the red for
Christmas packages. How many yards did she use ?
£X£RCIS£S
83. Subtract, giving results at sight :
1. 61 28 41 85 92 67 59 62
30 10 30 50 20 50 20 40
2.
44
87
98
74
86
93
89
71
20
70
40
20
40
30
60
30
3.
26
35
68
29
59
47
89
95
24
31
64
22
53
42
84
92
4.
69
46
85
67
76
93
81
79
39
26
55
57
26
13
61
39
94 PROGRESSIVE ARITHMETIC
WRITTEN £XSRCISSS
84. 1. From 4573 subtract 1625.
4573 Subtract as follows: 5 from 13 leaves 8;
write 8 under the units.
2 from 6, 4; write 4 under the tens. 6
2948 fj.Qjjj i^^ g. y^iQ 9 under the hundreds.
1 from 3, 2; write 2 under the thousands.
Read the remainder. Tell how you found it.
Test. — Add 1626 and 2948. The result should be 4673.
Subtract and test :
2. 3561
3.
7326
4.
5438
5. 9627
1846
3542
4259
2068
6. 4319
7.
8094
8.
7843
9. 5406
2684
4568
5786
2159
10. From 1608 subtract 843.
Subtract : 3 from 8, 5 ; write 5 under the
1608 units. 4 from 10, 6; write 6 under the tens.
843 8 from 15, 7 ; write 7 under the himdreds.
765 Read the remainder.
Tell how you found it.
Subtract and test :
11. 1406 12. 1924 13. 1736 14. 1802
572 980 848 971
15. 1672 16. 1534 17. 1372 18. 1706
948 569 1098 1052
FIRST BOOK 95
19. From 7000 subtract 796.
6 9 910 Subtract: 6 from 10, 4; 9 from 9, 0; 7
7000
]l from 9, 2; nothing from 6, 6 — writing each
— — • figure of the result in its proper place.
o204 Read the remainder. Tell how you found it.
Subtract and test :
20. 4000 21. 1000 22. 6000 23. 8000
821 248 732 508
24. 5004 25. 7005 26. 2000 27. 3002
756 680 561 499
WRITTEN EXERCISES
85. Subtract and test :
1.
506
341
2.
4642
2925
3.
7050
4182
4.
5236
3841
5.
725
486
6.
8000
547
7.
1791
384
8.
1920
981
9.
304
125
10.
6208
1432
11.
4281
3462
12.
5007
2574
13.
981
587
14.
8796
4321
IS.
3642
2975
16.
9700
1811
17.
613
408
18.
2790
1882
19.
7849
2994
20.
5555
3678
96
PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
86. 1, Mr. Pond's salary is $864 a year and his ex-
penses are $ 598. How much money does he save each year ?
Model Solution
$864, salary
$598, expenses
$266, savings
2. The Eiffel Tower is 984 ft.
high and the Washington Monument
555 ft. high. How much higher is
the tower than the monument ?
3. From a box containing 360 lem-
ons a fruit dealer sold 156. How
many of the lemons were left?
4. A loaded wagon weighed 3678
lb., and the wagon alone weighed
12351b. How much did the load weigh ?
5. There are 75 eggs in a box. How many will be left
after 4 dozen of them are sold?
6. How much change should Mrs. Bell receive out of a
dollar, if she buys apples for 25 ^ and potatoes for 39 ^ ?
7. A man who had $5750 bought a house for $2425.
How much money had he left?
8. From 4 cases of canned tomatoes containing 24 cans
each, 49 cans were sold. How many were left ?
9. While coasting, Floyd's sled went 716 ft. and Roy's
674 ft. How much farther did Floyd's sled go than Roy's ?
FIRST BOOK 97
ROMAN NUMERALS
87. 1. You have learned that the Romans wrote num-
bers with lettei-s. These letters are called Roman numerals.
2. There are seven Roman numerals. Only three have
been used so far. Can you tell which they are ?
3. I stands for 1. V stands for 5. X stands for 10.
4. When the Romans wrote 2, they used two I's, II.
5. When they wrote 3, they used three I's, III.
6. 4 is 1 less than 5, or 1 hefore 5, so for 4 the Romans
wrote I hefore V, IV. Sometimes they wrote it, IIII.
7. 6 is 5 and 1, or 1 after 5, so for 6 they wrote I after
V in this way : VI.
8. 7 is 2 after 5. They wrote 7 this way: VII.
9. 8 is 3 after 5. They wrote 8 this way : VIII.
10. 9 is 1 before 10. This is the way they wrote 9 : IX.
11. What Roman numeral is on a 5-dollar bill? on a
If
lO-doUar bill? Where have you seen Roman numerals?
88. 1. 11 equals 10 and 1, or 1 after 10.
2. How do you think the Romans wrote 11 ? Read XI.
3. Using Roman numerals, write : 12; 13.
4. 14 equals 10 and 4. How did the Romans write 10 ?
4 ? How do you think they wrote 14 ?
5. Read: XIV; XII; XIII; XV; XVI; XVIII; XVII.
6. How did the Romans write 10 and 9, or 19 ? Read
XIX.
7. Write the first 19 numbers with Roman numerals.
FIB8T PBOO. AB. — 7
98 PROGRESSIVE ARITHMETIC
89. 1. How many lO's are there in 20? Plow many
X's are needed to write 20 ? Write 20 with letters.
2. Read: XXII; XXIV; XXV; XXVI; XXIX.
3. How many lO's are there in 30 ? Write 30 with letters.
4. Use letters to write all the numbers from 20 to 39.
90. 1. The Roman numeral that stands for 50 is L.
2. 40 is 10 before 50. What two letters are used to
write 40 ? Which one is written before the other ? Write 40.
3. Arrange the same letters so that they will stand for 60.
4. Read: XLI; LIV; XLVII; LV; LXV; LXIX.
5. Write with letters the numbers from 40 to 69.
91. 1. Write the letter that stands for 50, and just after
it write the letters that stand for 20.
2. How many are 50 and 20 ? Read LXX.
3. How many are 50 and 30 ? Read LXXX.
4. Use letters to write the numbers from 75 to 85.
5. Read: LXXII; LXXXVII; LXXIV; LXXXIX.
92. 1. The letter C stands for 100, D for 500, M for 1000.
2. 90 is 10 before 100. Read XC; XCII; XCIX.
3. Write the following, using Roman numerals :
53 88 73 38 56 91 79 500
92 46 66 81 24 34 97 1000
4. Read the following :
MC XLIII LXVI XCVII XXVIII
DCC XCVII XXXII LXXXI LXXXIX
FIRST BOOK
99
NUMBERS TO SEVENTY ^^;<^ '"-v-*^ "^
93. Counting by sixes. ^"^^ ^ ) ^^^^^^---^^-^^^ ?> h^
Here is a picture of some daffodils. The parts ofjesLcrr ^
flower extending outward from the center are sepa ls^
1. How many sepals has 1 daffodil?
How many have 2 daffodils ? 3 daffodils ?
4 daffodils?
2. Tulips, also, have 6 sepals. How
many sepals have 5 tulips? 6 tulips?
7 tulips? 8 tulips? 9 tulips? 10 tulips?
3. When asparagus is not cut off to eat,
it grows tall and bears red berries, each
containing 6 seeds.
How many seeds are there in 2 berries ?
in 3 berries ?
4. How many seeds are 4 times 6 seeds ? 5x6 seeds ?
6x6 seeds? 7x6 seeds? 8x6 seeds? 9x6 seeds?
10x6 seeds?
5. Count these squares by 6's
in columns.
How many squares are there?
Test your answer by counting
them by lO's in rows.
6. Count by 6's in this way:
" Once 6 is 6, two times 6 are 12, three times 6 are 18,''
and so on.
Continue to ten times 6.
1
2
3
4
5
6
12
18
1x6= 6
6 X 6 = 36
2 X 6 = 12
7 X 6 = 42
3 X 6 = 18
8 X 6 = 48
4 X 6 = 24
9x6 = 54
5 X 6 = 30
10 X 6 = 60
100 PROGRESSIVE ARITHMETIC
7. Memorize this table of sixes :
8. The numbers 6, 12, 18,
etc., are called multiples of
6, because each is produced
by multiplying 6 by some
number.
Write the first ten multi-
ples of 6 in a row.
9. Draw an oblong 10 inches by 6 inches and divide it
into inch squares. Counting the squares by 6's, write the
multiples of 6 in the bottom row, as shown in exercise 5.
10. How many 6's are there in 12? in 18? in 24? in 30?
in 48? in 60? in 42? in 54?
u. Copy, complete, and read :
6-6= 18-6= 30-6= 42-^6= 54-6 =
12-6= 24-5-6= 36-^-6= 48-s-6= 60-6 =
12. Look at the first 12 squares that you have counted.
They are arranged in 2 columns of squares each.
^ of 12 squares = squares. J of 12= ?
13. In the same way find J of 18 ; f of 18 ; J of 24 ;
I of 24; I of 24; J of 30; ^ of 36.
EXSRCISES
94. Answer quickly, reading across the page :
1. 2x6= 6x2= 12-^6= 12-s-2= J of 12 =
2. 4x6= 6x4= 24-1-6= 24-5-4= Jof24 =
3. 5x6= 6x5= 30-6= 30-5= iof30 =
4. 3x6= 6x3= 18h-6= 18-^-3= iofl8 =
W- FIRST ^OK
101
Supply the missing numbers :
s.
6x6 = .?
6.
18h-? = 6
7.
lOx ? = 60
8.
24h-8=?
9.
?x6 = 30
10.
7x ? = 42
36 + 6=?
18-i-? = 9
9x ? = 54
30=?x6
40=?x5
60 = 10x ?
J of 36=?
? = 7x6
^of ? = 6
iof? = 6
6 = ^of ?
6 = Jof ?
imki;^
S^lii^kkSk
tlS,l&ikSk
&3^^itiitk
£4j<^^i^-i
95. Counting by sevens.
1. Here is a picture of Flora's
5ed)of tulips.
low many tulips are there in the
first horizontal row ? in each row ?
2. Count the tulips by 7's.
How many are 7-1-7, or two 7's?
7-1-7 + 7, or three 7's? four 7's? five 7's?
3. How many tulips has Flora? How many tulips
would she have, if she had 1 more row of 7 tulips ?
5x7=? 35 + 7=? 6x7=?
4. How many tulips are 6 times 7 tulips and 7 more
tulips ?
6x7=^? 42 + 7=?
49 = — 7's 49 + 7 = — 7's
56 = — 7's 56 + 7 = — 7's
63 = — 7's 63 + 7 = — 7's
5.
6.
7.
8.
9.
7x7= ?
49 + 7=? 8x7=?
56 + 7=? 9x7=?
63 + 7=? 10x7=?
Count rapidly by 7's from to 70.
Count by 7's to 70 in this way : " Once 7 is 7 ; two
times 7 are 14 ; '' and so on.
102
PROGRESSIVE ARITHMETIC
10. Count by 7's to 70 in this way : " In 7 there is owe 7 ;
in 14 there are two 7's;" and so on.
11. How many days are there in 1 week? in 2 wk.?
in3 wk.?
12. In 4 weeks there are 4 times 7 days, or -
- days.
In the same way teii how many days there are in 5 wk. ;
in 6 wk. ; in 7 wk. ; in 8 wk. ; in 9 wk. ; in 10 wk.
13. How many weeks are there in 7 days ? in 14 days ?
21 days = weeks.
28 days = weeks.
Continue in this way to 70 days = weeks.
14. Memorize :
1x7= 7
6 X 7 = 42
2 X 7 = 14
7 X 7 = 49
3 X 7 = 21
8 X 7 = 66
4x7 = 28
9x7 = 63
5 X 7 = 35
10 X 7 = 70
15. Copy, complete, and
read:
7-7 =
14-i-7 =
21 + 7 =
28 + 7 =
35 + 7 =
16. Copy the columns of 7's and write
the sums beneath.
Compare 14 and 7 thus :
14 x7;7 = of 14.
42 + 7 =
49 + 7 =
56 + 7 =
63 + 7 =
70 + 7 =
7
7
7
7
7
7
7
7
7
17. In the same way compare 21 and Z Z Z I Z
7; 28 and 7; 35 and 7.
18. Find f of 21 ; I of 28; I of 28; f of 35.
FIRST BOOK 103
EXERCISES
96. Tell the number of 7's in the sum, then tell the sum :
1. 7+7= 5. 7-1-7+7 + 7-1-7 + 7 =
2. 7 + 7 + 7 + 7= 6. 14 + 7 + 7+7 =
3. 7 + 7 + 7= 7. 21+7 + 7 + 7 + 7 =
*. 7 + 7 + 7 + 7+7= 8. 35 + 7 + 7 + 7 + 7 + 7 =
9- Tell the missing numbers in this mixed table of 7's :
X = 35 X = 70
= 21 = 7
= 42 =63
= 56 =28
= 14 =49
Answer quickly, reading across the page :
10. 2x7= 7x2 =
11. 4x7= 7x4 =
12. 6x7= 7x6 =
13. 3x7= 7x3 =
14. 5x7= 7x5 =
15. When you can buy 7 marbles for a cent, how many
can you buy for 5 cents? for 8^? for 10^?
16- Julia bought 4 pounds of rice at 7 cents a pound.
How much did the rice cost her?
17. If a pound of almonds costs 28 cents, what part of
a pound can you buy for 7 cents ?
14-^-7 =
14-!-2 =
^ofl4 =
28-7 =
28-s-4 =
iof 28 =
42^7 =
42-1-6 =
iof42 =
21-^7 =
21-h3 =
iof21 =
35h-7 =
35-5 =
^of35 =
104 PROGRESSIVE ARITHMETIC
EXERCISES
97. 1. Give the table of 2's to 10 times 2.
2. How many are five 2's? seven 2'8? 4x2? 9x2?
12 + 2 ? 16 + 2 ? How many 2's are there in 14 ? in 18 ?
3. Give the table of 4's to 10 times 4,
4. How many are two 4's? six 4's? 5x4? 10x4?
12 + 4? How many 4's are there in 16? in 32 ? in 36?
Tell the missing nmnbers :
5. Multiples of 3 6. Multiples of 6
15 = 5x3 24= 30 = 5x6 48 =
9= 12= 18= 24 =
21= 6= 42= 12 =
3= 27= 6= 54 =
18= 30= 36= 60 =
7. How many 3's are there in 6? in 2x6? in 5x6?
8. Give the table of 5 's to 10 times 5.
9. How many are 2x5? 4x5? 8x5? 9x5? How
many are J of 35 ? ^.of 15 ? J of 50 ?
10. Give the table of 7's to 10 times 7.
11. How many are 7x7? 3x7? 9x7? 42-5-7? 35-s-7?
12. How many dots are 8 times 4 dots ? ••••••••
4 times 8 dots ? What is the product of I**«IIII
4 and 8? 8x4=? 4x8=?
13. In a similar way find the product of 5 and 8 ; of 5
and 9 ; of 6 and 8 ; of 6 and 9 ; of 6 and 10.
6 times 8= ? 6 times 9= ? 6 times 10=?
FIRST BOOK 106
14. Find the product of 7 and 8 ; of 7 and 9.
7 times 8 = .? 7 times 9= ? 7 times 10= ?
15. Copy and complete as in the first colunm :
2x8=8x2=16 5x8= 2x9= 5x9=
3x8 = = 6x8= 3x9= 6x9 =
4x8 = = 7x8= 4x9= 7x9 =
16. See how rapidly you can go aroimd the first ring,
naming the multiples of 3 without making a mistake. Be-
gin with any number and go in either direction.
17. Give the multiples of 6 in the same way.
18. Give the multiples of 3 and 6 in pairs, beginning at
the top of the circle, thus :
12, 24; 15, 30; 6, 12; and so on.
19. See how rapidly you can go around the second ring,
multiplying by 5 ; by 6.
20. Next multiply each number around the second ring
by 5 and 6 in succession, beginning at the top, thtis :
10, 12; 25, 30; 40, 48; and so on.
21. Tell products rapidly :
8 75 7 9 8 7 6
56976798
106 PROGRESSIVE ARITHMETIC
22. Helen, Arthur, and I have 21 cookies in our lunch
basket. How many are there for each of us ?
23. One day every week Helen dusts 4 rooms for her
mother. How long does it take her, if she spends 10 min-
utes dusting each room ?
How many such rooms could Helen dust in an hour?
24. Arthur carries in the wood for the kitchen range,
6 sticks at a time. How many trips does he make to carry
in 30 sticks? 48 sticks?
25. Every Saturday I fill the coal box. It holds 24
hods of coal. I draw it from the coal shed on my sled,
3 hods full at a time. How many sled loads does it take
to fill the coal box?
26. We get the morning paper 6 days a week and Helen
pays for it every Monday morning. It costs 3 cent^ a
day. How much does she pay for it per week?
27. We pay the milkman every Wednesday morning for
7 quarts of milk at 6 cents a quart. How much does milk
cost us a week ?
28. On Friday our cook bakes 4 pans of rolls, with 9 rolls
in each pan. How many rolls does she bake?
29. We have 8 flatirons at our house. Each weighs
7 pounds. How much do all weigh ?
30. In a catalogue I found these prices for flatirons :
Weight, 4 1b., 5 1b., 6 1b., 7 1b., 8 1b., 9 1b., 10 1b.
Price, 20^, 25^, 30^, 35^, 40^, 45^, 50^.
How much do flatirons cost a pound?
FIRST BOOK 107
98. Inexact division.
EXERCISES
1. Find the value of 7 + 7 + 7 + 2.
Think " Three 7's and 2 ; 21 + 2 ; 23." Name the sum, 23.
Find the value of :
2. 5 + 5 + 2 7. 6 + 6 + 6 + 2
3. 2 + 2 + 2 + 1 8. 5 + 5+5+5+4
4. 4 + 4 + 4 + 3 9. 6 + 6 + 6 + 6+5
3. 6 + 6 + 2 10. 7 + 7 + 7 + 7 + 2
6. 3 + 3 + 3 + 1 11. 2 + 2 + 2 + 2 + 2 + 2 + 1
12. Frank bought eight 4-cent stamps and a 2-cent
stamp. How much money did he expend for stamps ?
13. A girl had seven 5-cent pieces and a 1-cent piece in
her purse. How much money had she in her purse ?
14. Andrew bought 9 pencils at 3 cents apiece and had
4 cents left. How much money had he at first?
Find the value of :
15. 5 + 5+5+5+5+3 24. Nine 2's and 1
16. 4 + 4 + 4 + 4+4 + 1 2S. Seven 3's and 2
17. 6 + 6 + 6 + 6 + 6 + 3 26. Six 7's and 5
18. 7 + 7 + 7 + 7 + 7 + 4 27. Eight 3's and 1
19. 6 + 6 + 6 + 6 + 5 28. Nine4'sand2
20. 10 + 10 + 10 + 10 + 2 29. Seven 5's and 1
21. 1 + 7 + 7 + 7 + 7 30. Eight 6's and 5
22. 2 + 6 + 6 + 6 + 6 + 6 31. Ten 6's and 3
23. 3+4+4 + 4+4+4 32. Nine 7's and 6
108 PROGRESSIVE ARITHMETIC
EXERCISES
99. 1. Findthe value of 26-4-4-4-4-4-4.
Think " 26 less six 4's ; 26 - 24 ; 2." Name the remainder, 2.
Find the value of :
2. 11-5-5 5. 18-5-5-5 8. 19-six3's
3. 8-3-3 6. 20-6-6-6 9. 39-nine4's
4. 17-7-7 7. 19-4-4-4 lo. 35 - three lO's
11. Howmany are 13-4? 13-4-4? 13-4-4-4?
12. What is the greatest number of 4's contained in 13,
and what is the remainder?
12 = three 4's. 13 - 12 = 1. 13 = three 4's and 1 over.
Read, filling blanks :
13. In 8 there are 3's and over.
14. In 19 there are 2's and over.
15. In 21 there are 4's and over.
16. In 32 there are 5's and over.
17. 5 is contained in 26 times and over.
18. 4 is contained in 41 times and over.
19. 30-5-6 = ; 31+6= and over.
20. 20 -*- 4 = ; 23 -*- 4 = and over.
21. 2)11 23. 3}26
— and — over. — and — remainder.
22. 7}36 24. 5)46
— and — over. — and — remainder.
FIRST
BOOK
109
Find quotient
} and remainders :
25. 2}9
30. 5)12
35.
3)28
40.
6)57
26. 3)16
31. 3)23
36.
6)65
41.
8)25
27. 4)18
32. 6)26
37.
7)16
42.
5)33
28. 2)17
33. 4)38
38.
4)27
43.
9)19
29. 4)21
34. 3)32
39.
7)25
44.
10)75
45. Divide by 3, 4, and 6, naming quotients and remain-
ders: 7, 14, 19, 22, 10, 17, 25, 11, 31, 29.
46. Divide by 5, 7, and 10, naming quotients and re-
mainders: 11, 17, 23, 29, 13, 44, 38, 43, 27, 48.
WRITTEN EXSRCISES
100. 1. A boy bought 9 oranges at 4 cents each and had
14 cents left. How much money had he at first?
4^ for 1 orange i orange cost 4^.
_9 9 oranges cost 9 times 4^, or 36^.
36^ for 9 oranges 9 times 4^ and 14^ over is equal
14^ left to 36/ + 14/^, or 50^.
50/ at first He had 50^ at first.
2. Robert bought 3 school papers at 10 cents each and
had 5 cents left. How much money had he at first ?
3. Grace bought 4 dolls' beds at 8 cents each and had 12
cents left. How much money had she at first ?
4. I have 1 cent more money than I need to buy seven
6-cent pencils. How much money have I?
110 PROGRESSIVE ARITHMETIC
5. Percy has 36 cents. How many 5-cent Christmas
toys can he buy, and how much money will he have left?
5/^)36^ '^^^ number of toys he can
7 times 1^ over ^^^^ ^® ^^^ ^^^^^ ^ *^^ nmnber of
7 tops, U over ^'"^^ ^6^ contams 5^.
36^ contains 5^ 7 times with
1 ^ over. He can buy 7 toys, and will have 1 ^ left.
6. Frank has 55 cents and wishes to buy Christmas toys
costing 10 cents each. How many can he buy? How
much money will. he have left?
7. Alfred has 45 cents. How many rubber balls can he
buy for his brother, and how much money will he have left,
if he buys as many 4-cent balls as he can ? 7-cent balls ?
8. If Helen has 30 cents and buys 4 Christmas presents
at 7 cents each, how much money will she have left ?
9. Belle's mother bought 5 dozen Christmas candles at
6 cents a dozen and gave the dealer 35 cents. How much
change was due her ?
10. Eva has 35 cents and wishes to buy 6 yards of tinsel
for a Christmas tree. How much money will she have left,
if she pays 4 cents a yard? 5 cents a yard? How much
more money does she need to buy the 6-cent kind ?
11. Mabel expended 47 cents for 6 dolls and a tea set.
If each doll cost 7 cents, how much did the tea set cost?
12. John bought a toy locomotive for 40 cents and 4
cars at 9 cents each. Find the cost of the train.
FIRST BOOK 111
MULTIPLICATION
EXERCISES
101. Multiply at sight :
1. 43276452
5693497 10
4. Joseph has nine 5-cent pieces in his bank and 8 cents
besides. How much money has he ?
5. Which costs more and how much more, a 50-cent
tool chest or 8 cameUag m arbles at 7 cents each ?
6. How many dimes are 6 times 3 dimes and 2 dimes
more?
How many tens are 6 times 3 tens and 2 tens more?
7. How many tens are 7 times 6 tens and 4 tens more ?
8. How many himdreds are 7 x 500 and 200 more ?
Multiply :
9. 4 40
44
700
700+40
740
744
2 2
2
2
2
2
2
10. 2 50
52
400
400 + 50
450
452
3 3
3
3
3
3
3
+c
C ^
2. 40 30 50 60 70 20 40 30
25372946
— — — — — _ — _-^
3. David has four 5-cent coins in his bank. How much ^ ">
less than a quarter of a dollar has he ? /
6
112 PROGRESSIVE ARITHMETIC
WBITTEN EXERCISES
102. 1. Multiply 756 by 5.
5 times 6 = 30. Write 0.
^^^ 5 times 5 = 25, 25 + 3 = 28.
Write 8 before the 0.
3780
5 times 7 = 35, 35 + 2 = 37.
Write 37 before the 8. Read the product.
Test your answer by adding five 756's.
In the following exercises, test the answers for the first row.
Multiply :
2. 627 3. 762 4. 250 5. 84 6. 288
_2 _3 _4 1 _1
7. 851 8. 96 9. 807 10. 85 n. 344
_2 ^ _5 J7 _3
la. 176 13. 555 14. 89 is. 625 i6. 506
2 4 6 4 7
17. 760 18. 389 19. 578 20. 444 21. 757
7 2 3 6 6
22. 518 23. 98 24. 770 2S. 543 26. 444
_3 _5 _4 7 7
27. 125 28. 609 29. 99 30. 666 3i. 999
7 4 6 5 5
FIRST BOOK 113
EXERCISES
103. 1. If you live 7 blocks from the schoolhouse and
can walk a block in 2 minutes, in how many minutes can
you walk to school? At what time must you start to
reach school at five minutes to nine, or at 9:55?
2. When we ride behind our horse, Jim, he trots 7 miles
an hour. How far can we ride in 5 hours ?
3. Lucy sailed on a steamboat for 4 hours. If the
steamboat went 12 miles an hour, how far did Lucy sail ?
4. If each of 7 children drops 5 cents into a slot
machine, how much money do they all drop in ?
5. If there are 8 rows of desks in a class room and 6
desks in each row, how many children will the room seat ?
6. How far can you ride in 6 hours on a train that goes
at the rate of 40 miles an hour ?
Find the change out of a quarter of a dollar for each of
the following purchases :
7. 7 newspapers at 2^ each; at 3^ each.
8. 4 calendars at 3^ each; at 5^ each.
9. 30 rubber bands at 3 for 1 ^ ; at 6 for 1 ^.
10. 4 papers of pins at 5^ a paper; at 6^ a paper.
11. Find the cost of 4 poimds of sugar at 6 cents a
pound and a poimd of ham, 20 cents.
12. At the baker's I bought 3 cakes at 20^ each and a
pie for 10^. How much money did I spend there?
FIRST PROG. AR. — 8
114 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
104. 1. A grocer bought three boxes of lemons. There
were 360 lemons in each box. How many lemons did
he buy?
360 lemons
1080 lemons
He bought 3 times 360 lemons,
or 1080 lemons.
2. At the fruit store Caroline saw 4 boxes of oranges
with ''150" stamped on. the end of each box, showing that
each box contained 150 oranges. How many oranges did
the 4 boxes contain ?
3. A fruit dealer bought 2 car loads of oranges. There
were 362 boxes in each car. How many boxes of oranges
did he buy ?
4. How many pineapples are there in three crates, if two
of them contain 24 each and the third contains 36 ?
5. Hope bought 2 pounds of coffee at 35^ a pound and
gave the grocer $1. How much change was due her?
35^ fori lb. $1= 100^
70^ for 2 lb. SO^j change due
6. A woman bought 3 poimds of butter at 28^ a pound
and paid the dealer $1. Find the change due her.
7. A. man bought 6 pounds of beef for roasting at 14^ a
pound. How much had he left out of $ 1 ?
FIRST BOOK 115
Find the change out of a dollar for each purchase :
8. 2 pounds of tea at 42 cents a pound.
9. 5 pounds of beefsteak at 18 cents a pound.
10. 7 bunches of celery at 14 cents a bunch.
11. 6 pounds of cheese at 15 cents a pound.
12. 4 dozen bananas at 22 cents a dozen.
13. 3 pounds of butter at 32 cents a pound.
14. A flour barrel holds 196 pounds of flour. How many
pounds of flour will 5 such barrels hold ?
15. A small bag of dairy salt holds 56 pounds, and a
large bag holds 4 times as much. How much more does
a large bag hold than a small one ?
16. How much more than half a dollar is needed to buy
5 dozen ears of sweet com at 13 cents a dozen?
17. Saturday morning our grocer had 2 whole cheeses,
w6ighing 40 pounds each, and 25 pounds of another cheese.
How many pounds of cheese had he ?
Find the amount of the purchases at each store :
18. At the hardware store, 2 cans of paint at 30 cents a
can and a paint brush for 35 cents.
19. At the drygoods store, 5 yards of ribbon at 15 cents
a yard and a 25-cent handkerchief.
20. At the florist's, a bunch of violets for 50 cents and
3 roses at 15 cents each.
21. At the bookstore, a 25-cent book and 2 boxes of
note paper at 35 cents a box.
116 PROGRESSIVE ARITHMETIC
DIVISION
EXERCISES
105. Divide at sight :
1. 2)10 3)18 4)24 5)35 6)48 7)28
2. 3)27 9)45 7)42 8)32 5)45 4)16
3. 2)46 3 )960 5)500 4)480 6)66 7 )707
Tell quotients and remainders :
4. 5. 6. 7. 8. 9.
2)20 2)21 2)44 2)45 3)18 3)19
10. 11. 12. 13. 14. 15.
4)45 4)83 5)50 5)53 5)_57 6)68
16. 17. 18. 19. 20. 21.
3 )360 3 )362 4 )485 5 )506 5 )559 6 )668
22. How many weeks are there in 63 days ?
23. How many weeks are there in a month of 31 days,
and how many days over ?
24. If 45 boys march 4 abreast, how many rows will
there be and how many boys over ?
25. How many gallons are there in 36 quarts ?
26. If Richard can skate around a pond in 10 minutes,
how many times can he skate aroimd it in half an hour ?
FIRST BOOK
117
Divide rapidly :
27. 3)6 3)60
3)66
3)666
3)6666
28. 6)12 6)120
6)1200
6)1206
6)1266
29. 3)21 3)219
3)2190
3)2196
3)2197
WRITTEN EXERCISES
106. 1. Divide 2197 by 3.
oxoiqy 3 is contained in 21 (hundreds),
732, 1 remainder 7 (hundreds) times. Write 7 mider
1, m hundreds place.
3 is contained in 9 (tens), 3 (tens) times. Write 3 under
9, in tens' place. 3 is contained in 7, 2 times with 1
remainder. Write 2 under 7, in units' place.
After 2 write a comma and then '' 1 remainder."
Test. — If the answer is correct, then 3 times 732 and 1 more
should give 2197. Test it by multiplying 732 by 3 and adding 1.
Do not write 732 and 3 again, but look at the process and note
that 3x2 = 6 and 6 + 1 = 7, which gives the units of 2197 ;
3x3 tens = 9 tens, the tens of 2197 ; 3 X 7 hundreds = 21 hun-
dreds, the hundreds of 2197.
Divide and test :
2.
2)1485
3.
3)1565
4.
2)1667
5.
3)2468
6.
4)1649
7.
5)1557
8.
4)2043
9.
5)2059
10.
3)1861
11.
4)1282
12.
6)307
13.
4)325
14.
3)2737
15.
5)4052
16.
5)4558
118 PHOGRfiSSlVfi AftlTHMETlC
17. Divide each of these numbers by
'2:
126,
185, 208,
405, 4248, 6265,
1400,
1483
.
18. Divide each of these numbers by 3 ; also by 6 :
126,
185, 248,
306, 367, 6605,
2400, 2461.
19. Divide each of these numbers b>
^5:
100,
105, 108,
1000, 1055, 5508, 4057,
3006.
Divide and test :
20.
21.
22.
23.
24.
4)843
3)1290
5)1500
4)287
6)421
25.
26.
27.
28.
29.
7)144
6)549
6)4262
5)259
4)8004
30.
31.
32.
33.
34.
3)9301
2)4621
7)2175
4)165
7)1403
35.
36.
37.
38.
39.
5)157
4)3606
7)5672
EXERCISES
5)358
6)5409
107. 1.
10^ =
-times 2^; 2^ =
of 10^
In the same way compare :
2. 12^ and 3^. 8. 15 apples and 3 apples.
3. 15^ and 5^. 9. 1 quart and 1 gallon.
4. 18 eggs and 3 eggs. lo. 1 foot and 1 yard.
5. 10 hats and 5 hats. ii. $20 and $5.
6. 8 sleds and 16 sleds. 12. $20 and $4.
7. 12 tops and 4 tops. 13. 1 pound and 8 ounces.
FIRST BOOK 119
14. If 2 lemons cost 5 cents, how much will 6 lemons
cost at the same price ?
Model Solution
2 lemons cost 6^.
6 lemons are 3 times 2 lemons.
6 lemons will cost 3 times 5^, or 15^.
15. If 4 peaches cost 5 cents, how much will 12 peaches
cost at the same price ?
16. If 2 pairs of shoe laces cost 5 cents, how much will
8 pairs cost at the same price ?
17. If you can walk 3 miles in 2 hours, how far can you
walk in 4 hours at the same rate ?
18. If a dozen oranges cost 30 cents, how much will 4
oranges cost at the same price ?
Model Solution
12 oranges cost 30 cents.
4 oranges are ^ of 12 oranges.
4 oranges will cost ^ of 30^, or 10^.
19. If a dozen eggs cost 32 cents, how much will 3 eggs
cost at the same price ?
Find the cost of :
20. 4 buns at 18 cents a dozen.
21. 21 plums at 3 plums for 5 cents.
22. 48 pears at 6 pears for 5 cents.
23. 6 bananas iat 22 cents a dozen.
24. 36 marbles at 4 marbles for 5 cents.
120 PROGRESSIVE ARITHMETIC
Find the cost of :
25. 6 pounds of grapes at 2 lb. for 15^.
26. 8 boxes of berries at 4 boxes for 25^.
27. 3 cans of tomatoes at 12 cans for $1.
28. 2 packages of oatmeal at 8 packages for $1.
29. 18 cakes of soap at 6 cakes for a quarter dollar.
30. If a street car runs 6 blocks in 5 minutes, how far
will it run in 20 minutes ? Suppose it runs 7 blocks in 5
minutes; 8 blocks in 5 minutes.
WRITTEN EXERCISES
108. 1. How many chairs at $2 each can be bought for
$120? for $75, with how many dollars over?
2. A blacksmith has 162 horseshoes. How many horses
can he shoe with 4 shoes each ? How many shoes will be
left?
3. A furniture dealer paid $2460 for beds at $6 each.
How many did he buy ?
4. If 2000 soldiers march 8 abreast, how many rows of 8
soldiers will there be ?
5. A certain church will hold 420 persons, if 6 persons
sit in each pew. How many pews are there ?
6. Three of the rows of trees in a large orchard contain
1500 peach trees, each row containing the same number of
trees. How many trees are there in each row ?
7. In a fire drill 365 children marched out of the school
building 2 abreast. How many rows of childr^ were
there and how many over? '^ .,
FIRST BOOK
121
1 inch
One
Cubic Inch
1 cu. in.
VOLUME
109. 1. How many corners has a cube? how many
edges ?
How do the edges of a cube compare in length?
2. How many flat sides, or faces, has a cube? How do
they compare in shape ? Are they squares or oblongs ?
How do the faces of a cube compare in area?
3. How long is the front face of
this cube ? how wide ?
4. What is the area of the front
face of this cube ? \
What is the area of each face ?
5. Each face of this cube is a
square inch.
6. A cube whose faces are each a square inch is called a
cubic inch.
7. How long is a cubic inch ? how wide ? how high ?
8. If each face of the cube were a square foot, what
would the cube be called ?
9. How long is a cubic foot ? how wide? how high?
110. 1. The box in the picture is 2 inches long, 1
inch wide, and 1 inch deep
(measured on the inside). IT^^I^B (^ ^M
How many cubic-inch blocks iB^ B ^l L
will the box hold? !^
2. If this box were 1 inch longer than it is, how many
cubic-inch blocks would it hold ?
122
PROGRESSIVE ARITHMETIC
3. Place 3 cubic-inch blocks in a
row; then, 3 blocks more in another
row, and put these rows side by side as
in this picture.
How many times 3 cubic inches do
you see in the picture ? how many cubic inches ?
4. Arrange another layer of cubic-inch blocks like the
one in the first picture and put one layer on top of the
other as in this picture.
How many times 3 blocks are there
in each layer ? How many times 2 x
3 blocks are there in the pile ?
There are 2 x 3 blocks in a layer and
2 times 2x3 blocks, or blocks,
in the pile.
5. How long is the pile ? how wide ? how high ?
6. How many cubic-inch blocks are there in a pile 3
inches long, 2 inches wide, and 2 inches high ?
7. Here is a picture of a block of
wood 4 inches long, 2 inches wide,
and 3 inches high. It is marked to
show cubic inches.
How many cubic inches are there
in a row running the longest way?
in 2 rows, or 1 layer ?
How many cubic inches are there
in 2 layers? in 3?
How many cubic inches does the block contain ?
3 times 2x4 cubic inches are cubic inches.
FIRST BOOK 123
8. A block is 5 in. long, 4 in. wide, and 3 in. high. Find
how many cubic inches it- contains.
Think of rows and layers of cubic inches.
In 1 row there are 5 cubic inches.
In 1 layer there are 4 x 5 cu. in., or cu. in.
In 3 layers there are 3 times 4 x 5 cu. in., or cu. in.
Then the block contains cu. in.
9. This is called the volume of the block.
WRITTEN EXERCISES
111. 1. Find the volume of a block 4 in. long, 2 in.
wide, and 2 in. high.
2. A box (measured inside) is |
4 in. long, 3 in. wide, and 3 in. deep.
How many cubic inches of sand will
it hold?
3. How many cubic inches does a cube contain, if its
edges are 3 in. long ? What is the area of its surface ?
Such a cube is called a 3-inch cube. What is a 5-inch cube ? a
2-foot cube?
4. In loading a wagon with clay a man dug. a hole 6 ft.
long, 2 ft. wide, and 2 ft. deep. How many cubic feet of
clay did he put into his wagon ?
^ 5. How many cubic feet of water will a tank hold, if it
is 5 ft. long, 4 ft. wide, and 4 ft. deep, inside ?
6. Find the volume of a 4-foot cube of granite. Find
the area th at is polished^ if 5 of. its, faces Jire polighed.
124 PROGRESSIVE ARITHMETIC
COMPARISON OF MEASURES
EXERCISES
112. 1. How many inches are there in a foot ? in J ft. ?
in i ft.? in I ft.? in J ft.? in | ft.?
2. How many feet are there in 1 yd. ? how many inches ?
How many feet are there in ^ yd. ? how many inches ?
What part of a yard is 2 feet ? 24 inches ?
3. Which is longer, and how much, 8 ft. or 3 yd. ? 2 ft.
or 22 in. ? 6 yd. or 17 ft. ?
4. This picture shows a square yard
divided into square feet. How many square
feet are there in 1 sq. yd. ? in J sq. yd. ?
What part of a square yard is 6 sq. ft. ?
5. How many pints are there in 1 qt. ?
in4qt.? in 1 gal.?
What part of a gallon is 1 qt. ? 2 qt. ? 3 qt. ? 2 pt. ?
4 pt. ? 6 pt. ?
6. Which is greater, 1 gal. or 7 pt. ? 2 gal. or 18 pt. ?
7. How many ounces are there in a pound ? in ^ lb. ?
What part of a poimd is 4 ounces? 12 oimces?
8. How much heavier is 35 ounces than 2 pounds ? how
much lighter than 2 J pounds ?
9. How many months are there in a year ? What part
of a year is 6 months ? 3 mo. ? 9 mo. ? 4 mo. ? 8 mo. ?
10. Flora spent June, July, and August in the country.
What part of the year was she in the coimtry ?
FIRST BOOK
126
11. What part of 28 days is 1 week ?
12. Jennie had 3 weeks' vacation, and Mary had 24 days.
Which girl had the longer vacation ? how many days longer ?
13. How many hours are there in a day ? in ^ of a day ?
in ;^ of a day ? in f of a day ?
What part of a day is 8 hours ? 16 hours ?
14. Florence spends 6 hours of the day in school. What
part of the day is she in school ?
15. How many minutes are there in J hr. ? in ^ hr. ?
in|hr.?
113. 1. Each square here represents
a square inch. How many square
inches are there in the oblong ? in |^ of it ?
2. What part of the oblong is 1 row ?
How many square inches are there
in f of the oblong ?
3. What part of the oblong is 1 column of squares ?
How many square inches are there in ^ of the oblong?
in f of it? in f of it? in f of it?
4. Which has the greater area, f of the oblong or f of
it? how many square inches greater?
5. This block, 5 in. long, 4 in.
wide, and 3 in. high, is marked into
cubic inches. How many are there in
the bottom layer ? in 2 layers ? in the
whole block?
How many cubic inches are there
in ^ of 60 cubic inches? in f of 60 cubic inches?
126 PROGRESSIVE ARITHMETIC
6. How many cubic inches are shown along the side of
the block? What part of the block do they form?
How many cubic inches is J of 60 cubic inches ? f , or ^,
of 60 cubic inches ? f of the block ?
7. How many cubic inches are shown on the front end
of the block ? What part of the block do they form ?
How many cubic inches is ^ of 60 cubic inches ? f ?
How many cubic inches is f of the block ? f ?
8. Which is greater, and how much, ^ of the block or J
of it? ^ of the block or i of it?
ADDITION AND SUBTRACTION
EXERCISES
114. Add and test :
1. 6
2.
4 3.
7
4.
8
5. 9
6. 5
3
2
7
5
8
2
4
8
6
7
4
6
7
9
8
6
6
9
2
3
7
6
8
9
6
7
5
8
7
7
8
5
9
4
9
8
Find results rapidly :
7. 8 + 7 + 4 + 8 + 5 + 9 11. 8 + 6 + 9 + + 9 + 7
8. 6 + 8 + + 9+8 + 7 12. 9 + 7-5-4 + 6-9
9. 7+9-5 + 8-7 + 6 13. 7 + 6 + 4 + 9 + 8 + 5
10. 9-7+8+9-6-8 14. 5 + 9 + 8-0-6-7
FIRST BOOK 127
EZBRCISES
115. Give answers at sight :
1. 38 85 27 56 39 72 61 44
+ 40 -20 +60 -26 -19 +22 -31 +11
2.
45
20
76 88
55
48 87
60
-15
+ 57 -
-26 -33
+ 40
+ 30 -82
+ 17
3.
576
698
326
441
247
324
+ 20
-58
+ 400
-141
-30
+ 22
4.
642
521
798
335
411
847
-32
+ 221
. -58
-235
+ 66
-500
£X£RCISES
116. 1. Edwin has read 30 pages of his reader. How
many pages more must he read to finish 50 pages?
2. Twenty boys and 15 girls were coasting on Scovel's
hill. How many children were coasting ?
3. A farmer has 56 cows in two stables. If there are 30
cows in one stable, how many are there in the other ?
4. Roy earned 35^ shoveling snow one week and 40^ the
next. How much did he earn in both weeks ?
5. A milliner had 325 hats and sold 125 of them on her
opening day. How many had she left ?
6. A boy bought skates for 60^ and a hockey stick for
20^. How much change did he receive out of $1 ?
t28
PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
in. Find the sum and the difference :
1. 4621
2. 6040
3.
1838
4. 5078
3849
2894
979
1999
». 3141
6. 8260
7.
4305
8. 7241
ICtxS
584
2572
2514
Add juui tost :
». 2346
10. 32SS
11.
20&4
12. 1668
IS24
964
496
3847
3(V>9
4891
52S3
2494
14v^T
546
1859
1865
!». T\V2
i«.
5l>3 15.
957
16. :
S4&
17. 632
46S
l^
4lXi
2S1
365
;^H
746
247
(
E)7S
777
Si^^
31V2
820
S9
438
2tU
Jsvl
675
561
592
Find rv^uUs:
!•. SlXX^ - iv<25 - 7iM - 2 17
Wk 2;iiv< - 4^*2 - 2»i>> -- -Vvi - SS
«1. 4:U ♦ VVvi» - Uv - S> - 42*3 - 24S
«. ivi2;> - ,"^-,\^ > xH - : ;>^- « 2-.U - 27
»Sk 49 ' iv< ' ;C * St - 4* - 72 --? :> - S6
•♦. Cv^ V : - 2:S V2 - 2 i - 4 a S^ - 4«* - 59
FIRST BOOK J29
WRITTEN EXERCISES
118. 1. How many feet of fence are needed to inclose a
lot 125 feet by 218 feet?
2. Mr. Hayes has 9248 bricks in twa piles. If one pile
contains 4135 bricks, how many are there in the other?
3. Maud ^vashed 8 plates, 4 cups, 5 saucers, a dozen
knives, 10 forks, and a dozen spoons. How many things
did she wash ?
4. If I buy groceries for 35 jz^ and meat for 28 f^, how
much change should I receive from 75^?
5.. Oliver counted the cars in six trains. There were
23, 37, 41, 38, 45, and 28. How many cars did he count?
6. If Ellen's father is now 37 years of age, in what year
was he bom ?
7. From a piece of cloth containing 46 yards, 13 yards
were sold at one time and 15 at another. How many
yards remained unsold?
8. The postman delivered 185 letters on Monday, 246
on Tuesday, 219 on Wednesday, and 227 on Thursday.
How many letters did he deliver in the four days?
9. Mr. Howard bought three loads of coal, the f;
weighing 4245 lb., the second 3984 lb., and the tV^^
4163 lb. How many pounds of coal did he buy? ^^^
10. A man bouglit a sofa for $65, a chair for $i cn
paid for them with a 100-dollar bill. How much k ^^^
did he receive? ^^iige
FIRST PROG. AR. ^
130
PROGRESSIVE ARITHMETIC
V )
NUMBERS TO ONE HUNDRED
119. Counting by eights.
1. How many hooks are
there in the top row?
2. How many hooks are
there in 2 rows? in 3 rows?
3. How many boys can hang
their hats on all the hooks ?
«
4. How many hooks are 2 times 8 hooks? 3x8 hooks?
4x8 hooks?
5. How many hats are 4 times 8 hats and 8 hats more ?
How many hats are 5 times 8 hats ?
6. Five8's = 40 6x8 = — 7x8 = —
One 8 =8 +8 -hS
Six 8's = -
7x8 = —
8x8 = -
7. How many are 8 x 8? Add 8 to 8 x 8 and find 9x8.
Add another 8 and find 10 x 8.
8. Coimt by 8's from to 10 times 8.
9. Memorize :
1x8= 8
6 X 8 = 48
2x8 = 16
7 X 8 = 56
3x8 = 24
8x8 = 64
4 X 8 = 32
9 X 8 = 72
5 X 8 = 40
10 X 8 = 80
10. Copy,
read:
complete, and
8 + 8 =
48 + 8 =
16 + 8 =
56 + 8 =
24-!-8 =
64 + 8 =
32 + 8 =
72+8 =
40 + 8 =
80 + 8 =
FIRST BOOK
131
120. Counting by nines.
1. How many men do you see in the nearest boat ? in
the second boat ? in each boat ?
2. How many men are there in 2 boats? in 3 boats?/ ^
in all the boats?
5x9 = 45
+ 9 f
6x9 =
+9
7x9 =
3. How many men are 2 times 9 men? 3x9 men?C*
4x9 men ? 4x9 men and 9 men more,
or 5 X 9 men ?
4. Add 9 to 5 X 9, or to 45, and find
6x9, as shown here.
5. Add another 9 and find 7x9.
6. 7 X 9 = 63. Then how many are 8x9?
7. 8x9=? 72 + 9=? 9x9=? 10x9=?
8. How many square feet are there in 1 square yard?
in 2 sq. yd.? in 3 sq. yd.? in 4 sq. yd.? in 5 sq. yd.?
How many square feet are there in 6 sq. yd. ? in 7 sq.
yd.? in 8 sq. yd.? in 9 sq. yd.? in 10 sq. yd.?
9. Coimt by 9's from to 10 times 9.
r- J
I' }
132 PROGRESSIVE ARirilMETIC
10. Memorize this table of nines :
1 X9= 9
6x9 = 54
2 X 9 = 18
7x9 = 63
3 X 9 = 27
8 X 9 = 72
4 X 9 = 36
9 X 9 = 81
5 X 9 = 45
10 X 9 = 90
11. How many times is 9
contained in 9? in 18? in
27? in 36? in 45? in 54?
63-5-9= ? 72-9=?
81-*-9=? 90-5-9=?
121. Counting by tens.
1. How many wires are supported by
the highest cross-arm of this telephone
pole?
2. How many wires will there be when
two of the cross-arms, counting- wfroax- the
top, are full? when three are full? four?
3. How many wires will the pole sup-
port on the cross-arms now empty ? How
many will all the cross-arms support ?
4. Count by lO's from to ten lO's.
5. Memorize :
1 X 10 = 10
6 X 10 = 60
2 X 10 = 20
7 X 10 = 70
3 X 10 = 30
8 X 10 = 80
4 X 10 = 40
9 X 10 = 90
5 X 10 = 60
10 X 10 = 100
6. How many lO's are
therein 10? in 20? in 30?
40-5-10=? 50-i-10=?
60-5-10= ? 70-5-10=?
80-5-10=? 90-5-10=?
100=? X 10; 100-5-10=?
2. Multiples of 6.
12 = 2x6
24 =
36 =
6=
18 =
30 =
42 =
54 =
60 =
48 =
• • •
• •
• •
• • •
• •
• •
• • •
• •
• •
FIRST BOOK 188
REVIEW EXERCISES
122. Tell the missing numbers :
1. Multiples of 5.
15 = 3x5 25 =
20= 50 =
35= 10 =
5= 45 =
40= 30 =
3. Coimt these stars by 'k
3's; by 2's; by 6's; by *
4's; by 8's. *
How many stars do you count in each case ?
24 + 3=? 24-!-8=? 24 + 6=? 24 + 4=?
Tell the niunber of lO's in the sum, then tell the sum :
4. 10 + 10 + 10 6. 40 + 10 + 10 8. 60 + 5 + 5 + 10
5. 20 + 10 7. 10 + 50 + 10 9. 70 + 10 + 5 + 5
Tell the number of 8's, or of 6's, etc., then the sum :
10. 8 11. 6 12. 7 13. 9 14. 9
8 6 14 18 27
8 18 7 9 9
16 ^ 11 J.
Which is greater and how much greater :
15. 2x9 or 3x7? is. | of 18 or ^ of 18?
16. 6x8 or 5x9? 19. J of 24 or J of 24?
17. 8x8 or 7x9? 20. ^ of 40 or J of 40?
1^4 PROGRESSIVE ARITHMETIC
123. The following exercises are for frequent review.
Give answers instantly :
1.
4x3
10x7
20 + 4
6x4
10x10
2.
7x3
4x4
12 + 6
3x3
72 + 9
3.
2x9
10x8
50 + 10
2x6
10x4
4.
5x3
5x5
32 + 4
3x9
10x6
5.
2x7
10x9
100+10
7x10
49 + 7
6.
2x5
6x10
48 + 6
9x6
28 + 4
7.
4x9
2x8
25 + 5
3x8
10x5
8.
5x8
3x10
90 + 9
7x9
.48 + 8
9.
4x5
6x3
54 + 6
6x5
35 + 7
10.
6x8
4x10
16 + 4
9x3
10x3
11.
9x7
8x8
64 + 8
7x4
^of 12
12.
5x6
9x9
63+7
8x2
iof21
13.
8x4
4x6
24 + 4
4x8
J of 24
14.
5x9
7x8
81 + 9
5x7
^of 15
15.
7x2
9x4
56 + 7
6x6
J of 24
16.
8x3
8x7
30 + 3
7x7
^of 18
17.
2x10
6x9
35 + 5
8x6
iof20
18.
6x2
3x6
42 + 6
9x5
^of30
19.
3x7
9x2
16 + 2
4x7
iof27
20.
5x4
6x7
72 + 8
7x6
iof 14
21.
8x5
3x5
24 + 3
9x8
iof 32
22.
9x10
8x9
20 + 10
8x10
^of 45
FIRST BOOK
135
1
2
2
4
3
6
4
8
5
10
6
12
7
14
8
16
9
18
10
^o'
124. 1. Draw a 10-inch square and divide it into inch
squares.
2. In the first column of squares write the numbers 1, 2,
3, 4, 5, 6, 7, 8, 9, and 10, beginning at the top.
3. Now fill the first roio with the multiples of 1 from
2 X 1 to 10 X 1, as shown below. Next fill the second row
with the multiples of 2, then the third row with the mul-
tiples of 3, and so on imtil all the rows are full.
Here are the first two rows :
I's
2's
4. In your table of multiples find the number that repre-
sents 4x2; 5x3; 6x10; 8x4; 4x8; 3x6; 6x3; also
1x1; 2x2; 3x3; 4x4; and so on to 10 x 10.
5. Find and compare 6x8 and 8x6; 3x9 and 9x3.
6. In your table find 24 in four places. What does 24
stand for in each place ?
126. 1. What numbers have 10 for their product?
12? 18?
10 = 5x2, or 2x5.
12 = 4 X 3, or 3 X 4, or 6 X 2, or 2 x 6.
18 = 9 X 2, or , or 6 X 3, or .
Give numbers that have the following as products :
2. 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21.
3. 24, 25, 27, 28, 30, 32, 35, 36, 40, 42, 45, 48.
4. 50, 54, 56, 60, 63, 64, 70, 72, 80, 81, 90, 100.
136 progrp:ssive arithmetic
Draw in as many ways as you can oblongs having the
following areas :
5. 12 sq. in. 7. 18 sq. in. 9. 24 sq. in.
6. 16 sq. in. 8. 20 sq. in. lo. 28 sq. in.
126. Tell quotients and remainders :
1. 5^ 6. 8)68 u. 6}64 16. 4 )39
2. 7)U 7. 9)85 12. 7)i76 i7. 8^
3. 9)60 8. 7)58 13. 8)62 18. 9^
4. 8)50 9. 6)47 14. 5)53 19. 10)65
5. 7)i65 10. 8)84 15. 7)48 20. 10)97
Tell quotients and remainders :
21. 66-5-7 25. 92-j-lO 29. 71-8-8 33. 96-5-9
22. 84^9 26. 68-1-7 30. 80-*-9 34. 69^8
23. 85-5-8 27. 75^8 31. 76-t-7 35. 59^6
24. 71-S-7 28. 88-8-10 32. 65-8-6 36. 104H-10
127. 1. Horace bought a box of paints for 50^ and 3
brushes at 9^ each. How much money did he spend?
2. I have 50^. How many 8-cent lamp chimneys can
I buy, and how many cents shall I have left ?
3. Harriet bought 6 glasses and a pitcher for 75^. The
glasses cost 9^ each. How much did the pitcher cost?
4. Ida bought a tea kettle for 49^ and 3 dippers at 10^
each. Find the cost of the four articles.
5. Frank has a dollar. If he buys 4 tickets for a ball
game at 10^ each, how much money will he have left?
FIRST BOOK
187
MULTIPLICATION
BXERCISES
128. Multiply at sight:
1. 5 7 9 10 20
30
50
500
10 10 10 10 10
10
10
10
2. What figure written after 5 will change it from 5
units to 5 tens, or to 10 times 5 ?
3. What figure written after 7 will give 7 tens, or 10
times 7 ? What figure written after 12 will give 12 tens,
or 10 times 12?
4. How can you multiply 15 by 10? 22 by 10? 18 by
10 ? any number by 10 ?
klultipl)
r by 10:
s. 4
8. 16
11. 48
14. 760
17. 900
6. 9
9. 19
12. 52
15. 816
18. 965
7. 10
10. 24
13. 60
16. 884
19. 999
Find the number of :
20. Days in 10 wk.
21. Ounces in 10 lb.
22. Minutes in 10 hr.
23. Cents in 10 dollars.
24. Pints in 10 gal.
25. Square feet in 10 sq. yd.
26. If a trolley car travels 18 miles every trip it makes,
andjf it makes 10 trips per day, how many miles does it
travel per day ?
138 PROGRESSIVE ARITHMETIC
129. Multiply:
X. 22 2.
8
WKITTEN BXBKCISES
34 3. 65 4.
9 7
99
4
5. 99
9
6. 250
7
7.
496
5
8. 372
7
9.
777
9
10. 707
6
n. 408
6
12.
382
8
13. 502
8
14.
545
8
15. 888
9
16. 608 17. 625 18. 907 i9. 392 20. 999
9 9 5 6 8
Find the product of :
21. 75 and 8 24. 360 and 5 27. 9 and 435
22. 49 and 7 25. 940 and 7 28. 8 and 598
23. 68 and 9 26. 480 and 9 29. 9 and 989
30. Find the cost of 24 chairs at $2 each.
$24 At $1 each, 24 chairs would cost $24.
2 At $2 each, 24 chairs cost 2 times $24,
$48 or $48.
Find the cost of : Find the value of :
31. 25 hats at $4 each. 34. 96 ten-dollar bills.
32. 32 pears at 3^ each. 35. ^8 five-dollar bills.
33. 325 books at $2 each. 36. 750 two-dollar bills.
37. If you can solve 3 exercises in a minute, how many
can you solve in an hour at the same rate ?
FIRST BOOK
139
38. I bought a dozen cans of tomatoes at 9 cents a can.
How much more than a dollar did I spend ?
39. A woman bought 15 packages of flower seeds at 8
cents a package. How much did they cost ?
40. The tailor has a pressing iron that weighs 14 poimds.
How much did it cost, at 5 cents a pound ?
130.
WRITTEN £X£RCIS£S
1. The sidewalk in front of these lots is 9 feet
wide. Mr. A's lot is 32 feet wide, Mr. B's 64 feet, and so \^
on, as marked. Find the length and area of the sidewalk. -^
2. How many square feet of sidewalk must each man
keep clear of snow in the winter time ?
3. How many square yards of flagging did it take to
make the sidewalk?
4. Mr. A's lot is worth $8 a front foot, or 32 times $8.
Find the value of each of the six lots at the same rate.
5. Mr. E's lot is worth $448, and his house is worth
7 times as much. How much is his house worth ?
6. When the street was paved, Mr. A had to pay $ 128,
and Mr. B had to pay twice as much. How much was
Mr. B obliged to pay?
^7
140 PROGRESSIVE ARITHMETIC
7. How many cubic feet of water will a trough hold
that is 16 ft. long, 2 ft. wide, and 2 ft. deep ?
8. How many cubic feet of snow will a cart hold that
is 9 ft. long, 4 ft. wide, and 3 ft. deep ?
9. The leg of a table was 28 in. long, 3 in. wide, and
3 in. thick. How many cubic inches did it contain ?
DIVISION
£X£RCIS£S
131. Divide at sight :
1. 8)40 7}56 9)54 6)48 5)45 9)81 8)64
2. 6)60 8)72 8}56 9}63 4)36 10)80 10 )100
3. 8 )480 6 )540 3 )150 9 )450 8 )640 7 )630 9 )810
Tell quotients and remainders :
4.
7)280
5.
7)282
6.
9)360
7.
9)365
8.
9)270
9.
9)545
10.
9)630
11.
9)810
12.
9)636
13.
8)649
14.
9)369
15.
8)729
16.
8)567
17.
9)458
18.
9)188
19.
6)545
20.
9)906
21.
8)807
22. How many lO's are there in 30? in 50? in 100?
in 120? in 150? in 240? in 480? in 500? in 6400?
Read all the numbers in this exercise as tens.
FIRST BOOK 141
23. When a number ends in 0, how can you find how
many times it contains 10 ?
24. Read as tens and imits ; then divide each number
by 10, giving quotients and remainders :
34, 56, 106, 128, 265, 381, 576, 5760, 5762
25. Which figure, or figures, of a nimiber tells how many
times it contains 10 ? Which figure tells the remainder, if
any ? If there is no remainder what is the units' figure ?
Divide by 10:
26. 75 28. 162 30. 287 32. 400 34. 9580
27. 98 29. 107 31. 356 33. 850 35. 4253
Divide :
36. 4)40 + 12 4)52 4 )40 -h 20 4)60 4 )40 + 32 4)72
37. 5 )50 + 10 5)60 5 )50 + 15 5)65 5 )50 + 45 5)95
38. 6)60 + 18 6)78 6)60 + 24 6)84 6)60 + 48 6)108
WRITT2N EXERCISES
132. 1. Divide 98 by 7.
7 is contained in 9 tens, 1 ten times,
^— with a remainder of 2 tens, or 20.
Write 1 in tens' place, under the 9 tens.
7 is contained in 20 + 8, or in 28, 4 times. Write 4 in
units' place, under the 8 imits. Read the quotient.
Test. — 7 times 14 = 98.
2. Divide 45 by 3. 4. Divide 64 by 4.
3. Divide 54 by 3. 5. Divide 84 by 6.
142 PROGRESSIVE ARITHMETIC
Divide and test :
6.
7.
a
9.
10.
5)70
6)96
7)294
8)96
6)504
u. '
12.
13.
14.
15.
7)105
5)125
8)120
9)108
8)200
16.
17.
18.
19.
20.
6)198
6)216
8)272
7)385
7)462
21. Divide 980 by 4.
A\qQr\ 4 is contained in 9, 2 times with a remainder
245 ^' ^' "^ ^^
20, 5 times
5, 4 tmaes with a remam(
. Read the quotient.
ler ot 2; in
Divide and test :
,
22. 23.
24.
25.
26.
3)747 2)576
4)932
8)920
6)864
27. 28.
29.
30.
31.
5)1345 2)1104
7)2359
6)1524
5)1880
Find quotients:
32. 133 -i- 7
37. 1074 H- 3
42.
1620-9
33. 282-S-6
38. 1350-!- 9
43.
7839^9
34. 196-5-7
39. 1360 -H 8
44.
7848-8
35. 594 + 6
40. 2097 + 9
45.
8010-^9
36. 243^-9
41. 3762-1-6
46.
5816 + 8
FIRST BOOK 148
£X£RCIS£8
133. 1. If 6 roses cost 30^, how much will 4 roses cost?
Model Solution
6 roses cost 30^.
1 rose will cost 30^ -s- 6, or 5^.
4 roses will cost 4 times 5^, or 20 ff.
2. If 2 pencils cost 8 cents, how much will 7 pencils
cost?
3. Find the cost of 10 quarts of oil when 4 quarts cost
12 cents.
4. Find the cost of 5 quarts of molasses at 36 cents a
gallon ; at 28 cents a gallon.
5. The rate of postage on books is 1^ for 2 ounces.
How much will it cost to mail a book weighing one poimd?
6. Find the cost of 9 pints of milk at 6 cents a quart.
7. If 5 telephone calls cost 25 cents, how much will
8 calls cost?
8. When 6 peaches cost 12 cents, how much must be
paid for 10 peaches ?
9. Albert bought 3 egg plants for 27 cents. At that
price how much would 8 have cost ?
10. A woman bought 10 pineapples for a dollar and sold
3 to a neighbor at cost. How much did she receive for the
pineapples she sold ?
11. If 5 railroad tickets cost a dollar, how much will 8
such tickets cost ?
144 PROGRESSIVE ARITHMETIC
EXERCISES
134. 1. Point to ^ of 12 marks. Now . . . . . . , . ....
point to f of 12 marks.
2. f of 12 marks = times ^ of 12 marks = .
3. Find f of 20.
Solution.—^ of20=:4; fof20=:2 times 4 =: 8.
Find the value of :
4. I of 21 7. I of 24 10. f of 35 13. f of 50
5. i of 28 8. f of 30 u. f of 25 14. | of 32
6. ^ of 15 9. f of 18 12. f of 27 15. ^ of 45
16. Find the cost of f of a yard of oilcloth at 30 cents a
yard.
17. Find the cost of f of a pound of meat at 16 cents a
pound.
135. 1. If 4 boys divide 1 pie equally, what part of the
pie will each receive ?
J of 1 == fourth.
2. If 4 boys have 2 pies to divide equally instead of 1,
how many fourths of a pie will each boy receive ?
^ oi 2 pies = f of 1 pie.
^ of 2 = fourths of 1, or fourths-
3. How does ^ of 3 pies compare with ^ of 1 pie?
J of 3 = fourths.
4. How does ^ of 3 pies compare with j of 1 pie?
^of 3 = fifths.
FIRST BOOK 145
5. If 4 hats cost $3, what part of a dollar does 1 hat
cost?
6. Five boys hire a boat for $2. What part of a dol-
lar should each pay ?
7. If 3 girls divide 2 muskmelons equally, what part of
a melon will each receive ? j
8. If 3 girls divide 4 melons equally, each girl will -■
receive 1 melon and of a melon more. ";
J of 4 melons = 1 melon + ^ melon = Ij melons.
SXERCISSS
<?
J
1. ^ of 5 apples = 1 apple H apple = apples, x.
2. \ of $6 =$1 + $^ =S1J; $6 ■*-5 = $lf J
3. \ of S7 =$1 + $ = $ ; $7 +5 = . X'
4. \ of $8 =$1 + $ = $ ; $8 ^5 = . J
5. \ of $12 = $2 + $ = $ ; $12-i-5 = . ^
Find: ;
6. ^ of S7 10. $15 + 2 14. ^ of 23 ft.
1. \ of $9 11. $11-h5 15. \ of 19 qt. ' «^
8. ^ of Sll 12. J of $33 16. 13hr.-J-3 -
9. \ of $10 13. \ of $16 17. 16min.-i-5 <^
Answer quickly :
18. \ of 14 22. \ of 25 26. 21-S-2 30. 25 + 6
19. ^ of 28 23. ^ of 49 27. 20 + 3 3i. 30 + 7
20. \ of 33 24. \ of 28 28. 15 + 4 32. 19 + 8
21. \ of 19 2S. \ of 19 29. 32+5 33. 38 + 9
FIRST PROO. AR. — 10
-J
146
PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
186. Divide:
1. 2.
2 )575 3 )473
287i
1571
6.
7.
2)347
2)1451
11.
12.
5)867
5)3744
16.
17.
6)9041
8)755
21.
22.
8)2005
10)4371
3.
4 )839
209|
8.
3 )419
13.
6 )493
18.
7 )5833
23.
9 )5665
4.
5 )643
128|
9.
4 )751
14.
6 )8507
19.
8 )6663
24.
10 )8433
5.
8 )1007
125^
10.
4 )5263
15.
7 )936
20.
9 )1000
25.
9 )6847
EXERCISES
137. 1. How many valentines can be bought for 15
cents at 2 valentines for 5 cents?
Model Solution
2 valentines cost 5^.
15^ = 3 times 5^.
15^ will buy 3 times 2 valentines, or 6 valentines.
2. When 4 jelly glasses cost 10^, how many can be
bought for 20^? How much will a dozen cost?
FIRST BOOK
147
3. Mabel expended 25 cents for peaches at 6 for 5 cents.
How many peaches did she buy ?
4. If a boy can read 2 pages of a book in 3 minutes, how
many pages can he read in half an hour ?
5. At the store Eva saw piles of oranges marked thus:
3 for 10^
2 for 5^
3 for 5^
4 for 5^
She had 40 cents. How many oranges of the first kind
could she buy ? of each of the other kinds ?
6. Find the cost of a dozen oranges of each kind.
REVIEW
EXERCISES
138. 1. Count by 6's from 1 to 49 and back again ; from
3 to 57 and back ; from 5 to 65 and back.
2. Count by 7's from 2 to 58 and back again; from 4
to 67 and back ; from 6 to 76 and back.
3. Count by 8's from 3 to 59 and back again; from 5
to 77 and back ; from 7 to 87 and back.
4. Count by 9's from 4 to 76 and back again; from 6
to 87 and back ; from 8 to 98 and back.
Find results rapidly :
5. 3 + 4-2 + 5 + 7-3 + 4 + 2-7-6 + 9 + 0-5
6. 9 + 8-0 + 4-6 + 2-8 + 5 + 6-5 + 3 + 9-6-4
7. 150
-60
410
x8
4 )280 6 )300
999 ; 2000
+ 1 -100
148 PROGRESSIVE ARITHMETIC
8. Read: 101, 110, 1010, 4005, 9099, 8056.
9. How many pans costing 6 cents each can be bought
for 50 cents, and how many cents will be left ?
10. A street car conductor exchanged a dollar bill for
5-cent coins. How many 5-cent coins did he receive ?
11. If a boat sails 10 miles an hour, how long will it
take to sail 120 miles ?
How far will it sail in 24 hours ?
12. How many yards are there in 96 feet ?
13. A man had $650 in the bank and drew out $240.
How much money had he left in the bank ?
14. How many hours is it from 9 a.m. to 4 p.m. ?
15. A pudding put into the oven at 10 : 30 a.m. is to bake
40 minutes. At what time will it be done ?
WRITTEN EXERCISES
139. 1. Write in words: 1001, 2005, 4056, f.
2. Add: seven hundred twenty, sixty-nine, four thou-
sand eight hundred seven, ninety-six.
3. Divide two thousand forty-five by five.
4. Find 6 times 857, then 4 times 857. Add the prod-
ucts. The answer should be times 857.
5. How much less than $1000 is $825?
Multiply : Multiply : Divide :
6. 485 by 3 9. 307 by 9 12. 1208 by 4
7. 766 by 8 10. 448 by 7 i3. 3699 by 9
8. 959 by 9 11. 519 by 10 14. 7280 by 8
FIRST BOOK 149
Add : Subtract :
15. 2564 + 833 + 275 + 688 19. 400-85
16. 4826 + 725 + 487 + 853 20. 900-56
17. 408 + 1269 + 672 + 6220 21. 2050-765
18. 198 + 1827 + 222 + 4489 22. 9000-5280
Find the value of :
23. I of 1600 25. J of 375 27. ^ of 2440
24. ^ of 1860 26. i of 3400 28. ^ of 5280
29. If a boy goes 2 feet at every step, how far will he go
in 20 steps? in 100 steps?
30. How long will it take an automobile to run 168 miles
at the rate of 8 miles an hour ? ^
31. Edward stood halfway between two street lights
that were 330 feet apart. How far was he from each?
32. A baker made 96 pies. If ^ of them were lemon
pies, how many lemon pies did he make ?
33. If a cow gives 8 quarts of milk twice a day, how
much milk does she give in a week ?
34. If 1 lb. of cheese can be made from 10 lb. of milk,
how much cheese can be made from 1280 lb. of milk?
35. How many ounces are there in 8 poimds ?
36. Find the volume of a brick 8 inches long, 4 inches
wide, and 2 inches thick.
37. If it costs 25 cents to telephone 5 minutes from New
York to Brooklyn, how much will it cost a man who speaks
15 minutes?
160
PROGRESSIVE ARITHMETIC
EXERCISES
140. Make and solve as many problems as you can about
the following :
1. Paul has 60 marbles, George 10 marbles.
2. Marbles cost 1^ for 6, 1^ for 3, 2^ for 5, 3^ for 5,
1^ each, 2^ each. Use prices in your city.
3. A wild rose has 5 petals.
4. A spider has 8 legs ; a bee, 6 legs ; a horse, 4 legs.
5. A cat has 5 toes on each fore paw and 4 toes on
each hind paw.
The following are prices at a fruit stand :
6. Dates, 8^ a poimd.
7. Figs, 20^ a pound.
8. Bananas, 2 for 3^.
9. Oranges, 2 for 5^, 3
for 10^.
10. Nuts, 16^ a poimd.
u. Lemons, 2i each.
12. Grapes, 15 ^ a poimd.
Here are some prices at a stationer's store :
13. Pencils, 1^, 2^, 3^, 5^ each; 10^ a doz., 25^ a doz.
14. Pens, 6 for 5^.
15. Books, from 25^ to $1 each.
16. Blotters, 8 for 5^.
17. Ink, 5^ a bottle, small size; 25^ a bottle, large size.
FIRST BOOK 161
UNITED STATES MONEY
141. 1. Write, using the sign $: eight dollars; eleven
dollars; twenty-five dollars; one hundred five dollars; six
hundred forty-eight dollars.
2. One dollar thirty-eight cents is written in this way:
$1.38.
The period that is used to separate the dollars from the
cents is called the decimal point.
Read :
$3.25 $7.42 $18.69 $145.75 $168.94
$9.81 $5.36 $48.20 $201.47 $500.60
Write : two dollars forty-five cents ; twelve dollars forty
cents ; ten dollars eleven cents ; one hundred twenty dollars
seventy-two cents; five hundred thirty dollars sixty-one
cents.
3. Eighty-five cents is written in this way: $.85.
When there are no dollars the sign $ is written, then the
decimal point, and after that the number of cents.
Sometimes is written just before the decimal point in
this way: $0.85.
Read:
$.75 $0.24 $.50 $0.72 $.44 $.13
$.86 $0.99 $.25 $0.94 $.60 $.49
Write the following in two ways, using the sign $ :
Ten cents. Sixty-four cents. Thirty-six cents.
Forty cents. Thirty-two cents. Ninety-five cents.
Eleven cents. Eighty-one cents. Seventy-nine cents.
152 PROGRESSIVE ARITHMETIC
4. Three dollars nine cents is written in this way : $3.09.
When the number of cents is less than 10, the figure is
written in the first place after the decimal point.
Read: $1.05; $.03; $.09; $0.08; $8.06; $25.04;
$840.07; $264.00; $326.01.
Write : two dollars five cents ; eight cents ; five hundred
dollars six cents ; eight hundred twenty-five dollars ; sixty-
three dollars seven cents.
EXERCISES
142. 1. Read the following :
$8.08 $.70 $80.60 $139.79
$0.62 $.15 $49.25 $375.00
$3.02 $.06 $93.38 $608.04
2. Write in columns so that decimal points shall stand
in a column :
Thirteen cents.
Twenty-four dollars.
Eight dollars four cents.
Fifty dollars one cent.
Sixty dollars ten cents.
Fifty-six dollars two cents.
Thirty-eight dollars sixty-nine cents.
Seventy-seven dollars twenty-three cents.
One hundred seventy-five dollars fifty cents.
Four hundred twelve dollars five cents.
Seven hundred eighty dollars eighteen cents.
Nine hundred ninety-nine dollars ninety-nine cents.
FIRST BOOK
153
ADDITION
AND SUBTRACTION
148. Add quickly :
EXERCISES
1. $25
34
$37
22
$42
35
$23
56
$64
13
$56
42
Subtract :
'
2. 68^ '
24^
75^
42^
89^
53^
76^
34^
88^
35^
94^
41^
Give answers at sight
',
3. 35^
+ 13^
$.35 .
+ .13
69^
-25^
$.69
-.25
$.33
+ .54
$.84
-.31
4. 100^
+ 40^
$1.00
+ .40
156^
-33^
$1.56
-.33
$2.34
+ .25
$3.86
-.62
5. $3.20
+ .65
$4.68
-.32
$5.37
+ .22
$5.96
-.43
$3.75
-.52
$6.23
+ .66
WRITTEN EXERCISES
144. 1. Findthesumof $39.82, $7.31, $.49, and $18.08.
$39.82 Arrange the numbers so that the deci-
7.31 mal points shall stand in the same column.
.49 Add as you have added other numbers.
18.08 Put the decimal point in the sum under
$65.70 the other decimal points. Read the sum.
164 PROGRESSIVE ARITHMETIC
Copy, add,
and test :
2. $22.68
3.. $16.83
4. $46.32
5. $28.75
15.96
45.67
19.87
6.42
32.11
9.84
20.78
.53
19.84
20.45
14.85
32.19
6. $16.46
7. $27.34
8. $35.44
9. $17.45
2.39
.05
10.10
12.99
8.47
41.20
.16
58.80
9.26
13.98
46.89
18.34
Subtract, putting the decimal point in the remainder
under the other decimal points :
10. $4.09 11. $18.72 12. $83.04 13. $60.35
2.75 9.38 24.96 39.76
14.
$9.13
IS.
$54.00
16.
$67.18
17.
$94.62
5.64
.75
39.28
8.94
la
$7.36
19.
$80.00
20.
$91.07
21.
$58.27
.98
14.37
45.45
.85
22.
$6.24
23.
$74.84
24.
$85.05
25.
$77.77
4.85
6.95
56.31
8.88
26.
$9.00
27.
$40.41
28.
$90.06
29.
$96.03
8.46
9.66
38.39
76.05
30. How much more is $87.24 than $28.56?
31. Find the difference between $36.03 and $9.45.
FIRST BOOK 155
These examples have been added and tested in less than
8 minutes. Practice until you can do as well or better.
32.
36.
44.
$8.65
33. $45.68
34. $21.57
35. $17.84
9.99
8.74
17.98
.55
4.87
14.08
12.49
26.79
2.12
.97
16.35
31.99
7.75
26.79
29.78
3.08
$5.73
37. $10.98
38. $31.44
39. $19.69
8.99
7.49
28.39
27.97
4.27
26.78
14.16
18.48
9.68
43.42
10.10
16.76
6.77
9.99
15.28
9.85
$7.06
41. $25.47
42. $15.86
43. $38.47
3.92
8.68,
6.73
19.71
8.45
29.22
12.97
5.63
6.39
14.62
.89
6.42
9.86
3.93
32.76
16.98
5.98
18.08
11.69
12.79
$4.96
45. $38.06
46. $23.65
47. $37.50
2.63
7.36
.89
10.99
8.47
13.91
8.43
4.65
9.24
22.88
6.78
23.76
7.65
4.76
42.39
5.84
6.38
13.03
5.20
17.26
48. What is the sum of $27.94, $6.81, $45.30, and $ 18.00 ?
49. Find the sum of $9.34, $ .69, $34.15, $8.75, and $47.07.
166
PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
145. The following table shows how much money the
children in the third grade of a certain school deposited in
their school savings bank from January to June, and how
much they drew from the bank each month.
Jan
A CLASS
B CLASS
Deposited
Withdrawn
DlPOSITSD
Withdrawn
$1.36
#0.18
$1.41
$0.37
Feb
1.36
.42
1.19
.16
Mar. . . .
1.66
.28
1.48
.39
Apr
2.26
.60
1.62
.26
May ....
1.75
1.19
1.96
.37
June ....
1.73
1.06
2.10
1.16
1. During January how much more did the A class de-
posit than they withdrew, or how much did they save f
2. Did the B class save more or less than the A class
during January, and how much more or less ?
3. How much more did the A class deposit during Febru-
ary than the B class ?
4. Which class saved the greater amotmt of money
during February, and how much greater ?
5. Compare the savings of the two classes during
March ; during April ; during May ; during June.
6. At the end of January, how much money was there
in the bank belonging to each class ? to both classes ?
7. Which class had the greater amount of money in the
bank at the end of June, and how much greater ?
"^ y^^>^ Tr FIRST BOOK 167
0^ <" O^ FRACTIONS
^ (^ 146. 1. Into how many equal parts is this oblong
^divided? What is each part called?
How many fourths are shaded ? how many halves ?
How many fourths are there in ^ of the oblong ?
To how many fourths is ^ equal ?
2. Into how many equal parts is this oblong
divided ? What is each part called ?
How many sixths are shaded ? how many halves ?
How many sixths are there in ^ of the oblong ?
To how many sixths is ^ equal ?
3. How many sixths of this oblong are shaded ? how
many thirds ?
How many sixths are there in ^ of the oblong ?
To how many sixths is J equal ?
4. How many sixths of the oblong are light ? how many
thirds?
How many sixths are there in f of the oblong ?
To how many sixths is | equal ?
,Qr_more of the equal parts of anything is calledj .
Name some fractions.
EXERCISES
Draw lines or oblongs and divide them to show that
t1 — 2 q1 — 2 -1__3. »
1- 2""¥ ^' S"^ ^' 2 — Q ^
2. | = i 4. t = f 6. | = i
f=i
y
cf
8.
158 PROGRESSIVE ARITHMETIC
147. Adding and subtracting halves.
1. How many halves are 1 half and 1
half ? how many ones ? How many halves
are 2 halves + 1 half ? how many ones and
how many halves over ?
4+4=? 1+4==? 1+4=? 4+4+4=?
2. How many halves are there in 1 ? How many halves
are 2 halves less 1 half? f-J? 1 -i?
How many halves are f — ^? how many ones?
How many are l^-J? 2-^? 2^-1?
EXERCISES
148. Give answers :
1. $4 + ^4 3. l^oz.+^oz. 5. ^qt. + ^qt.+|qt.
2. 2ft.-ift. 4. ilb. + 2|lb. 6. Spt.-^pt.-^pt.
7. 3^ 8. 1| 9. 5 10. 4^ u. 7^
+2_ +^ 11 -14 +i
12. GJ 13. 4^ 14. 8^ 15. 3 16. 9^
-24 +34 -5_ +24 -6|
17. Find the sum of 2^ gal., ^ gal., and 5§ gal.
18. Edna bought 6 yards of ribbon and used 3^ yards of
it for her dress. How many yards did she have left ?
19. If it takes 2^ yards of cloth for a jacket and 6^
yards for a skirt, how many yards are needed for both ?
FIRST BOOK 169
WRITTEN EXERCISES
149. Find the sum and the difference:
1. 48^ 2. 39 3. 28^ 4. 62^ 5. 30
22| ^ _9| 37_ 14|
6. 72^ 7. 61^ 8. 51 9. 44^ 10. 82
31^ 42| 25i 36|- 17|
Find answers:
n. 64-2(% 13. 20-14^ is. 46^+28-36^
12. 43i-25i 14. 67-46| 16. 31^ + 24^+9^
17. What is the perimeter of a room that is 20j feet , y
long and 17 feet wide ? . ^
18. From a piece of dress goods 40^ yards long a X£&s^
chant sold 14| yards. How many yards were left? ^
150. Adding and subtracting thirds. -»^ A\ O'
1. How many thirds are \, \, and ^* ' '
\t how many ones? How many
thirds are f and f ? how many ones
and how many thirds over?
i+Hi= ? 1+1= ? i+f = ? Hi+i+i+i= ?
2. How many thirds are there in 1 ? How many thirds
aref-i? 1-i? f-f? 1-f?
How many thirds are | — f ? how many ones ?
How many are If- 1? 1|-J? lf-1?
160 PROGRESSIVE ARITHMETIC
BZSKCISKS
151. Add and subtract :
1. li
2. 3
2|
3. 2|
4. 6f
4f
5 4i
2
Add:
6. 3
4
7. 2i
8. 4i
3
n
9. 5f
34
10. 3f
2f
li
11. From 7f dozen subtract 3^ dozen.
12. How many years are 3^ yr., 2f yr., and 1^ yr. ?
WRITTEN EXSRCISES
152. Add and subtract :
1. 27|
14
2. 46|
314
3. 78
194
4. 51i
26i
5. 47i
39f
Add:
6. 25
38|
19i
7. 37i
234
13
8. 35f
184
404
9. 42|
154
18|
lo. 25|
22f
41f
Find the value of :
*
11. 23 +
m+^H
13.
97-384-
434 + 12^
12. 79-
24i + 16|
14.
36f + 14i
-274-18
FIRST BOOK 161
153. Adding and subtracting fourths.
1. How many fourths are J, J, J,
and ^? how many ones?
How many fourths are f and J ?
how many ones and how many fourths
over?
i+i+i+i=? |+i=? l+i=? |+i=?
2. How many fourths are there in 1? How many
fourths are |-i? 1-i? f-|? 1-|?
How many fourths are f — J^? how many ones?
li-i=? 2i-l=? li-l=? 2i~2=?
3. How many fourths are ^ and f ?
how many ones and how many
fourths over?
How many halves are f ?
Then f and f are how many ones
and how many halves over ?
In answers, for f we should always write ^.
EXERCISES
154. Find the value of :
1. i + f 3. l-i
s.
$i+$i+$i+$i
2. i + i 4. 1|-|
6.
$i-$i-$i-$i
Add and subtract :
7. 5i 8. 6| 9.
2| 2|
8
10. 4f 11. 6
3| • 3|
FIRST PROfl. AH. 11
162
PROGRESSIVE ARITHMETIC
12. What is the sum of $3J, $4f, and $lj?
13. How much more is 3f pounds than IJ poimds?
14. Mrs. James bought 5 gallons of kerosene and at the
end of a week there were 2^ gallons left. How many gal-
lons had she used?
WRITTEN EXERCISES
155. Add and subtract :
Add
24i
16
2. 63i
25i
3. 59|
32f
4. 35
19i
s. 61
33f
13i
24i
m
7. 52|
9
20J
8. 25J
38|
17i
9. 12|
44J
36f
10. 23f
32f
41f
\>
156. Adding and subtracting sixths.
1. How many sixths are there in 1?
How many sixths are f + i? how many
ones and how many sixths over ?
How many are 1 + ^? 2 + ^? 2^ + 2?
2. Fmd l-i; 1-i; f-f; l-f
Howmany arel^-^? 2^- J? 1^-1? 2^-2?
3. How many sixths are ^ + ^? how many thirds f
How many sixths are ^4-^ + ^? how many halves ?
How many sixths are f — ^ ? how many thirds f
In answers we should write ^ instead of f , J instead of
f , and f instead of f .
FIRST BOOK 168
WRITTEN EXERCISES
157. Add and subtract :
Add
45
2. 78
14f
3. 67i
23i
4. 36^
21i
5. 43t
m
d:
14
13i
7. 25f
8. 38i
14i
9. 30f
28|
xo. 16
7f
60f
158. Adding and subtracting halves and fourths.
1. We wish to add f and ^. Can we do so without
changing either fraction ?
To how many fourths is ^ equal?
How many fourths, then, are f and f ?
how many ones and how many fourths
over?
Then what is the sum of f and ^ ?
2. Can you find f — J without changing either fraction ?
Which fraction should be changed ? To what equcd fraction
should it be changed?
Then what is the value of f — f , or of f — J ?
159. Find the value of :
1. i-i 3. i + 2i 5. i + i + i
2. ^ + i 4. If^i 6. i + l-i
J
164 PROGRESSIVE ARITHMETIC
Add and subtract :
7. 2i 8. 7 9. 5| 10. 6i 11. 8|
li 4| 3| 2^ 4|
12. Find the perimeter of an oblong rug 3^ feet long and
2j feet wide.
13. Edna had If qt. of lemonade. When ^ qt. of it
was used, how much was left ?
14. Ralph has earned $2f, and his brother $lj. How
much have both boys earned ?
15. From a pound of sugar, J lb. was used for coffee and
^ lb. for a pudding. What part of a pound was left ?
WRITTEN EXERCISES
160. Find the missing numbers :
1. 25i
2. 42i
3. 58|
4. 58f
5. 61|
12i
26i
37i
22^
48i
Add:
6. 41^
28J
16i
7. 23J
45i
8. 32i
24i
35|
9. 59i
27f
10. 17i
36f
44i
Find answers :
u. 14^ +
18i + 26|
13. 441+391
8^-21i
12. 85|-
28i+13|
14. 76
-i4i-:
30^ + 191
FIRST BOOK
166
161. Halves and sixths, thirds and sixths.
1. Which of the fractions f or ^ must be changed
before we can add them ?
To how many sixths is ^ equal ?
How many sixths are f + f? how
many ones and how many sixths over?
how many thirds over ?
Then what is the sum of f and ^ ?
2. How many sixths are f — f ? how many thirds ?
Then what is the difference between f and ^ ?
3. How many sixths are there in ^? in ^ + ^?
How many halves are ^ -h ^ ? /-^^/v
4. How many sixths are there in ^ — ^? L — ^- — A
EXERCISES
162. Find the value of :
1- i + i
3. l-i
5. 3 + li-2^
2- f + l
*• f-i
6. 4f-2i + 5
Add:
1. ^
4f
8. 6i 9. 41
2i H
10.
5i 11. 3|
li 2|
:5
Find the missing numbers :
12. 8i 13. 4^ 14. 2J
+
3i
n
^
IS.
21
16. 7|
166 PROGRESSIVE ARITHMETIC
17. Mabel picked 4^ dozen violets and If dozen tulips.
How many dozen flowers did she pick ?
18. From a bunch of bananas containing 8f dozen a
dealer sold 2| dozen. How many dozen had he left?
WKITTEir
EXERCISES
163. Add and subtract :
1. 42f
28^
2. 36^ 3.
14*
52f
34*
4. 63i
25*
s.
38|
19*
Add:
6. 14i
46^
7. 31^ 8.
9*
24*
48|
6*
37*
9. 27i
12*
42*
10.
64*
5*
13f
Find answers :
u. 12i
+ 25| + 8|
13. 4I- + 291-
-14*
12. 75-
-13*-24f
14. 88|-17i
+ 8*
15. Anna has a flower bed in the shape of a triangle, the
sides being 22^ feet, 19f feet, and 21f feet long. How far
is it around the bed ?
)16. Homer threw a baseball 4Qf yards , and Alfred 38^
yaids. How much farther did Homer throw it than Alfred ?
17. Louise is 28j years younger than her mother. How
old is her mother, if Louise is 9^ years old?
How old will Louise be in 23f years ?
FIRST BOOK 167
164. Finding parts of numbers.
1. How many are ^ of 6? f of 6? | of 6?
2. Find i of 12; f of 12; | of 12; f of 12.
3. How many are ^ of 20? f of 20? | of 20? f of 20?
fof 20?
4. Find ^.of 30; f of 30; | of 30; f of 30; f of 30;
f of 30.
EXSRCISES
166. 1. Find f of 42.
iof42 = 7; I of 42 = 5 times 7 = 35.
Find:
2. f of 15 6. f of 20 10. f of 48 14. f of 40
3. I of 40 7. f of 36 11. f of 25 is. | of 32
4. f of 45 8. f of 18 12. I of 24 16. f of 50
5. I of 27 9. f of40 13. f of45 i7. f of 54
18. Find the weight of f of a 30-poimd cheese.
19. Find the cost of f of a dozen eggs at 21 cents a
dozen.
20. How nhich will f of a pound of coffee cost at 36
cents a poimd ?
21. George paid 35 cents for a ball and f as much for a
bat. How much did the bat cost ?
22. If it takes William |- of an hour to walk to school,
how many minutes is he on the way ?
168 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
166. 1. Find I of 572.
4 )572
143 We find i of 572 by dividing 572 by 4.
3 i of 572 = 143; | of 572 = 3 times 143 = 429.
429
Find:
2. I of 168 6. f of 720 10. f of 762
3. f of 145 7. f of 455 u. I of 624
4. I of 224 8. f of 516 12. f of 845
5. f of 250 9. I of 896 13. I of 936
14. George can run |- as fast as Edward. How far can
George run while Edward is running 55 yards ?
15. A park contained 63 elm trees and f as many
maple trees. How many maple trees did it contain?
16. Henry has 350 stamps, and Frank has | as many.
How many stamps has Frank ?
17. Helen counted 225 roses in the garden, and |- of
them were white. How many white roses were there ?
18. Stephen's kite string is 120 yards long* and Arthur's
is f as long. How long is Arthur's kite string ?
19. Our snowball bush bore 90 snowballs this year. We
gave away f of them. How many did we give away ?
20. Mr. Avery's salary is $984 a year, and his expenses
are f as much. How much are his expenses a year ?
FIRST
BOOK
169
MULTIPLICATION
•
EXERCISES
167. Multiply at
sight :
1. 72
840
71
410
81
622
3
2
7
8
8
4
2. 61
711
906
843
709
823
6
9
4
2
5
3
3. 85
475
94
386
80
792
10
10
10
10
10
10
4. If 2 hats cost $3, how much will 20 hats cost at the
same price ?
20 hats are times 2 hats.
20 hats will cost times $ 3, or .
5. How long will it take a boy to work 42 problems at
the rate of 6 problems in 5 minutes ?
6. If a woman can make 4 buttonholes in 10 minutes,
how long will it take her, at that rate, to make 36 ?
7. If 2 pairs of shoes cost $7, how much will a dozen
pairs cost at the same price per pair ?
8. A man earns $3 in 8 hours. At that rate how much
will he earn in 72 hours ?
9. Find the charge for telephoning 18 minutes between
two distant places at $5 for every 3 minutes.
170 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
168. Multiply:
1. 465
5
2. 574
6
3. 867
6
4. 745
7
5. 684
7
6. 527
8
7. 488
9
8. 789
8
9. 867
9
10. 994
9
11. Multiply $4.86 by 5.
-, , ^„ Multiply 486 by 5, placing a decimal point
in the product imder the other decimal point.
Wiite the dollar sign before the dollars of
$24.30 ^jjg product. Read the product.
Multiply :
12. $2.40 13. $3.25 14. $1.44 is. $7.75
6 7 8 4
16.
$5.75
7
20.
$6.85
5
24.
$0.75
8
28.
$7.77
7
17.
$9.89
4
21.
$0.95
4
25.
$4.96
7
29.
$4.86
8
18.
$7.65
4
22.
$3.66
6
26.
$6.25
8
30.
$1.85
9
19.
$9.27
5
23.
$8.24
6
27.
$9.40
6
31.
$2.60
9
FIRST BOOK 171
EXERCISES
169. 1. How many are 2 times 5 ? 4 times 5 ? Find the
sum of 2 times 5 and 4 times 5.
2. Find the sum of 2 times 5 and 4 times 6, in this way :
2 times 5 and 4 times 5 are 6 times 5, or 30.
Find the sum of :
3. 7 times 2 and 3 times 2. 6. 6 x 8 and 4x8.
4. 3 times 4 and 2 times 4. 7. 2 x 7 and 5x7.
5. 9 times 6 and 3 times 6. 8. 4 x 9 and 6x9.
9. How many 2's are 10 x 2 and 1x2? What is the
sum of 10 X 2 and 1 X 2? What is the value of 11 x 2?
10. Let us find the value of 12x6. How many 6's
must be added to ten 6's to give twelve 6's ?
12 x 6 = 2 X 6 added to 10 x 6, or 60 + 12, or 72.
11. Find the value of 13 x 5 as follows :
13x5 = 3x5 added to 10x5= .
In the same way find the following products :
12. 12x4 17. 13x6 22. 14x3 27. 11x7
13. 12 x 5 18. 13 X 7 23. 14 x 5 28. 11 x 8
14. 12x7 19. 13x4 24. 15x6 29. 11x9
15. 12x8 20. 13x8 25. 16x4 30. 16x6
16. 12x9 21. 13x9 26. 17x3 3i. 18x5
32. A street car conductor had 16 5-cent pieces in one
pocket. How much money had he in that pocket ?
33. Find the cost of 18 rockets at 3 cents each.
172 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
170.
. Multiply 43 by 12.
43
43
12
12
2 times 43 . . .86
86 (units)
10 times 43 . . .430
43 (tens)
12 times 43 . . . 516
516
Explain the first process.
What figure has been omitted from the second process?
In the second process we multiply 43 by 2 (units) and
write the product 86 as units by placing 6 in units' column.
We then multiply 43 by 1 (ten) and write the product
43 as tens by placing 3 in tens' column.
The right-hand figure of each product is vmtten under the
figure by ivhich we are multiplying.
Multiply :
2. 32 by 12 6. 35 by 13 lo. 64 by 15 14. 31 by 19
3. 41 by 12 7. 27 by 14 n. 33 by 16 is. 50 by 18
4. 56 by 11 8. 62 by 15 12. 18 by 17 16. 84 by 16
5. 51 by 13 9. 73 by 14 13. 22 by 18 17. 92 by 15
18. Multiply 34 by 20.
34 (units) times 34 = (units). Write
20 in units' place in the product. 2 (tens)
680 times 34 = 68 (tens). Write 68 before the 0.
FIRST BOOK
173
Multiply :
19. 24
20
20. 32
30
21. 45
30
22. 42
40
23. 36
50
24. 72
60
25. 84
60
26. 36
70
27. 49
80
28. 66
90
29. Multiply 62 by 23 and test the result.
62 23
186 46
124 138
1426 1426
Teet — The correctness of the result obtained by multiplying 62
by 23 may be tested by multiplying 23 by 62 as in the second
process.
Multiply, and test results :
30. 45 31. 75 32. 61 33. 92 34. 66
24 25 32 31 39
35. 54 36.
58
37. 94
38. 51
39. 68
45
48
29
49
55
40. 64 41.
94
42. 77
43. 82
44. 83
63
69
71
75
79
Multiply:
45. 85 by 81
47.
99 by 88
49.
225 by 12
46. 96 by 95
48.
132 by 11
50.
2f75 by 13
174
PROGRESSIVE ARITHMETIC
Multiply :
51. 462 by 14
52. 585 by 15
53. 332 by 25
57. 122 by 69
58. 118 by 78
59. 106 by 81
63. $2.65 by 39
64. $6.25 by 14
65. $0.96 by 92
54. 261 by 31 60. $1.08 by 88 66. $5.75 by 17
55. 128 by 47 6i. $4.27 by 23 67. $3.64 by 26
56. 135 by 52 62. $0.75 by 84 68. $2.88 by 29
N
WRITTEN EXERCISES
171. 1. Find the cost of 4 pairs of skates at $1.50
per pair.
2. Which of these roofs has the greater area and how
much greater?
3. There are 30 dozen eggs in a case. How many dozen
r, eggs are there in 18 cases ?
\ ^ 4. How many crates of strawberries are there on a train
:L x<rf^'2D cars, each of which contains 225 crates?
5. How much must be paid for 50 crates of strawberries
at $2.85 per crate?
6. A man bought 44 crates of cantaloupes at $2.50 per
crate, and sold them at $3.15 per crate. How much did
he gain on each crate ? on all ?
FIRST BOOK 175
DIVISION
EXERCISES
172. Divide at sight :
1. 7)28 3}24 2)U 5)35 4)36 6)54 8)64 9)63
2. 3)189 2 )168 4 )1648 7 )217 6 )4260 9 )4590
3. 7)2877 6 )3066 2 )1462 8 )4088 3 )1536 9 )2709
Answer quickly :
4. ^ofl8= iofl5= iof20= ^of50 =
5. iof21= iof24= ^of35= iof24 =
6. i of 120= iof88= i of 960= ^ of 100 =
7. ^ of 1200= i of 636= i of 2408= ^ of 1550 =
8. If 3 valentines cost 10 cents, how many valentines
of the same kind can you buy for 40 cents ?
9. Eliza bought 6 small flags for 5 cents. At the same
price how many could she have bought for 25 cents ?
10. One Saturday Hiram saw 24 robins and ^ as many
bluebirds. How many bluebirds did he see ?
11. John planted 40 beans, but only ^ of them came up.
How many did not come up ?
12. Lewis had 20 cents, which he expended for glass
marbles at 4 for 5 cents. How many did he buy ?
13. Anna has 21 cents to buy Easter cards. How many
can she buy at 3 for 7 cents ?
176 PROGRESSIVE ARITHMETIC
WRITTEN
EXERCISES
173. Divide,
testing each
answer :
1.
2.
3.
4)1824
6)3462
7)4466
4.
8)5456
5. 6. 7. 8.
7)5292 6)2970 5 )4445 9 )5553
9. 10. 11. 12.
$8 )17168 $ 9)17074 $8 )$7832 $ 9)$ 8883
13. Find i of $38.72, or divide $38.72 by 4.
4")$ 38 72 Divide 3872 by 4, placing a decimal point
*?9 68 ^^ *^® result under the other decimal point.
Write the dollar sign before the dollars of
the answer. Read the answer.
Test. — 4 times $9.68 = $38.72.
Find the value of the following, testing each answer :
14. ^ of $7.44 17. i of $17.55 20. ^ of $20.22
15. ^ of $9.24 18. ^ of $27.45 21. ^ of $48.85
16. J of $3.72 19. ^ of $31.68 22. ^ of $59.82
Divide :
23. $55.44 by 6 28. $55.58 by 7 33. $47.75 by 5
24. $64.75 by 7 29. $47.34 by 9 34. $97.35 by 5
25. $4374 by $6 30. $31.12 by 8 35. $78.64 by 8
26. $7452 by $6 3i. $96.30 by 9 36. $80.82 by 9
27. $5288 by $8 32. $99.92 by 8 37. $79.76 by 8
FIRST BOOK
177
174. Multiply:
1. 11 11 11.
11 11
11
11
11
11
12 3
4 5
6
7
_8
9
Divide :
a. 11)44 11)55 11)77 11 )110 11)88 11)99
3. 11)^ 11)220 11)33 11 )220 + 33 11 )253
WRITTEN BZESCISBS
1. Divide 253 by 11.
23, quotient
11)253
Subtract 20x11 = 220
23
11)253
22
33 left to be divided
Subtract 3x11= 33
33
33
How many ITs are subtracted from 253 the first time?
How many more ll's are subtracted afterwards?
How many ll's are subtracted in all? Can more ll's
be subtracted? Then how many ll's are there in 253?
(1) Divide . . . Thus, in shorter process, 25 -5-11=: 2
(2) Write quotient figure Write 2
(3) Multiply 2x11=22
(4) Subtract 25-22 = 3
(5) Bring down next figure .... 3 tens -|- 3 = 33
Test, -r 11 X 23 or 23 x 11 should give 253, the number divided.
FIRST PROO. AR. — 12
The
five steps
in
dividing
178
PROGRESSIVE ARITHMETIC
Point out the steps in the following :
672
563
718
11)7392
11)6193
11)7898
66
55
77
79
69
19
77
66
11
22
33
88
^
33
88
Divide :
5. 11)473 7
11)286
9. 11)2585
11. 11)5951
6. 11)385 8
11)517
10. 11)3586
12. 11)4598
13. Divide 420
by 12.
4.
2.
35
12)420
12)420
12)420
48.
24
36
Quotient too large
18
60
Quotient too small
60
Since 42 contains 10 only 4 times, 42 does not contain
12 more than 4 times, but perhaps only 2 or 3 times.
The first figure of the quotient cannot be 4, for 48 cannot
be subtracted from 42. It is not 2, for the remainder 18,
being larger than 12, will contain 12 again. It is 3, for
3 X 12 can he subtracted from 42, and the remainder 6 is
less than 12.
FIRST BOOK 179
Since 60-«-10 = 6, try 5 for the second figure of the
quotient. Since 5 x 12 = 60, there is no remainder. Then
the quotient is 35.
Divide and test :
14. 12)276 16. 12)636 18. 12)2580 20. 12)1704
15. 12)384 17. 12)528 19. 12)2808 21. 12)5052
Find quotients :
22. 616^11 26. 957-*- 11 30. 1404 -^ 12
23. 648-5-12 27. 912-5-12 31. 2100-5-12
24. 803-^11 28. 1353-11 32. 2057-11
25. 564-*- 12 29. 3465-11 33. 6248-11
175. Divide :
1. 2)6 $2)$6 2 tens ) 6 tens 20)60
— times — times — times — times
2. 3U2 3 dimes ) 12 dimes 3 tens ) 12 tens 30 )120
3. 4)8 4 doz. )8 doz. 4 tens ) 8 tens 40)80 40)800
WRITTEN EXERCISES
1. Divide 840 by 20.
2(1)) 84(b ^*^'"' ^* *^^® ; 20 = 2 tens.
-^o^ 84 tens contains 2 tens as many times
as 84 contains 2.
Then cut off or cancel the last figure of each number and
divide 84 by 2. What is the quotient ?
180 PROGRESSIVE ARITHMETIC
2.
ride :
640 by 20
8.
$650 by $50
14.
720 by 60
3.
960 by 30
9.
$420 by $60
15.
490 by 70
4.
750 by 30
10.
$870 by $30
16.
540 by 90
5.
360 by 20
11.
$1200 by $50
17.
5600 by 80
6.
760 by 40
12.
$1560 by $40
18.
5120 by 80
7. 350 by 50 13. $3450 by $50 19. 6580 by 70
20. Divide 1395 by 31.
.. 31 is not contained in 1 nor in 13, but is
contained in 139 about as many times as
31 ) 1395
1 94 30 ^^ contained in 139, or about as many
-r^ times as 3 is contained in 13, or 4 times.
.«« Write 4 in the quotient over 9, the last
— - figure of 1395 used. Multiply 31 by 4,
giving 124. Subtract 124 from 139, giving 15 for a
remainder. Does this remainder show that 4 is the correct
figure in the quotient ? Tell why.
Tell how the process is completed. Test the answer.
Find quotients and test :
21. 525^21 28. 1071-21 35. 1364-^22
22. 672-21 29. 1147-31 36. 1088-32
23. 744-^31 30. 1224-51 37. 1134-^42
24. 496-31 31. 2132-41 38. 1890-52
25. 945-21 32. 2601-5-51 39. 1664-52
26. 943 -H 41 33. 1488-31 40. 1536-^32
27. 682-^22 34. 1100-»-22 4i. 2444-52
FIRST BOOK
181
Divide:
42.
5661 by 51
50.
1672 by 22
58.
Sepi by 61
43.
6500 by 52
51.
2079 by 21
59.
8733 by 71
44.
9828 by 42
52.
2728 by 31
60.
9020 by 82
45.
9922 by 41
53.
3040 by 32
61.
2976 by 62
46.
7392 by 32
54.
2856 by 42
62.
4608 by 72
47.
9982 by 31
55.
3567 by 41
63.
3645 by 81
48.
9086 by 22
56.
4284 by 51
64.
3094 by 91
49.
9345 by 21
57.
3900 by 52
65.
4784 by 92
WRITTEN EXERCISES
176. 1. If a gallon of choice maple sirup costs $1.12,
how much will a quart of it cost at the same price ?
2. Mrs. H^y bought half a dozen spoons for $3.90. How
much did they cost apiece ?
3. PhiUp bought an 8-po\md basket of cherries for $1.20.
How much did he pay for them per pound ?
4. A fruit grower packed 3000 pears in boxes holding
60 pears each. How many boxes did he use ?
5. A man boarded 8 days at a hotel and was charged
$20.00. How much did it cost him a day?
6. Dora's hoop rolls 11 feet in making one turn. How
many turns will it make in going 154 feet?
7. I have 1001 strawberry plants to set out in 11 rows.
How many plants are there for each row ?
8. There were 132 bananas in a bimch. How many
dozen bananas were there in the bunch ?
182 PROGRESSIVE ARITHMETIC
REVIEW
EXERCISES
17
7. Add at sighl
k:
1.
$1.23
$2.25
$0.26
$1.60
$0.60
.30
.33
1.40
.25
.40
2.
$2.70
$3.25
$4.24
$3.26
$1.30
.14
.41
.44
.70
.55
3.
20
122
31
48
347
264
36
705
250
21
4.
50^
50^
80^
80^
70^
70^
40^
50^
60^
20^
40^
30^
50^
90^
5_
10
Hi
2f
2f
6^
i
n
li
i
2
i
11
1
i
6.
4i
H
m
^
H
16J
f
1
i
i
13
±
i
m
Subtract at sight
I
7.
$1.50
$2.75
$3.87
$5.66
$2.98
.40
.25
.37
.45
.50
8.
$2.56
$0.99
$3.56
$7.48
$4.29
.43
.83
.05
.15
.25
FIRST BOOK 183
Tell the missing numbers or amounts of money :
9. 80 10. 75 11. 40 12. 32 i3. 100
4- - + + . -
100 50 65 52 50
14. $1.00 15. $ 16. $ 17. $1.00 18. $1.50
-.50 -.60 -.80 -.70 +
$ $.40 $.70 $ $2.00
19. 1 20. 3 21. 5i^ 22. 3^ 23. 2^
+ + + +
If 2i 6 ^ 3|
24. $1-$^=$ , or p.
25. $l-$f = $ , or ^.
26. $J+$ = $i or ^.
27. Add each number of cents outside . 20<^
the ring to 100 cents, or $1, and then to ®V
99 cents. Give answers in dollars and q,m 99 cents L^^
cents. Add rapidly in either direction. V 100 cents
28. Next subtract each number of Wf^v..__jX^9^
cents outside the ring from 99 cents and
then from $1, or 100 cents. Give answers in cents. Sub-
tract rapidly in either direction.
Subtract from 99^, then from $1 :
29. 79^ 32. 58^ 35. 55^ 38. 84^
30. 69^ 33. 88^ 36. 85^ 39. 76^
31. 49^ 34. 68^ 37. 35^ 40. 43^
v\.*
184 PROGRESSIVE ARITHMETIC
Find the cost of :
41. 3 dozen camera films @ 40^.
This means "3 dozen camera films at 40 cents a dozen."
42. Developing 4 films at 24^ a dozen.
43. Printing and mounting 7 photographs @ 9^.
44. 2 tennis balls at 30^ each; and a racket, $2.25.
45. A baseball, 25^; a bat, 20^; and a glove, 80^.
46. A fishing rod, 95^; hooks, 5^; and a line, 10^.
47. How much rope does Ralph need i
Y to make a swing like this? It reaches t o ^
^'7 \^ • jyjtliin 1 foot of the ground. The limb is
.■^^ 15 feet from the ground. The sides are 2^
feet apart. It takes S^ feet of rope to tie ||| '|
both ends of the rope to the limb. M i
48. A grocer bought raspberries at ^"" ^'^
9^ a box and sold them at 12|^ a box. How much did
he gain on every box that he sold ?
49. If 3 boxes of strawberries cost a quarter of a dollar,
how much will a dozen boxes cost at this price ?
50. Miss Smiley bought 6 bimches of rhubarb at 7^ for
2 bunches. How much did she expend for rhubarb ?
51. If a dozen eggplants cost 90^, how much will 4
plants cost at the same price ?
52. If 3 bimches of beets cost 5^, how many bunches at
this price can be bought for half a dollar ?
53. If j hnnphfts of mint mst 30^, how much will 9
bunches cost at the same price a bimch ?
FIRST BOOK 186
WRITTEN EXERCISES ^
178. 1. Write in figures and add : six dollars eight cents,
seventeen dollars, ten dollars seventy-five cents, eight dollars
seven cents, ninety-two cents.
Add the following, testing the sum of each column as
you find it :
2. 3. 4. 5. 6.
$18.45 $68.27 $29.90 $77.67 $58.00
6.96 9.39 .87 16.08 6.86
28.79 15.83 40.66 4.82 27.99
7.
8.
9.
10.
11.
$39.95
$17.77
$12.00
$29.95
$35.99
8.49
9.36
8.85
8.78
9.87
6.67
8.98
7.76
7.89
7.97
16.84
7.69
.95
9.88
16.89
.88
8.67
8.57
7.96
.85
8.75
38.84
9.29
,.99
■ 18.85
12.
13.
14.
IS.
16.
$36.64
$18.81
$16.68
$27.00
$42.75
8.85
8.98
6.79
6.95
8.55
13.37
17.96
5.99
7.88
9.95
9.69
7.87
12.09
9.99
9.85
7.89
6.49
8.69
4.97
8.95
9.58
8.89
9.21
8.98
9.95
10.67
7.95
20.65
2.99
9.95
186 PROGRESSIVE ARITHMETIC
Subtract :
17. 18. 19. 20. 21.
$10.00 $10.00 $10.00 $10.00 $10.00
8.68 7.85 9.62 9.23 8.55
22.
23.
24.
25.
26.
$20.00
$20.00
$15.00
$25.00
$50.00
18.75
15.67
12.70
22.52
47.25
Multiply :
27. 78 by 64 3i. 223 by 36 35. 92 by 85
28. 96 by 73 32. 119 by 59 36. 89 by 89
29. 89 by 56 83. 176 by 48 37. 96 by 95
30. 87 by 78 34. 365 by 27 38. 99 by 94
Divide :
39. 4386 by 51 44. 5538 by 71 49. 6561 by 81
40. 4828 by 71 45. 5734 by 61 so. 5904 by 72
41. 4650 by 62 46. 5332 by 62 si. 8281 by 91
42. 4779 by 81 47. 6039 by 61 52. 7872 by 82
43. 4992 by 52 48. 4176 by 72 S3. 8740 by 92
Find answers :
54. 30x24 S9. 740-*- 20 64. f of $14.80
55. 40x81 60. 760-*- 40 65. f of $16.50
56. 60x75 61. $1050-!- $70 66. f of $11.76
57. 70x32 62. $1120 -^ $80 67. f of $21.45
58. 80x47 63. $1330 -J- $90 68. f of $38.10
FIRST BOOK
187
69. One day this shoemaker did the following work :
Soling and heeling 1 pair men's shoes, $1.25, and 2 pairs
ladies' shoes @ 75^; sew-
ing 4 seams @ 10^; 3
patches, 10^, 15^, 20^.
How much did he receive
for this work?
70. Find the receipts that
day for the work of an as-
sistant : 1 pair sewed oak
taps, $1.00; 2 pairs nailed
taps @ $ .75 ; 3 pairs leather
heels® $.25.
71. Another assistant put on a pair of rubber soles and
heels, $1.50; 3 pairs rubber heels @ $.50; and cemented 3
patches @ 10^. Find the receipts for his work.
72. Find the total receipts of the shop that day.
Find the cost of the following tools and supplies :
73. 4 knives @ 13^; 2 hammers @ 30^; 2 heel burnishers,
25^ and 40^; 3 shoe rasps @ 35^; 2 doz. awls @ 10^.
74. A side of sole leather, 27 lb. @ $.33; 8 lb. patches
@ $.38; 4 doz. pairs half soles @ $2.25, and f doz. pairs @
$3.20.
75. 10 balls thread at $.25 for 2 balls; | doz. balls
wax @ 10^; 4 oz. bristles @ $.85.
76. 3 qt. pegs @ 5^; 4 lb. nails @ 4^; 8 lb. nails @ 10^.
77. 5 lb. sheet rubber @ $.55; 3 bottles cement @9^;
12 pairs rubber heels @ $ .20.
188 PROGRESSIVE ARITHMETIC
EXERCISES
179. Make and solve problems about the following :
1. Ruth is 9^ years old ; Pauline is 8^ years old.
2. A boy had $lj and afterward spent $^,
3. A girl bought a pie, ate J of it, and gave J away.
4. Alfred had 42 marbles. He lost ^ of them.
5. Horace bought some tissue paper for a kite at 3
sheets for 2 cents.
6. The tail of Horace's kite was 6 yards long at first.
Afterward Hora^ce cut oflf 4 feet of it.
7. The kite string was 180 feet long. We often measure
string in yards.
8. Edward spent ^ of his money for a goat and ^ of his
money for a wagon.
9. Patrick had $1 and bought several rosebushes at 20
cents each.
10. JuUa planted 300 sweet peas. Some did not come
up.
11. It takes 3 weeks for eggs to hatch into chickens.
The hen has been sitting 9 days.
12. Edna and Mabel colored 2 dozen eggs for Easter.
One third of them were red and two thirds were blue.
13. A horse can gallop 20 miles in 2 hours.
14. Frank has 60 cents. The price of oranges is 3 for
10^. The price of bananas is 20^ a dozen.
15. Some berry pickers picked 8| crates of strawberries
in the forenoon and 4^ crates in the afternoon.
PART III
READING AND WRITING NUMBERS
180. 1. Count by tens to 100; by hundreds to 1000; by
thousands to 10,000 ; by ten-thousands to 100,000 (100 thou-
sand); hy hundred-thousands to 1,000,000 (1000 thousand,
or 1 million).
2. How many tens are there in 100? hundreds in 1000?
thousands m 10,000? ten-thousands in 100,000? hundred-
thousands in 1,000,000?
3. Count by thousands from 10 thousand to 20 thousand,
thus: "10 thousand, 11 thousand, 12 thousand," etc.
Count by thousands from 40,000 to 50,000.
4. To help in reading numbers, we use commas to sepa-
rate the figures into groups of three, beginning at the right.
These groups are called periods.
There may be only one or two figures in the left period.
5. Read :
20,000 22,000 36,000 80,000 125,000
21,000 25,000 57,000 99,000 342,000
6. Write in figures :
Thirty thousand. Ninety-nine thousand.
Thirty-eight thousand. One hundred thousand.
Seventeen thousand. Nine hundred sixty thousand.
Forty-seven thousand. One million.
189
190 PROGRESSIVE ARITHMETIC
7. The number 264,895 is composed of 264 thousands,
and 895 units; and is read, "Two hundred sixty-four
thousand, eight hundred ninety-five.''
EXERCISES
181. 1. Read, and then write in words :
19,632 40,285 278,718 580,058
52,969 64,047 352,387 709,045
94,151 56,309 485,704 920,004
73,100 81,006 246,070 800,025
2. Write in columns, with units under units, tens under
tens, etc. :
Seventy-five thousand.
Eighty-seven thousand, one.
Twenty-six thousand, thirty.
Sixty thousand, four hundred eighteen.
Forty-four thousand, eight hundred seventy.
Ninety-seven thousand, three hundred fifty-two.
One hundred seven thousand, three hundred ninety.
Five hundred thirty thousand, eighty-three.
Nine hundred sixteen thousand, five hundred four.
Six hundred thousand, four hundred sixty-seven.
Three hundred sixty-five thousand, fifteen.
Four hundred seventy-eight thousand six hundred
seventy-seven.
Seven hundred eighty-three thousand, eight hundred
thirty-four.
Nine hundred ninety-nine thousand, nine hundred
nii:iety-nine.
FIRST BOOK 191
ADDITION AND SUBTRACTION
EXERCISES
182. Add and subtract rapidly :
1. 38 43 55 72 94 69 51 86
10 30 20 40 60 30 40 50
65
72
98
56
84
93
78
67
40
30
60
20
50
40
20
40
3. 47 First add the tens of one number to the
+ 25 whole of the other and then the units to
"~ that result, thus: 47 + 20 = 67; 67 + 5 = 72.
Add rapidly in this way: "47, 67, 72."
In the
same way
add:
4. 48
15
• 24
38
43
29
36
35
22
69
55
38
77
17
31
49
5. 34
59
65
25
28
43
57
29
48
38
64
27
26
66
88
19
Subtract rapidly
in this
way:
"85,
25, 19."
6. 85
66
32
14
56
28
45
17
78
49
33
16
92
57
84
69
7. 72
48
61
35
43
25
57
38
94
46
62
35
47
29
73
36
192 PROGRESSIVE ARITHMETIC
8. Two electric cars were chartered for 83 children for
an excursion to Ocean Beach. 45 rode in the first car.
How many rode in the second ?
9. Thirty-six minutes after starting they reached Castle
Rock, and after another period of 48 minutes they arrived
at Ocean Beach. How long were they on the way ?
10. The conductor said that it was 18 miles to Castle
Rock and 25 miles farther to Ocean Beach. How far was
it to Ocean Beach ?
11. The children collected 37 starfish and 25 sea urchins.
How many sea animals did they collect ?
12. They collected 44 different kinds of shells for their
school cabinet, which already contained 26 of these kinds.
How many new kinds did they find ?
13. They collected 55 specimens of rock, but kept only 17
of them for the cabinet. How many did they throw away ?
EXERCISES
183. 1. Count by 2's from 1 to 99 ; by 3's from 2 to 98 ;
by 4's from 3 to 99; by 5's from 4 to 99.
2. Count by 6's from 1 to 97 ; from 3 to 99. Count by
7's from 2 to 100; from 5 to 96.
3. Count by 8's from 4 to 100 ; from 7 to 95. Count
by 9's from 5 to 95; from 8 to 98.
4. From 100 count backward by 2's to ; by 3's to 1 ;
by 4's to 0; by 5's to 0; by 6's to 4; by 7's to 2; by 8's
to 4; by9'sto 1.
FIRST BOOK
193
These columns have been added and tested in less than
2 minutes. Practice until you can do as well or better.
3 6. 7 7. 1 8. 9 9. 5 10. 8 11. 7 12. 9
4
6
2
8
2
7
6
8
6
a
2
9
9
5
9
9
8
4
1
7
7
9
8
7
5
5
4
3
9
4
7
2
2
6
7
4
8
8
8
5
7
7
3
6
9
a
9
4
1
8
6
7
8
9
9
8
a
9
5
2
7
1
8
7
9
4
7
8
8
5
7
3
5
5
4
9
7
8
9
BZEBCISES
184. Tell answers at sight :
1. 3i 8f 2J 7f
+ 5i -4i +5i -3i
6i 4^ 9f
-2i +5i -7i
2. 55
43
78
61
89
34
95
-32
+26
-34
+28
-54
+ 63
-44
3. 75
63
47
54
25
67
82
+34
+76
+ 81
+ 93
+84
+ 72
+ 67
4. 103
-43
126 114 165 148 153 137
-36 -54 -85 -63 -71 -45
FIRST PROO. AR. 13
194
PROGRESSIVE ARITHMETIC
EXERCISES IN MAKING CHANGE
186. In these exercises use toy money, if it is obtain-
able; if not, use colored slips of paper — a different color
for each coin. Write on
each slip its value.
Give each pupil, except the
storekeeper, a dollar and two
half dollars. The storekeeper
may have several of these coins;
also quarter dollars, dimes, 5-
cent pieces, and 1-cent pieces.
Let each pupil be the store-
keeper for five or ten sales, and
let a record be kept of his mis-
takes, the others keeping close
watch of his work and taking
turns as buyers. The buyer
has first chance to correct
errors. If he neglects to do so, it counts against his record for the
day, and the class may then make corrections.
When the storekeeper announces the cost, the buyer pays
with as few and as small coins as possible. The store-
keeper then counts out the change, naming the cost first.
1. Emily buys three cans of com, 25^; and 1 lb. of cof-
fee, 39^. The storekeeper announces the cost, ''64 cents."
Is he right ?
Emily hands him $1, and he hands back a cent, a
dime, and a 25-cent piece, saying as he does so, ''64 cents,
65, 75, 1 dollar." Is he right?
2. Buy of the storekeeper 2 doz. pickles @ 10^.
3. Buy 6 lb. rice at 7^. 4. Buy 5 qt. beans @ 8/.
FIRST BOOK 195
/
Conduct these exercises as suggested on the previous
page and supply others, if needed, by changing prices.
5. 2 lb. tea @ 40^.
6. 3 lb. honey @ 17^.
7. 4 lb. almonds @ 18^. ^
8. 1 lb. cocoanut, 19^; and 8 lb. prunes @ 8^.
9. 10 lb. sugar @ 6^; and 2 lb. codfish @ 13^.
10. A pint bottle of olive oil, 35^; and a pound of bak-
ing powder, 60^.
11. 3 lb. lard @ 14^; and 1 sack flour, 80^.
12. ^ lb. chocolate @ 40^; and 2 lb. mixed nuts @ 18 ^
13. 1 qt. maple sirup @ $1.00 a gal.; and 3 lb. butter
@ 30^.
14. 4 lb. figs @ 15^; and 5 lb. raisins @ 20^.
15. 9 doz. clothespins at 5^ for 3 doz.; and a clothes-
line, 17^.
16. 1 doz. bars laundry soap at 25^ for 6 bars; and j^
doz. cakes toilet soap at 8^ a cake. * »
17. 5 lb. cheese @ 16^; and 4 doz. eggs @ 24^.
18. 6 boxes breakfast food at 25^ for 2 boxes; and 8 lb.
oatmeal @ 4^.
19. 3 lb. cornstarch @ 9^; J lb. mustard @ 32^; and
2 gal. kerosene @ 12^.
20. 1 lb. dates @ 8^; 3 doz. oranges @ 40^; and 1 doz.
lemons @ 25^.
21. Basket of peaches, 75^; 3 baskets of grapes @ 17^;
and 2 bunches of celery @ 18^.
196 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
186. The exercises in the first row have been added and
tested in less than 4 minutes, and all on the page in less
than 15 minutes. Practice until you can do better.
1.
2.
3.
4.
5.
$87.54
$136.49
$275.96
$342.79
$129.88
95.75
24.68
140.03
87.60
241.62
14.63
30.00
9.71
23.94
108.74
28.34
572.14
67.99
209.48
194.16
85.47
98.08
332.48
125.75
237.95
30.45
62.71
96.83
235.22
108.24
6.
7.
8.
9.
10.
$94.86
$124.75
$208.64
$312.17
$189.00
78.09
246.89
100.36
84.03
75.63
7.47
37.41
9.99
9.86
82.97
75.85
90.17
7.58
67.94
245.92
8.93
53.74
215.96
196.16
93.69
69.00
368.43
106.25
58.38
137.05
82.46
• 241.00
315.45
125.60
100.89
11.
12.
13.
14.
15.
2,341
34,231
57,243
63,789
47,680
1,462
53,645
61,502
25,641
86,239
3,024
12,345
3,426
31,052
14,168
2,232
32,204
7,562
87,465
90,753
5,324 50,631 34,214 46,346 59,646
4,101 27,341 3,623 20,574 76,894
1,234 31,426 84,563 74,683 92,687
FIRST BOOK 197
Add and subtract :
16. 57i 17. 83| 18. 35| 19. 62f 20. 75|
32| 41i 17i 28| 49f
21. 89| 22. 64| 23. 48f 24. 56J 25. 91|
46| 35| 29| 371 53|
From 93,064 subtract 57,625.
93,06^^^nuend \ Test. — Add the remainder, to the
57,625j\^ subtrahend ) subtrahend. The sum should equal the
35,439, '
^mainder/
minuend.
Subtract and test:
Practice until you can
5 minutes.
do exercises
27-46 correctly
in less than
27.
52,849
24,638
28.
87,246
9,384
29.
20,000
374
30.
68,930
12,598
31.
94,328
72,789
32.
$374.60
98.73
33.
$506.03
174.45
34.
$136.98
59.89
35.
$473.56
87.95
36.
$213.12
35.16
37.
$574.33
293.84
3a
$304.20
92.50
39.
$623.59
45.39
40.
$840.00
463.25
41.
$419.35
243.77
42.
$200.00
173.20
43.
$646.84
375.96
44.
$900.06
85.29
4S.
$507.13
168.19
46.
$724.05
299.16
198 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
187. 1. The sum of two numbers is 8391, and one of
them is 5624. What is the other number?
2. A boy's kite string was broken into three pieces,
32j yai;ds, 57j yards, and 41^ yards long. How long
was the string?
3. Shakespeare was bom in 1564 and died in 1616.
How old was he when he died ?
4. Fby's watch cost her father $32.50, and the chain
$12.35. How much change did he receive out of $50.00?
5. From a 1000-gallon tank of water 573 gallons ran
out, and 247 gallons ran in. How many gallons were
there then in the tank?
Standing Army of the United States
Officers
Enlisted Men
Cavalry .
760 .
12,728
Infantry .
. 1600
26,193
Artillery. . •
661
. ' . 17,762
6. How many officers are there in these three branches
of the army? how many enlisted men? how many of
both?
7. How many more enlisted men are there in the in-
fantry than in the cavalry ? than in the artillery ?
8. Additional branches of the army, as engineers,
scouts, hospital corps, etc., are not included in the table
above. If the total strength of the army is 3856 officers
and 60,385 enUsted men, how many officers belong to these
branches ? how many enlisted men ?
>^
y ^ y FIRST BOOK 199
^ ^ FRACTIONS
188. 1. How many whole circles do you see? how many
fourths of a circle over ?
Write two ; three
fourths; two and three
fourths.
2. A number that stands for one or more whole things
is called a whole number, or an integer.
3. An integer and a fraction together are called a mixed
number.
Add and subtract these mixed numbers :
4. 3^ 5. 7| 6. 5^ 7. 8^ 8. 6|
2i 4| 3| 5i 3i
WRITTEN EXSRCISES
68i
42^
189. 1. From 68i subtract 25|.
Can you subtract f from J?
Then take 1 from the 8 to unite with \.
How many fourths are 1 4- J, or f-fj?
How many fourths are |- — f ? how many halves ?
Write ^ under the fractions.
How many units have been taken from the whole nimi-
ber? Then subtract 25 from 67 instead of from 68.
Read the entire answer. Tell how you found it.
Add and subtract :
2. 45i 3. 88i 4. 53^ 5. ^^ 6. 951
24| 43| 25f 38| 57|
200
PROGRESSIVE ARITHMETIC
7. A tank contained 98j gallons of kerosene. How
many gallons were left after 22^ gallons had been sold ?
8. Ellen has saved $25^, and her brother $15f . How
much more money has Ellen saved than her brother?
9. An ice house is 152f feet long and 56f feet wide.
How much greater is its length than its width?
10. From a cheese weighing 30^ pounds a grocer sold
6| pounds to one person and 3j pounds to another. How
many pounds of the cheese were left ?
190. Eighths and twelfths.
1. This rule is 4 inches long,
parts is the first inch divided?
Into how many equal
i
1
i
2
f
f
f
3
4
2. One of the eight equal parts of anything is called
one eighth of it.
3. Look at the second inch and tell how many eighths
are equal to ^ ; to f .
4. Look at the third inch and tell how many eighths are
equal to J ; to f ; to f ; to |^.
5. In the right-hand inch point to |^ in. ; J in. ; \ in.
6. Draw a rule 6 inches long and divide it into halves,
fourths, and eighths of an inch. How many half inches
will it contain? how many quarter inches? how many
eighth inches?
FIRST BOOK
201
7. Into how many equal parts is this oblong
divided?
8. One of the twelve equal parts of anything
is called one twelfth of it.
9. How many twelfths of this oblong are
shaded? how many halves?
How many twelfths are equal to ^?
10. How many twelfths of this oblong are
shaded? how many thirds?
How many twelfths are equal to ^?
11. Look at the oblong again and tell how
many twelfths are equal to f.
12. Look at this oblong and tell how many
twelfths are equal to J; to f.
13. How many twelfths are equal to ^? ^
how many are equal to f ? m
14. How many inches are there in a foot ? Then what
part of a foot is 1 inch ? How many twelfths of a foot are
2 inches ? how many sixths of a foot ?
15. What part of a foot are 3 in. ? 4 in. ? 5 in. ? 6 in. ?
C
WRITTEN EXERCISES
191. Draw lines and divide them to show that :
1. I=i
»• A=i
9- i = l
13.
A=l
2. A=i
6. i=A
10. M = f
14.
f=f
3. i = |
^. i=A
11- 1 = 1
15.
l=A
*. A = i
8. i=A
". A=i
16.
i=H
202 PROGRESSIVE ARITHMETIC
192. Comparing fractions.
1. Into how many equal squares is this oblong divided?
How many squares are there in ^ of it ? in J of it ?
Which is greater, ^ of the oblong or J
of it? how many squares greater? how,
many twelfths of the oblong greater?
2. How many squares are there in ^
of the oblong? in ^ of it?
Which is less, ^ of the oblong or ^ of it? how many
squares less ? how many twelfths less ? how many sixths ?
3. Which is greater, ^ of the oblong or ^ of it ? what
part of the oblong greater?
4. Looking at the oblong compare j^ and ^; ^ and f.
WRITTEN EXERCISES
193. Draw an oblong 1 inch long and ^ inch wide, and
divide it into squares J inch on a side.
Looking at your oblong, compare :
1. ^ and ^ 2. J and ^ 3. ^ and f 4. f and f
Draw oblongs or lines, and dividing them into parts,
compare :
5. ^ and ^ 9. ^ and ^ 13. f and f
6. ^ and f 10. ^ and ^ 14. f and f
7. ^ and f 11. f and ^ 15/ f and |
8. ^ and I 12. f and ^ 16. f and ^
FIRST BOOK
208
194. Adding and subtracting eighths.
1. How many eighths are ^ + f ? how many ones and
how many eighths over? how many
ones and how many fourths' over?
How many eighths are -g^ — f? how
many halves?
i+i=i i-|=? l+i=? l-i=?
2. Is it possible to add f and ^ without changing either
of the fractions ? How many eighths are
there in ^? Then, how many eighths
are 1+^, or f +f? how many ones
and how many eighths over?
How many eighths are f — ^, or f — |?
3. Find the sum :
c^
i+ i +
= f +
A
$
+ f =
EXERCISES
195. Do as the signs indicate, giving results promptly :
1- i + i 5. f-i 9. i + i 13. i-i
2. 1-1 6. i + l 10. l + i 14. i + f
3. f + i 7. i + i 11. f-l 15. i + i
Add and subtract :
18. 6J
17. 4|
2|
li
19. 8|
5|
20. 5^
21. 9i
6i
204 PROGRESSIVE ARITHMETIC
22. i+| + |=? 24. i+J+l = ? 26. |4-i + i = ?
23. i-| + f=? 25. | + 1-|=? 27. ^ + i-l = ?
28. Some children ate | of a watermelon. What part
of t^e melon was not eaten ?
29. Earl caught two trout, one weighing J lb. and the
other f lb. How much did both weigh ?
30. When Eleanor had used 3| lb. of butter from 8J lb.
that she bought, how many pounds were left ?
31. A druggist made 2| gal. of strawberry sirup and J
gal. less of pineapple sirup. How much sirup did he make ?
WRITTEN EXERCISES
196. 1. From 62^ subtract 38^.
62J = 62| = 61-V^
38| = 38| = 38|_
23|
Add and subtract :
2. 47i 3. 68J 4. 36| 5. 75^ 6. 41^
24| 42| 19| 38| 21i
7. 56i 8. 84| 9. 65| 10. 90| ii. 72|
29| 37| 28| 341 46|
12. John weighs 71| lb. and Edward 64f lb. ' When both
ride on their pony, what weight does the pony carry ?
13. Edward drew on his cart 24| lb. flour, 16 lb. sugar,
^ lb. mustard, and | lb. ginger. How much did the load
weigh ?
FIRST BOOK 205
197. Adding and subtracting twelfths.
EXERCISES
1. Find the sum and the difference of ^ and ^.
Solutions. H + i^ = i^ = 1t\ = Hf *^® sum.
H - 1^ = A = i> *^® difference.
2. Find the sum and the difference of ^V ^^^ i-
Solutions, t^ + i = tV 4- tu = ir^ *^® sum.
A - i = A - A = t\ = i <^^e difference.
Find the sum and the difference of :
3.
^ and^
7. ^ and ^
11.
1 and ^
4.
iand^
8. ^ and I
12.
f and,^
5.
f and^^^
9. ^ and i
13.
iiandf
6.
land 3^
10. ^ and f
14.
li and ^
WRITTEN EXERCISES
98
>. Add and subtract :
1.
45H 2.
31i
54f
3. 48xV ♦•
33A
111
5. 64J
32H
6. 87i 7. 93^^ 8. 75^ 9. 68^ lo. 81^^
52^ 65|_ 36|_ 29^ 45|
Do as the signs indicate :
U- A + A + f "• l-A + i 13. 1 + ,^-f
206 PROGRESSIVE ARITHMETIC
14. Helen's height is 4^1^ ft. and her mother's is 5^ ft.
How much taller is Helen's mother than Helen ?
15. Fred rowed down the river for 2|- hr., and it took
him 3^ hr. to row back. How long was he gone ?
16. Richard could jump 3^ ft., but by running he could
jump 6^ ft. How much farther could he jump by running ?
199. Adding and subtracting halves and thirds.
1. Can you add the fractions ^ and ^ as they stand?
Can you subtract one from the other?
2. How many sixths are there in ^ ? in J ?
3. Add f and f. Subtract f from f .
4. What must be done to different kinds of fractions
before they can be added or subtracted ?
SXBRCISSS
200. Do as the signs indicate :
1- l + i »■ i-i
5.
li-j
.2. i + l 4. I-i
6.
H-i
Add and subtract :
7. 15f 8. lOi 9. 17^
8i 6i 5i
10. l^
iif
11. K
1
12. How many hours are 11 J hours and 3^ hours?
13. What is the sum of Sf years and 7^ years ?
14. Find the difference between 6^ yards and 4f yards.
FIRST BOOK 207
201. Adding and subtracting thirds and fourths.
WRITTEN EXERCISES
1. Find the sum of ^ and J.
Solution. ^ + i = ^4^ + ^ = ^.
2. Subtract f from f .
Solution. | - | = ^^ - ^ = ^.
Find answers :
3. l + i 5. f-i 7. i + l 9. li-i
4. t-i 6. I+I 8. i-i 10. IJ-I
11. 23J 12. 54f 13. 76J 14. 27i 19. 63^
+ 42^ -19i -38^ +46f -24f
24. 36|
2S. 41|
+
+
94i
78|
16. 82J 17. 38i 18. 14| 19. 66f 20.
-56f +45| -h83| -29J -57f
Find the missing numbers :
21. 38i 22. 24| 23. 52f
-h + +
62^ 73| 81i
26. If it takes 3^ hr. to drive to Schuyler Falls and
f hr. to go by train, how much time does it save to go by
train ?
27. It takes 14f yd. of carpet for our hall and lOf yd.
for the stairs. How many yards are needed for both?
28. A bunch of bananas contained lOf dozen. How
many dozen were left after 6j dozen had been sold ?
208 PROGRESSIVE ARITHMETIC
202. Finding parts of numbers.
EXEKCISIS
1. Find i of 12; ^ of 15; | of 15; J of 20; f of 20;
J of 25; I of 25.
2. How many are ^ of 18? | of 18? ^ of 30? | of 30?
f of 30? ^of 36? iof 36?
3. Find i of 40; | of 40; ^ of 48; | of 48; i of 56;
I of 56; I of 64; | of 80.
Find:
4. iof30
9.
iof72
14.
f of 28
19.
|of45
5. ^of90
10.
iof46
15.
|of 35
20.
f of 36
6. iof80
U.
iof 39
16.
|of 40
21.
f of 54
7. ^of55
12.
iof 88
17.
fof 60
22.
|of 64
8. |of42
13.
|of24
18.
|of48
23.
^of 32
84. How many minutes are there in J of an hour? in J
of an hour ?
25. If you breathe 18 times in a minute, how many
times do you breathe in f of a minute?
26. Of the 36 boys in the third grade last year f were
promoted. How many were promoted ? How many were
not promoted ?
27. A hen had 12 chickens. If f of them were yellow
and the rest black, how many were there of each color?
28. Kenneth had 45^, and he paid f of it for a purse.
How much did he pay ? How much did he have left ?
FIRST BOOK
209
203. Find:
1. ^ of 336
f of 423
^ of 648
I of 512
WRITTEN BZBRCISBS
2.
3.
4.
5.
6.
7.
f of 408
I of 744
i of 872
I of 968
9.
10.
U.
12.
I of 1264
f of 3656
I of 5472
i of 8688
4.'
13. Since each part of rope 6 sustains
^ the weight of the barrel, the man must
pull only ^ its weight to raise it. How
many poxmds must he pull to raise the
barrel of flour, which weighs 196 lb. ?
14. When a pound of tea is worth 60^,
how much will f lb. cost ?
15. I bought a horse for $176 and sold him for ^ of the V^
cost. How much did I get for him? How much did I ^
lose? I
16. James had $ 1.75, and he paid f of it for a hat. How jc
much did the hat cost ? ' 5
17. Andrew and Oliver bought a box containing 144 ^
screws. Andrew used f of them and Oliver J of them.C,^
How many screws were left in the box ? ^^
18. Pauline bought 2 packages of f^iH. jjflifiVs, 100 in esichjC
package. She used ^ of them. How many did sHe^use ? '^
How many were left ? ''i^
19. Mark had $2.25. He spent f of his money for a
pair of skates and j of it for straps. How much money
did he spend? What part of the $2.25 had he left?
FIRST PROO. AR. — 14
210 PROGRESSIVE ARITHMETIC
204. Multiplying by a mixed number.
1. How many cents are 4 times 6 cents? ^ of 6 cents?
the sum of 4 x 6^ and ^ of 6^?
Then how many cents are 4^ x 6^?
You have multiplied 6^ by 4^, by multiplying 6^ by 4,
finding ^ of 6^, and adding the results.
2. In a similar way multiply 8 in. by 2^; 4 doz. by 3j;
5 gal. by 6J.
3. Find 7^ times 10 min. ; 4^ x 6 hr. ; 5j x 8 yd.
£X£RCIS£S
205. 1. How many dollars are 5^ x $9 ?
Solution. — 6^ x f 9 means the sum of 5 x f 9 and ^ of 39.
5xf 9 = lp45,and^of $9 = $3; thenS^ x $9 = $45 + f 3 = $48.
Find: Find: Multiply:
2. 3^x4 ft. 6. 2^xl2qt. lo. $30 by %
3. 2^ X 6 mo. 7. 1^ X 16 yd. ii. 20 hr. by 4j.
4. 5^x8 gal. 8. 7^xlOpt. 12. 40^ by 2|.
5. 3J^ X 9 min. 9. Ij x 24 min. 18. 60 min. by 1^.
14. How many quarts are there in 4^ gallons ?
15. Find the cost of 5j yards of ribbon at 8 cents a
yard.
16. How many ounces are there in Ij pounds?
17. I buy pens at 8^ a dozen and sell them at 1^ each.
How much do I ^ain on 1 doz. ? on 1 J doz. ? on 5j doz. ?
18. How many feet are there in 8^ yards ?
FIRST BOOK 211
19. There are 8 pints in 1 gallon. How many pints are
there in 3^ gallons? in 7 J gallons? in 9^ gallons?
20. How much will 4| pounds oi nuts cost at 20 cents a
pound ?
21. At 32 cents a pound, how much will 1^ pounds of
butter cost ?
22. Find the cost of 2^ dozen bananas at 12 cents a dozen.
WRITTEN EXERCISES
206. 1. Multiply 376 by 7|.
376
376 multiplied by f= 282
376 multiplied by 7 =2632
376 multiplied by 7| = 2914
Multiply :
2. 48by5| 5. 284by9f 8. 735 by 24f
3. 65by8f 6. 195by7f 9. 896 by 72J
4. 72by6f ". 464by8| lo. 942 by 89|
. Find the cost of :
11. 7| yards of cloth® $.72.
12. 8f yards of carpet @ $1.08.
13. 12f dozen window pulleys @ $.40.
14. 15| gallons of molasses @ $ .24.
15. 25|- dozen ears of green com @ $.18.
16. llf dozen eggs for hatching @ $.90.
212 PROGRESSIVE ARITHMETIC
17. A few days before Thanksgiving Day our grocer
bought turkeys, weighing in all 72 J pounds, at $.16 per
pound. How much money did he invest in turkeys ?
18. We bougjit a turkey of him at $ .20 a poxmd. It
weighed 10 pounds when he bought it and 9f poxmds when
he sold it to us. How much did he gain ?
19. He bought a bag of mixed nuts containing 96j
pounds, for which he paid $.12 a pound. He sold them at
$.18 a poxmd. How much did he gain?
How much did we have to pay for 2 J pounds ?
207. Finding the whole when one part is given.
1. A pie is cut into 4 equal pieces worth 5 cents each.
How much is the whole pie worth ?
If J of the cost of a pie is 5 cents, what is the whole cost ?
2. If ^ of the cost of a baseball bat was 9 cents, how
much did the bat cost ?
3. If ^ of a number is 4, what is the number?
EXERCISES
208. Find the cost of:
1. A pint of cream, when \ pt. costs 10^.
2. A pound of coffee, when \ lb. costs 9^.
3. A dozen bananas, when ^ doz. costs 3^.
4. A pound of tea, when \ lb. costs ^^,
5. A pound of cocoa, when \ lb. costs 11^.
6. A yard of velvet, when \ yd. costs 12;^.
FIRST BOOK 213
7. If f of a cake costs 20 cents, how much will the
whole cake cost?
8. If J of a pound of macaroons costs 10 cents, how
much must be paid for a pound ?
9. Julia bought half a pound of candy for 30 cents. How
much did she pay for the candy per pound ?
WRITTEN EXERCISES
209. 1. A bookcase was sold at auction for 36128. which
was only half of its value. How much was it worth?
2. I sent out 16 Christmas cards, which was ^ of the
number I had bought. How many cards did I buy ?
3. If J of a yard of flannel costs 15 cents, how much
does the flannel cost per yard ?
4. Mr. Sage owns ^ of a store. He values his share at
$8^p. How mu ch doe§ he think the store is worth?
5. Some boys bought a football. James paid $ .35 towar3\^ ^
it, and this was ^ of the cost. Find the cost. j
6. A man bought a lot and paid J of the cost in cash. ^^
He paid $225 cash. Find the cost of the lot. f "j
7. A house rented for $375 a year, or for ^ of its value.
What was the value of the house ?
8. If ^ of the inhabitants of a city vote, and the voters
number 8200, what is the population of the city ?
9. An excursion ticket to Chicago cost 50 cents, or 5 cents
less than half of the regular fare. What was the regular
fare?
<i
214
PROGRESSIVE ARITHMETIC
NUMBERS TO ONE HUNDRED FORTY-FOUR
210. Counting by elevens.
1. Multiply, then give the table of 11 's to 9 times 11 :
• 11 11 11 11 11 11 11 11 11
2. How is a number multiplied by 10? How many,
then, are ten times 11 ?
3. How many are ten ll's and one 110
11, or 11 times 11 ? +11
110
+ 22
s.
4. How many are ten ll's and two
ll's, or 12 times 11 ?
Give the table of ll's to 12 times 11.
Memorize :
7. How many ll's are
there in 22? m33? in 44?
in 55? in 66?
77-1-11= ? 121-«-ll=?
99 + 11=? 110-«-ll=?
88 + 11=? 132 + 11=?
8. Compare 11 times 10 with 10 times 11.
9. Tell the number of ll's in the sum, then the sum :
11 11 11 11 11 44 44 44
11 11 11 44 66 22 33 66
11 22 33 11 11 33 55 11
1 X 11 = 11
7x11= 77
2 X 11 = 22
8x11= 88
3 X 11 = 33
9x11= 99
4 X 11 = 44
10 X 11 = 110
5 X 11 = 65
11 x 11 == 121
6 X 11 = 66
12 X 11 = 132
FIRST BOOK
216
10. Find i of 22; ^ of 33; ^ of 66. 11 is J of what
number? | of what number?
211. Counting by twelves.
1. Tell the number of 12's in the sum, then the sum :
12 24 36 48 60 60 60 60 60
12 12 12121224364860
2. Multiply, then give the table of 12's to 10 times 12 :
12 12 12 12 12 12 12 12 12
23456789 10
4. Memorize ;
1 X 12 = 12
7 X 12 = 84
2 X 12 = 24
8 X 12 = 96
3 X 12 = 36
9 X 12 = 108
4 X 12 = 48
10 X 12 = 120
6 X 12 = 60
11 X 12 = 132
6x12 = 72
12 X 12 = 144
3. .How many eggs are
2 dozen eggs? 3 doz. ? 4
doz. ? 5 doz. ? 6 doz. ? 7
doz. ? 8 doz. ?
5. How many pens are 9
dozen pens? 10 doz.? 11
doz. ? 12 doz. ?
12 dozen = 144 = 1 gross.
6. Compare 12 times 10 with 10 times 12.
7. Compare 12 times 11 with 11 times 12.
8. How many 12's are there in 24? in 36? in 48?
in 60? in 72? in 84? in 96?
108-!- 12=? 120-5-12= ? 132^-12=? 144h-12=?
9. Tell the number of 12's in the sum, then the sum :
120 108 72 120 108 72 84 96
12 24 60 24 36 72 60 48
216
PROGRESSIVE ARITHMETIC
EXERCISES
212. 1. How many squares
are 12 times 2 squares?
How many squares are 2
times 12 squares?
2. Compare 12 times 2 with 2 times 12. What is the
product of 2 and 12 ?
3. Draw an oblong 11 inches long and 3 inches wide;
divide it into inch squares. Count the squares by ll's;
by 3's. Find in two wa3rs the product of 11 and 3.
Find in two ways the product of :
4. 12 and 5 6. 7 and 11 s. 11 and 8
5. 12 and 4 7. 6 and 12 9. 10 and 12
10. Since 4 times 11 = 44, Uptimes 4 = . Find 12
times 4.
11. Give the table of 4's to 12 times 4.
Drill on this table, giving the multiples of 4,
first in regular order up and down the ladder,
next in various orders, pointing to different rungs
of the ladder.
12. In the same way extend the table of 5's
to 12 times 5, and drill on the table.
Give these tables and drill on each:
13. The 6's to 12 times 6. is. The 8's to 12 times 8.
14. The 7's to 12 times 7. 16. The 9's to 12 times 9.
17. Give the table of lO's to 12 times 10.
FIRST BOOK
217
Answer quickly, thus : looking at 32 say "4 times 8."
18. Multiples of 8. i9. Multiples of 12. 20. Multiples of 9.
32 80 24 108 36 27
48 40 48 120 54 45
64 88 96 72 72 90
24 96 36 144 108 81
21. Multiples of 6. 22. Multiples of 7.
36 24 14 28
72 48 35 42
18 30 70 84
54 66 63 77
23. Multiples of 11.
11 77
55 121
110 44
132 99
24. Write all the multiplication tables to 12 times 12, thus :
1x1 = 1 1x2 = 2 1x3= 1x4= and so on.
2x1=2 2x2=
4 2x3= 2x4=
etc. etc.
etc. etc.
25. ^of36=?
30. 1 of 33= ? 35.
|of96=?
26. ^of 44= ?
31. ^Of 60= ? 36.
|of48=?
27. |of 60=?
32. |of 88= ? 37.
f of 55=?
28. ^of66=?
33. f of 72= ? 38.
iof 66=?
29. ^of96=?
34. fof55=? 39.
|of 96=?
Give quotients, and remainders if there are any :
40. 4)50 44.
8)90 48. 8)75
52. 11)100
41. 5)60 45.
9)100 49. 9)75
53. 12)100
42. 6)70 46.
8)100 50. 12)75
54. 11)120
43. 7)80 47.
7)75 51. 12)125
55. 12)120
218
PROGRESSIVE ARITHMETIC
Are
MEASURING
213. Measuring dry and bulky articles.
1. What measures are used to measure milk ? oil ?
the same measures used to measure oats ? potatoes ?
2. Dry and bulky articles, as grain, vegetables, berries,
etc., are measured by these measures. Name them.
Pint
Peck
BUSHBL
QUAKT
3. Take a pint measure such as is used to measure pea-
nuts or cranberries. Fill it with grain (or sand) and
empty it into the quart measure.
Do this again. Is the quart measure full now ?
How many pints of grain equal a quart of grain ?
4. How many pints of nuts equal a quart of nuts?
5. A quart of cranberries = pints of cranberries.
2 pints equal 1 quart.
6. Fill the quart measure with grain and empty it into
the peck measure.
Continue to measure by quarts until you find how many
quarts equal a peck.
7. How many quarts of peas equal a peck of peas?
FIRST BOOK 219
8. A peck of beans = quarts of beans.
8 quarts equal 1 peck.
9. Measure by pecks and find how many pecks equal a
bushel.
10. How many pecks of com equal a bushel of corn ?
11. Learn this table of dry measures.
2 pints (pt.) = 1 quart (qt.)
8 quarts = 1 peck (pk.)
4 pecks = 1 bushel (bu.)
EXERCISES
214. 1. How many quarts are there in 2 pk. ? in 3 pk. ?
inlbu.? m^bu.? infbu.? in2bu.?
2. John's father bought 1^ bushels of tomatoes. How
many pecks of tomatoes did he buy ? how many quarts ?
3. How many quarts are there in ^ pk. ? in J pk.?
What part of a peck is 1 qt. ? 2 qt. ? 4 qt. ? 6 qt. ?
4. Mr. Davis bought a 2-bushel bag of oats for his horse.
He gave the horse 4 quarts of oats at a feed. For how
many feeds did the oats last ?
5. How many quarts of strawberries or of peaches will
a bushel crate hold ?
6. Mrs. White bought 24 quarts of fruit. How many
pecks of fruit did she buy? How much less than a bushel
of fruit did she buy ?
220 PROGRESSIVE ARITHMETIC
H. Lester picked 10 quarts of plums oflf his plum tree.
How many pecks of plums did he pick?
8. Mary picked a 10-quart basket of cherries full 4
times. She picked 1 bu. and — — qt., or pk.
9. A potato barrel sometimes holds 10 pecks of pota-
toes. How many bushels does such a barrel hold ?
10. If a pint of peanuts costs 5 cents, how much will a
quart cost at that price ? a peck ?
11. How many bushels of com meal are required to feed
32 cows, if 1 quart is given to each cow?
How many bushels of com meal are required per day to
feed 32 cows 2 quarts apiece, both morning and evening?
215. Meastuing length or distance.
1. How many inches are there in a foot? in a yard?
How many feet are there in a yard ? in ^ yard ?
2. Which of these three measures should you use to
measure the width of this book ? the width of the street ?
the length of a piece of cloth ?
3. Measure 5^ yards along a board in the floor. This
distance is called one rod.
4. Stand 1 rod from the door. Walk 1 rod.
5. How many feet are there in 5 yards? in ^ yard?
in 5^ yards? in 1 rod?
5^ yards, or 16| feet, equal 1 rod.
6. What measures might be used to measure the length
and width of a lot? of a pasture? the length of a fence?
FIRST BOOK
221
7. Tell the distance between some two towns or cities
near you; between the ends of some long street. What
measure is used to measure long distances ?
8. Mention a place about a mile from the schoolhouse.
9. In some cities 20 blocks make a mile. In such cities
a block is 16 rods long. How many rods equal a mile ?
10. In other cities 12 blocks equal a mile, and each block
is 440 feet long. How many feet equal a mile ?
11. Learn this table of measures of length :
12 inches (in.)= 1 foot (ft.)
3 feet =1 yard (yd.)
161 feet = 1 rod (rd.)
320 rods = 1 mile (mi.)
A mile is equal to 5280 feet.
WRITTEN EXERCISES
216. 1. How many yards are 5^ yd. + 5^ yd., or 2 rd. ?
How many feet are there in 11 yd., or in 2 rd.? in 4 rd.?
2. The bases of a baseball diamond are 90 feet apart.
How many yards must a boy run to make a home run ?
3. A football field is 110 yards long. Express the
length in feet. Compare the length with that of a block
in your city.
4. How many rods of fence are required to inclose a
farm J of a mile long and |- of a mile wide ?
5. How many yards are there in a mile ? in ^ mile ?
222 PROGRESSIVE ARITHMETIC
r
EXERCISES
217. 1. In this map, or plan, 1 inch represents 64 feet.
If you measure the plan of the house, you will find that
it is 1 inch long. Then the house is 64 feet long.
SIDiWALK
SECOND AVENUE
S
, , i r
2. Since 1 inch represents 64 feet, what distance does
^ in. represent ? J in. ? f in. ? f in. ? 2 in. ?
Using a rule divided to eighths of an inch, find :
3.
4.
5.
6.
11.
Width of lot. 7.
Length of lot. 8.
Width of house. 9.
Length of bam. lo.
Width of bam.
Width of alley.
Width of Pine Ave.
Width of Second Ave.
How wide is each sidewalk on Pine Ave. ? on Second
Ave. ? How wide is each street between the sidewalks?
12. How far is the house from the front of the lot on
Pine Ave. ? from the side of the lot on Second Ave. ? from
the other side of the lot ? from the back of the lot ?
6
16'
FIRST BOOK 228
WRITTEN SXSRCISES
218. 1. In drawings we do not write the words "feet"
and " inches." I ^
In this plan of the floor of ^^^
a room, 16 feet is written 16' ;
11 inches is written 11''; 3
feet 4 inches is written 3'-4''.
In the plan, 1 inch rep-
resents 8 feet, or the scale
is r = 8', or "8 feet to the
inch." Scale: 1"= 8' ,;
2. Draw the plan of a room 20 ft. by 16 ft., using 1 inch ^
to represent 4 feet. Write 20' and 16' on the plan in the
proper places, and write the scale below. +^
Draw the plan of each of the following : ^
3. A room, 21 ft. by 18 ft., scale 1 in. = 4 ft. i
4. A garden plot 42 ft. by 37 ft., scale 1 in. = 8 ft. ^
5. A croquet ground, 30 yd. by 20 yd., scale 1 in. = 5 yd. ^
6. A tennis court . 78 ft. bv 30 ft., scale 1 in. = 12ii^
7. A hall, 30 ft. by 8 ft., paved with tiles 2 ft. square,
scale 1 in. = 4 ft. Show the tiles in the plan.
8. A celery patch, 75 ft. by 27 ft., with 9 ro>vs of cel-
ery 3 ft. apart, scale 1 in. = 8 ft. Show rows by dotted
lines.
9. An orchard, 40 rd. by 25 rd., scale 1 in. = 8 rd. Di-
vide the ground into squares 2 rd. on a side, and show a
tree in the middle of each square, thus :
224
PROGRESSIVE ARITHMETIC
219. Meastuing area.
1. How long is each side of an inch square ? of a foot
square ? Can a foot square be drawn on this page ?
2. In this picture of a square foot divided into square
mches, the scale is 1" = 8". The
square is drawn one eighth size.
On. the blackboard draw a
square foot divided into square
inches, full size.
Draw another one, on paper,
07ie half size. Draw another one,
one fourth size.
3. Since there are 12 inches in a scalk §
foot, how many square inches are there in each row?
in 2 rows ? in 3 rows ? in 12 rows, or in 1 square foot ?
1
s
QUIAIRIE
F
O
o
T
144 square inches equal 1 square foot.
4. Draw full size on the blackboard a yard square divided
into foot squares. Draw the same one half
size; one fourth size.
5. This is a yard square drawn to a still
smaller scale. Measure, and find the scale. Ex-
press the scale in the form, scale : V = .
6. How many square feet are there in a square yard ?
7. Learn this table of measures of area :
144 square inches (sq. in.) = 1 square foot (sq. ft.)
9 square feet = 1 square yard f sq. yd.)
FIRST BOOK 226
WRITTEN EXERCISES
220. 1. Find the area of an oblong 6 ft. by 4 ft.
Model Solution
In 1 row there are 6 sq. ft.
In 4 rows there are 4 x 6 sq. ft., or 24 sq. ft.
Area = 24 sq. ft.
I
Draw, and find, as above, the area of: scalb: i"=8'
2. An oblong, 8 in. by 10 in., scale ^.
3. An oblong, 9 in. by 7 in., scale J.
4. A square, 7 ft. by 7 ft., scale 1 in. = 8 ft.
5. An oblong, 18 yd. by 9 yd., scale 1 in. = 4 yd.
6. A table top, 6 ft. by 5 ft., scale 1 in. = 4 ft.
7. A floor, 6 yd. by 9 yd., scale 1 in. = 4 yd.
8. A rug, 4 yd. by 7 yd., scale 1 in. = 4 yd.
9. An oblong kite, 30 in. by 18 in., scale ^.
10. A window, 7 ft. by 3 ft., scale 1 in. = 2 ft.
u. A roof, 40 ft. by 28 ft., scale 1 in. = 8 ft.
12. A flower bed, 25 ft. by 15 ft., scale 1 in. = 10 ft.
For review or for class work vary the foregoing exercises thus :
(a) Let each pupil draw the -figure for one exercise to some con
venient scale, and write the scale below.
(b) Let the pupils exchange papers.
(c) Let each pupil find, by measuring the figure received and by
using the scale, the true length and width and then the area.
How many square inches are there in :
13. 2 sq. ft. ? 15. 2i sq. ft. ? 17. 3f sq. ft. ?
14. 1^ sq. ft.? 16. 5| sq. ft.? 18. 4| sq. ft.?
FIRST PROG. AR. — 16
226
PROGRESSIVE ARITHMETIC
How many square feet are there in :
19. 2 sq. yd. ? 21. If sq. yd. ?
20. 15 sq. yd. ? 22. 4^ sq. yd. ?
23. A room is 24 ft. long and 21 ft. wide. How many
yards of carpet 1 yard wide are needed to cover the jBioor ?
Explain with a plan, scale 1 in. = 4 yd.
24. Draw a plan of a garden 160 ft. by 80 ft. to the scale
1 in. = 16 ft. Find the perimeter and the area.
25. Find the area and the perimeter of a city lot 32 feet
wide and 150 feet long.
26. Estimate the length, width, area, and perimeter of
your schoolroom jBioor. Measure the length and the width ;
find the area and the perimeter.
Draw a plan of the floor, to any convenient scale.
27. Estimate and find by measuring, the area of doors,
windows, blackboards, etc., in your schoolroom.
221. Meastuing volume.
1. The inside of this box is 1
foot long, 1 foot wide, and 1 foot
deep. How many cubic feet
will the box contain ?
2. To find how many cubic
inches it will hold, put a layer
of inch cubes in the bottom of
the box, as in the picture.
Since the bottom of the box is
1 foot square, how many cubic inches are there in this layer ?
^^-^
^^
^m||| 1 ' i
^-^^
1
_^,.^ ^,y^ ^.^
nl ill ' y
^^.^^^
IPiullfl I
^^^ \
Iftliill P
fflinUii 1
^- -;-;;; J
IW
\ f ( ( f ( ( r r r f jtI
nwpr^
^r
F1K8T BOOK
227
s. Since the box is 1 foot high, how many such layers
are required to fill the box? Find by multipUcation the
number of cubic inches in a cubic foot.
4. Each edge of this block is 1
yard long. What is the volimie of
the block?
I«^f
^ ^ _rtifl
"-^ ^^^ ^^ .JK/flfk
— -^ — ^ . .^mm/M
H
H
—w
5. Since the top face of the block is
1 yard square, how many cubic feet
are there in the top layer of foot
cubes ? in each layer ?
6. Since the block is 1 yard high, how many such layers
are there ? 1 cu. yd. = cu. ft.
7. Learn this table of measures of volume :
1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.)
27 cubic feet = 1 cubic yard (cu. yd.)
WRITTEN SZSRCISES
222. 1. Joel's wagon box is 20 inches long, 16 inches
wide, and 5 inches deep, measured on the inside. How
many cubic inches of sand are required to cover the bottom
to a depth of 1 in. ? 2 in. ? 4 in. ?
How much more or less than a cubic foot of sand will
the wagon box hold?
2. How many cubic feet of ice are required to fill a
wagon box 10 feet long and 3 feet wide to a depth of 1
foot? to a depth of 2 feet?
How many cubic yards of ice are required to fill the
wagon box to a depth of 3 feet ?
228 PROGRESSIVE ARITHMEIIC
3. Mr. Sheldon has a water tank 18 ft. long, 4 ft. wide,
and 3 ft. deep. How many cubic feet of water are there
in the tank when the water is a foot deep in the tank ?
2 ft. deep ? when the tank is full ?
4. A man loaded a car that was 8 ft. wide and 7 ft.
high, inside measurements, with boxes 2 ft. by 2 ft. by 1 ft.,
laying the boxes flatwise. How many boxes were required
for one tier across the end of the car ?
How many boxes did the car hold, if it was 38 ft. long ?
5. How much more than
2 cu. ft. of space will a crate
like this occupy ?
6. Each half of the crate
is 12 in. by 11^ in. by llj in.,
inside dimensions. How much less than 2 cu. ft. will the
crate hold?
7. George and Alfred estimated the dimensions of a room,
then found the exact dimensions by measuring, thus :
Length
width
Height
George's estimate . .
. 20 ft.
20 ft.
lift.
Alfred's estimate . .
. 22 ft.
18 ft.
10 ft.
Measured dimensions .
. 21 ft.
18 ft.
9 ft.
What was the actual volume of the room ?
What was the volume according to George's estimate?
How many cubic feet too much did his estimate give ?
What was the amount of error in Alfred's estimate ?
Whose estimate was the more accurate ? .
i-J.
:^4
1^,
09
FIRST BOOK
229
Some boys and girls did the following work in estimating
and measunng. Only the best estimates are given here.
Find the true volume and the error in each case.
A.-
Thing Measured
8. Box
9. Chalk box
"4
10. Room
\\
11. Bookcase
Estimated Dimensions
16" by 12" by 9"
7" by 4" by 4"
17' by 14' by 9'
50" by 16" by 60"
12. Stone step 96" by 12" by 12"
13. Coal bin 15' by 6' by 8'
Measured Dimensions
15" by 12" by 10"
6" by 4" by 3^'-
18' by 12' by 9'
54" by 14" by 60"
90" by 10" by 10"
14' by 5' by 8^'
14. Estimate and measure the dimensions and volume
of various things, as boxes, rooms, cabinets, etc.
MULTIPLICATION
EZERCISBS
223. Add in this way : "two 13's, 26; three 13's, 39;" etc.
1. 13 26 14 28 15 30 16 32
13 13 14 14 15 15 16 16
Multiply rapidly :
13 14 14 16 15 16 16.
3 '^ ^ 2l ^ 1 —
4. Multiply the numbers from 17 to 24 by 2. 2 x 25 = ?
'4
if •:
1' -
.1 } ;.
"i
2. 17
18
19
20
21
22
23
24 X '
17
18
19
20
21
22
23
24 5^;
230 PROGRESSIVE ARITHMETIC
5. Give the table of 2's to 25 times 2.
6. Give the table of 3's to 16 times 3.
Multiply
rapidly :
7. 12
24
11
9
8
16
9
12
4
2
n
8
6
3
7
11
8. 9
3
7
12
25
5
9
10
5
15
7
12
2
10
12
11
9. If 2 pineapples cost 30 cents, how much will 24 pine-
apples cost at the same price ?
10. If 3 peaches cost 2 cents, how much will 4 dozen
peaches cost?
11. If 3 apples cost 2 cents, how much will 45 apples
cost at the same price ?
12. If 1 plum tree bears 13 pecks of plums, how many
pecks will 3 such trees bear ?
13. If 5 cofifee trees yield 8 pounds of cofifee, how many
pounds will 60 trees yield? 600 trees?
Tell products at sight :
14. 3000
3100
2110
120
110
80
7
8
9
9
11
12
15. 1300
12
150
3000
91
120
3
50
30
16
80
12
16. 142
121
303
202
194
202
30
70
14
17
20
16
FIRST BOOK 231
WRITTEN EXERCISES
224. When you multiply by 11 or by 12, you should
obtain the product by a single multipUcation.
1. 465
11
5115
2. 523 3
12
6276
4051
12
48612
An
Itiplj
r by 5, 6, 7, 8, 9,
11, and 12:
4.
75
9. 127
14. 1025
19.
6087
5.
59
10. 243
IS. 1962
20.
5871
6.
84
11. 506
16. 2888
21.
6009
7.
78
12. 782
17. 5207
22.
7407
8.
96
13. 365
18. 3670
23.
8333
24. Multiply each of the following numbers by 5, writing
only the products :
48 96 87 58 344 4001
64 75 128 242 504 5280
25. Multiply the same numbers by 6 ; by 7 ; by 8 ; by 9 ;
by 11; by 12.
EXERCISES
226. 1. How many are 10 times 4? 10 x 12? 10 x 25?
How may any number be multiplied by 10 ?
2. How many are 100 times 5? 100x7? 100x11?
How many zeros annexed to 5 will change 5 units to 5
hundreds ?
How may any number be multiplied by 100 ?
232 PROGRESSIVE ARITHMETIC
3. How many are 1000 times 3 ? 1000 x 16 ? 1000 x 150 ?
How many zeros annexed to 3 will change 3 units to 3
thousands ?
How may any number be multiplied by 1000 ?
Multiply :
4. 256 by 10 7. 225 by 100 lo. 75 by 1000
5. 481 by 10 8. 105 by 100 ii. 364 by 1000
6. 5000 by 10 9. 400 by 100 X2. 100 by 1000
WKITTBH BZSKCISES
226. 1. Multiply 43 by 2000.
1000 times 43 = 43,000.
2000 times 43 = 2 times 43,000.
„„'^yy. First write three zeros in the product, for the
' product must be some number of thousands.
Next multiply 43 by 2 to find the number of thousands.
Multiply :
2. 81 3. 411 4. 2314 s. 163
2000 300 ^ J^
6. 256 by 70 12. 27 by 800 is. 15 by 7000
7. 409 by 80 is. 166 by 600 i9. 44 by 2000
8. 890 by 90 14. 225 by 400 20. 32 by 3000
9. 67 by 110 15. 625 by 120 21. 480 by 1200
10. 82 by 120 I6. 435 by 200 22. 750 by 1100
11. 175 by 120 17. 875 by 110 23. 23 by 4000
FIRST BOOK 283
24. Multiply 346 by 278.
346, multiplicand 2768 is the first partial product ;
278 , multiplier 2422 tens, or 24,220, is the second
2768 partial product ; 692 hundreds, or
2422 69,200, is the third partial product
692 The sum of the partial products,
96188, product or 96,188, is the entire product.
Test the answer by multiplying 278 by 346.
Find products and test :
25.
135 X 247
30. 78 X 967
35.
99x999
26.
225 X 144
31. 166x585
36.
830 X 87
27.
396 X 95
32. 228x417
37.
281 X 281
28.
89 X 788
33. 756x121
38.
197 X 287
29.
415 X 175
34. 537x145
39.
199 X 267
40.
Multiply $.47 by 206.
S.47
206
282 The partial product by
00 tens may be omitted, as in
94 the second process.
$.47
206
282
94
$96.82
$96.82
Find products and test :
41. 16x436 43. 89 X 77 45. 101x202
42. 106x436 44. 89x707 46. 308x207
234 PROGRESSIVE ARITHMETIC ^.xjlIj.^I^
Find the cost of :
47. 144 hats @ $2.25. 55. 66 shotguns^ $14.10.
48. 800 horses @ $132. 56. 809 tickets @ $.75. ;^
49. 704 books @ $1.10. 57. 42 cameras @ $22.50. \
50. 64 pianos @ $475. 58. 55 automob iles (a\ %&75i
51. 48 rings @ $16.75. 59. 120 pairs gloves @ $.95.
52. 120 bicycles @ $37. 60. 288 pairs shoes @ $3.15.
53. 56 watches @ $15.85. 6i. 2000 bu. of com @ $.42.
54. 200 hammocks® $1.35. 62. 326 bottles perfume® $.85.
63. Find how much it will cost to fence in a lot 18 rods
long and 8 rods wide at $1.25 a rod.
64. How much will it cost to construct a sidewalk 12
feet wide in front of a lot 33 feet wide, at $2.25 per square
yard?
65. A man bought 20 bushels of wheat for $17.50.
Afterward he bought 400 bushels at the same price. How
much did the second purchase cost him ?
66. How many cubic feet are there in 115 cubic yards?
67. A car contained 170 barrels of flour. A barrel of flour
weighs 196 pounds. How many pounds of flour were there
in the car?
68. Find the cost of 8 dozen boxes of writing paper at
$.27 per box.
69. A yard 165 feet square is inclosed on three sides by
a tight board fence 6 feet high. Find the cost of painting
both sides of the fence at $.15 a square yard.
FIRST BOOK 285
DIVISION
«
EXERCISES
227. Answer quickly :
1. 8)48 9)63 11)99 12)96 ll^m 12)108
2. iof81=? xVofl44=? iof84=? ^ofl32=?
3. 26^2=? 26^13=? 32^16=? 48 + 3=?
4. 45 + 15=? 42 + 3=? iof39=? lof34=?
5. Of what two numbers is 12 the product ? Give two
others.
6. Of what two numbers is 24 the product? Answer
the question in as many ways as you can.
7. Do the same with other numbers from 10 to 50.
When eggs cost 24^ per dozen, find the cost of :
8. 1 egg; 7 eggs; 12 eggs 4- 7 eggs, or 19 eggs.
9. ^ doz. eggs, or 4 eggs; 12 eggs + 4 eggs, or 16 eggs.
10. Find the cost of 15 oranges at 36 cents a dozen,
without finding the cost of 1 orange.
11. When photographs cost $4 a dozen, how many pho-
tographs can be bought for $1 ? for $10?
12. I paid the milkman $2 for 34 quart tickets. How
many quarts of milk did he sell for a dollar ?
13. A woman paid 42 cents for 3 dozen buttons. How
much did they cost per dozen ?
14. When 2 boxes of berries cost 15 cents, how many
boxes can be bought for 45 cents ?
rv.
236 PROGRESSIVE ARITHMETIC
Tell quotients at sight :
15. 11)77 11)770 7 )5600 7 )5670 7 )5607 '
16. 8 )6400 9 )5418 11 )2233 12 )3648 12 )48072
WRITTEN EXERCISES
228. 1. Divide 3072 by 12.
256 , quotient
Divisor, 12)3072, dividend 12 )3072
24 256
67
60_ The
72 long
• 72 sbocli division
rocess is called
vision'^ the second,
Hereafter you should always use short division when the
divisor is not greater than 12.
Practice on the following exercises until you can work
them all correctly in 3 minutes or less :
8. 8 )50792
9. 9 )77778
2. 2 )16170
3. 3 )48210
4. 4 )70204
5. 5 )32615
6. 6 )43224
7. 7 )29442
10. 8 )10000
11. 9 )10152
12. 8 )91056
13. 11)10010
14. 12 )1728
15. 12 )10056
16. 11 )79387
17. 11 )10505
18. 12 )11088
19. 12 )89424
FIRST BOOK 237
20. Find xV of 20,000.
How is -^ of any number
12 )20000 found? How many times does
1666^^, or 1666| 20,000 contain 12, and how many
units remain to be divided by 12 ?
How is ^ of 8, or 8-^12, written as a fraction? In
what other form may we write -^ ?
Find the value of :
21. I of 1860 26. I- of 39,893 3i. ^ of 34,621
J of 76,870 32. i3^ of 10,000
J of 39,958 33. jV of 32,200
29. 1 of 45,184 34. ft of 90^20
30. I of 58,626 35. 3-V of 96,873
36. How many feet are there in |^ of a mile ?
37. A dozen collars cost $1.80. Find the cost of one.
38. If 12 boys weigh 1032 pounds, what is their average
weight ; that is, the weight of each, supposing that all weigh
the same ?
39. Louise received 86 credits in arithmetic, 78 in lan-
guage, 88 in geography, and 91 in history. What was her
average of credits in these four studies ?
40. If a man earns $22.50 in 6 days, how much does he
earn per day?
41. A block of candy 1 foot square and 1 inch thick was
cut into inch cubes and divided equally among 9 children.
How many cubes did each child receive ?
22.
i of 2726
27.
23.
1 of 3895
28.
24.
^ of 4273
29.
25.
i of 2874
30.
238 PROGRESSIVE ARITHMETIC
EXERCISES
229. 1. Divide 90 by 10; 120 by 10; 200 by 10; 450
by 10. How may any number be divided by 10 ?
2. How many times is 100 contained in 500? in 900?
in 1100? How may a number be divided by 100?
3. How many times is 1000 contained in 4000 ? in 24,000 ?
How may a nmnber be divided by 1000 ?
Divide :
4. 470 by 10
8. 1600 by 100
12.
10,000 by 1000
5. 3750 by 10
9. 8900 by 100
13.
53,000 by 1000
6. 3800 by 10
10. 9000 by 100
14.
100,000 by 1000
7. 5000 by 10
11. 10,000 by 100
15.
720,000 by 1000
230. Divide:
1. 2 dimes ) 18 dimes 2 tens ) 18 tens 20 )180
2. $5 )$15 5 hundreds ) 15 hundreds 500 )1500
3. 4^ )12ff 4 thousands ) 12 thousands 4000 )12000
WRITTEN EXERCISES
1. Divide 360 by 40; 1600 by 400; 76,000 by 4000.
4 0)360 400 ) 16# 4000)76^
9 4 19
4 tens is contained in 36 tens as many times as 4 is con-
tained in 36 ; 4 hundreds in 16 hundreds, as many times as
4 is contained in 16 ; 4 thousands in 76 thousands, as many
times as 4 is contained in 76.
FIRST BOOK
289
Divide :
2.
920 by 40
7.
33,500 by 50
12.
$48,000 by $240
3.
5760 by 80
8.
49,630 by 70
13.
$34,170 by $170
4.
5280 by 110
9.
39,000 by 130
14.
$42,140 by $140
5.
1080 by 120
10.
32,000 by 1600
15.
$54,000 by $2000
6.
7680 by 120
11.
45,000 by 1500
16.
$81,000 by $3000
17. How many lots costing $500 each can be bought for
$16,000?
18. How long will it take a train to run 600 miles at the
rate of 40 miles an hour ?
EXERCISES
231. 1. How many times is 12 contained in 24 ? How
many times is 8 contained in 24 ? Why is the quotient larger
in the latter case ?
2. Divide 60 by 12 ; by 10. Which result is the larger ?
Which gives the larger quotient, 480 h- 12 or 480 -s- 10 ? Why
is the quotient larger ?
Tell quotients : Estimate quotients : Estimate quotients :
3. 60^12 = 5 60 + ll = 5 + rem. 60 -f- 13 = 4 + rem.
4. 100-s-20 = 5 100 + 19 = 5+ 100-1-21 = 4+
5. 160-«-20 = 8 160-»-19=? 160 + 21= ?
6. 210-!-30=? 210-!- 29=? 210 + 31=?
7.160 + 40=? 160 + 39=? 160+41=?
8.250 + 50=? 250 + 49=? 250 + 51=?
9.240 + 30=? 240 + 28=? 240 + 32=?
10.320 + 40=? 320 + 38=? 320 + 42=?
240 PROGRESSIVE ARITHMETIC
Give quotients at sight, reading across the page :
11.
180 + 20
180 -!- 19
180 -s- 21
180 -5- 22
12.
270-5-30
270 -i- 29
270 -H 31
270 + 28
13.
200 H- 40
200 -s- 39
200 H- 41
•200 -s- 42
14.
400 H- 50
400 -s- 48
400 -i- 52
400 -J- 49
15.
360-*- 60
360 -i- 59
360-S-61
360-5-63
16.
420 + 70
420 H- 68
420-1-72
420 -t- 67
17.
320-^80
320 -s- 77
320 -H 81
320-*- 84
18.
450-!- 90
450 + 88
450-5-92
450 -i- 87
WRITTEN EXERCISES
232. 1. Divide 25,272 by 78.
324 Since 78 is only a little less than 80, the
78)25272 first figure of the quotient is estimated by
234 dividing 252 by 80, or 25 by 8, which gives
187 3. Multiplying 78 by 3 and subtracting the
156 product from 252 gives a remainder less than
312 the divisor. Therefore 3 is the correct figure
312 in the quotient.
The second figure of the quotient is esti-
mated by dividing 18 by 8, giving 2, which is shown to be
the correct figure by multiplying and subtracting as before.
Since 31 -^ 8 is nearly 4, and the true divisor is a Uttle
less than 80, we estimate the last figure of the quotient to
be 4. The test by multiplication and subtraction shows
that 4 is the correct figure, and that the division is exact.
The quotient, then, is 324.
FIRST BOOK 241
Divide :
2. 456 by 19 15. 1449 by 69
3. 672 by 21 16. 2414 by 71
4. 986 by 29 17. 3318 by 79
s. 1302 by 31 is. 2916 by 81
6. 1092 by 39 19. 3738 by 89
7. 1066 by 41 20. 4914 by 91
8. 1218 by 29 21, 3168 by 99
9. 2842 by 49 22. 1616 by 101
10. 2346 by 51 23. 4687 by 109
11. 1716 by 52 24. 2664 by 111
12 4425 by 59 25. 3927 by 119
13. 2074 by 61 26. 4114 by 121
14. 1922 by 62 27. 5246 by 122
EXERCISES
233. Estimate the first figure of the quotient ; test your
estimate by multiplying mentally : (Read across the page.)
1. 1700 -s- 32 2000 -i- 42 2600 h- 52 3200 + 62'
2. 2160-5-54 2500-5-64 2970-5-74 3700-5-94
3. 1380 + 23 3200 + 53 3100 + 53 4250 + 73
4. 1080 + 36 1400 + 46 3000 + 76 2900 + 96
s. 3640 + 52 4400 + 62 5040 + 72 5700 + 82
6. 3600 + 18 5740 + 28 7790 + 38 1360 + 68
PIR8T PROG. AR. — 16
242 PROGRESSIVE ARITHMETIC
WRITTEN EXKRCISES
234. 1. Divide $10,812 by $53.
204 204
$53)$ 10812 $53)$ 10812
106 106
21 212
00 212
212
212
What is the first remainder? Annexing 1, what is the
new dividend?
When we see the new dividend 21, why do we write in
the quotient?
The figures 00 written under 21 may be omitted, as in
the short process. As soon as is written in the quotient,
2, the next figure of the dividend, may be brought down to
form the next new dividend.
Test the answer by multiplying $ 53 by 204.
Divide, and test :
2. $1792 by 32 9. $3612 by 84 ie. 13,068 by 99
3. $6150 by 82 lo. 33,852 by 84 17. 17,475 by 75
4. $2156 by 22 u. $2080 by 65 is. 21,952 by 64
5. $4745 by $73 12. 19,630 by 65 19. 28,992 by 96
6. $2438 by $53 i3. 17,458 by 68 20. 16,037 by 79
7. $3196 by $94 14. 12,654 by 57 21. 29,078 by 67
8. $lo!feby$45 15. 15,756 by 78 22. 28,101 by 87
FIRST BOOK 243
EXERCISES
235. Estimate the first figure of the quotient ; test your
estimate by multiplying mentally : (Read across the page.) •
1. 1610^23 2350 + 33 3000-5-43 3790-^53
2. 2010 + 67 2310 + 77 2700-5-87 2900 + 97
3. 5400 + 18 8400 + 28 2000 + 68 2700 + 38
4. 1840 + 46 2640 + 66 3500 + 86 2200 + 56
5. 2040 + 34 8425 + 14 4411 + 74 7377 + 94
6. 5700 + 19 8800 + 29 1160 + 39 1500 + 49
7. 3780 + 54 5000 + 74 1600 + 24 3000 + 44
8. 5120 + 64 6720 + 84 2800 + 34 7500 + 94
9. 2450 + 35 3180+45 5700 + 85 4500 + 65
WRITTEN EXERCISES
236. Find quotieiriis, and remainders if there are any :
1.
1,671 + 23
' 6.
2,760 + 87
11.
2,904 + 46
2.
2,400 + 77
7.
5,598 + 18
12.
8,428 + 14
3.
2,750 + 87
8.
2,108 + 68
13.
5,629 + 74
4.
3,700 + 53
9.
20,468 + 68
14.
3,080 + 54
5.
4,440 + 63
10.
26,664 + 46
15.
27,380 + 54
16.
6,100 + 19
21.
18,174 + 78
26.
41,985 + 27
17.
5,000 + 74
22.
19,900 + 99
27.
76,641 + 46
18.
12,597 + 39
23.
51,712 + 64
28.
90,816 + 86
19.
18,375 + 75
24.
21,312 + 48
29.
21,864 + 24
20.
17,328 + 57
25.
65,195 + 85
30.
40,000 + 99
244 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
237. 1. Divide 8512 by 243; also 85057 by 243.
243)8512
729
1222
1215
7
Divide :
2.
6,900 by 156
3.
50,160 by 114
4.
27,375 by 125
5.
86,450 by 133
6.
33,785 by 145
7.
51,500 by 156
a
41,976 by 198
9.
12,100 by 354
10.
85,580 by 389
11.
11,571 by 133
12.
58,410 by 177
13.
71,111 by 176
14.
32,107 by 331
15,
25,801 by 344
243)85057
729
1215
1215
7
16.
46,420 by 844
17.
30,649 by 928
18.
35,310 by 535
19.
34,899 by 646
20.
34,515 by 767
|t,720 by 868
21.
22.
77,895 by 577
23.
97,356 by 244
24.
63,875 by 666
25.
43,967 by 999
26.
98,175 by 187
27.
84,668 by 244
28.
76,874 by 266
29.
84,501 by 229
FIRST BOOK 246
1
f
WRITTEN EXERCISES ^
238. 1. How many days are there in 2520 hours ?
2. A fruit dealer bought 44 crates of pineapples for
$63.80. Find the price per crate. ^J
^J^i 25 village lots cost $3125, how much will 1 lot .J
cost? 7 lots? • S
4. At a clambake 2160 clams were provided for 135 j
persons. How many wei^ provided for a family of four?
5. The cost of making a mile of new gravel road was % j
$3840. How mudi did it cost per rod? - 5
6. A newspaper press has a capacity of 308 papers per "^
minute. How long will it take to. print 18,480 papers? ^1
7. A bushel of wheat weighs 60 pounds. How many
bushels are there in a car load weighing 31,200 pounds? ^^
8. A car containing 672 bushels of grain was unloaded ^
in 16 minutes. How many bushels were unloaded in 1 <
minute'? in 5 minutes?. <H
9. In one season 69,750 crates of strawberries were y
shipped on the cars from one county in Delaware. How "^
many car loads was that, taking 225 crates as a car load ? «|
. 10. A fast frpiigrjif. ran Q22 miles from Npiw Orleans to /^
Chicap ;o in .^.^ honrg .^ Find its rate per hour^ . .
11. A fruit auctioneer sold 26 car loads of oranges in 130
minutes. If each car contained 360 boxes of oranges, how
many boxes did he sell per minute on the average ?
12. A grocer bought a car load of oranges, 362 boxes, for
$814.50. How much did he pay for a box? for 50 boxes?
246 PROGRESSIVE ARITHMETIC
REVIEW
\
239. 1. ^Tiat measures are used in measuring short
lengths or distances ? Ipng ones ?
2. Give the table of measures of length. ^^
3. What measures are generally used to measure milk?
oil? peanuts? meat? potatoes? candy? rice? com? mo-
lasses? sugar? cloth? carpet? area of a floor? volume of
a small box ? volume of a room ?
4. Give the table of hquid measures ; spf dry measures ;
of area measures ; of volume measures.
5. Draw a diagram and show that a square yard equals
9 square feet. Show that 1 cu. yd. = 27 cu. ft.
6. Show how the number of square inches in a square
foot is obtained ; the number of cubic inches in a cubic foot.
EXERCISES
240. Name these fractions in order of size, beginning
with the fraction of least value in each case:
1- I h h I 3. i, i, i, I, I I I
2- I h h i- *• h ^, 1 1 A, i tt-
5. How many dozen oranges are there in a box con-
taining 96 oranges ? 126 oranges ? 150 oranges ?
6. Our Thanksgiving Day turkey weighed 14j pounds.
Find the cost at $ .20 a pound.
FIRST BOOK 247
7. Percy spent 5 cents, or J of his money, for peanuts.
How much money had he at first? What part of his
money had he left ?
8. Ethel had 25 cents and spent f of her money riding
on a merry-go-round. How much money did she spend?
What part of her money had she left ?
Frank, Clara, Mabel, and Alfred made pop corn balls
and candy according to the following recipes:
Pop Corn Balls Peanut Candy Walnut Candy
^ pt. molasses f pt. molasses 1 pt. molasses
I lb. butter \ lb. butter | lb. butter
\ lb. red sugar 5 «[t. peanuts | lb. brown sugar
2^ lb. shelled pop corn salt 2^ lb. English walnuts
salt 1 tablespoon vinegar
9. Frank bought the molasses. How many pints did
he buy ? How much did it cost at $.32 a gallon ?
10. Clara bought the butter at $.24 a pound and the pop
com at $.10 a pound. How much did she expend?
u. Mabel bought the sugar. She paid 4 cents a pound
for brown sugar and 2 cents an ounce for red sugar. How
much did she expend for sugar ?
12. Alfred bought the peanuts at 5 cents a quart and the
English walnuts at 16 cents a pound. How much did both
cost?
13. Find the cost of all the materials, allowing 1 cent
for the cost of salt and vinegar.
248 PROGRESSIVE ARITHMETIC
WSIXXEN EXERCISES
241. 1. Add: $150, $17.85, $42.60, $984.10, $2012.
2. Subtract these numbers from 100,000: 100; 1000;
10,000; 576; 8576;
62,384.
3. Subtract from $5.00:
$4.10 $3.27
$3.16 $1.85
75^ $.63
$4.75 $2.50
$4.19 $2.71
48^ $.82
Multiply :
4. $426 by 8
9.
264 by 120
14. 751 by 128
5. $375 by 9
10.
322 by 130
15. 265 by 379
6. $785 by 11
U.
303 -by 160
16. 301 by 103
7. $496 by 12
12.
$796 by 87
17. 285 by 320
8. $989 by 70
13.
$948 by 96
18. 909 by 102
Find parts :
Find quotients :
Divide :
19. ^ of 3275
29.
$5720-1-65
39. 57,420-!- 660
20. ^ of 7623
30.
$3510 -J- $78
40. 45,280-5-56
21. ^ of 3252
31.
$2442-^-37
41. 29,811-^828
22. ^ of 5280
32.
$3648 ^$48
42. 73,855-5-746
23. i of 3212
33.
$4089 -J- 47
43. 82,940-1-319
24. f of 1624
34.
$5226-8- $78
44. 26,680-5-117
25. 1 of 5004
35.
$8763-1-127
45. 86,245-5-98
26. J of $38.76
36.
$7303-!- 109
46. 89,991-5-99
27. ^ of $32.64
37.
$9591 -s- 139 "
47. 98,010-5-99
28. xV of 17,028
38.
$9652-1-508
48. 64,280-5-309
FIRST BOOK
249
4ir
►^
EXERCISES
242. 1. Hugh's horse Dexter lost a shoe, and the other
three were loose. At Mr.
Daly's shop he found that
it cost $.35 a shoe to reset
the old shoes and $.50 for a
new shoe; but he had 4
new shoes put on. How
much less would it have
cost to use the old shoes?
2. It took 2 hours to
s}nc^(^ tllf V>nrsP If shoCS,
calks, and nails cost 34^,
how much did Mr. Daly receive per hour for his work?
3. .Mr. Daly selected 21-ounce shoes for the front feet
and 18-ounce shoes for the hind feet. He shaped the
shoes and welded a toe calk weighing 3 ounces to each
shoe. How much did Dexter's shoes weigh?
4. Mr. Daly told Hugh that he had shod a race horse
with 11-ounce shoes in front and 6-oimce shoes behind;
also a draught horse with 30-ounce shoes all around. How
much heavier shoes did the draught horse wear than the
race horse ?
5. The nails used in the draught horse's shoes were 2f
inches long, and the shortest ones in the race horse's
shoes 1y\ inches. Find the difference in length.
6. A 100-pound keg of horseshoes contained -65 horse-
shoes and cost $5.20 (520^). Find the cost per pound and
per shoe.
250 PROGRESSIVE ARITHMETIC
ADDITION AND SUBTRACTION
EXERCISES
243. 1. Count by 3's from 1 to 100; by 4's from 2 to
98; by 5's from 3 to 98.
2. Count by 6's from 2 to 98; from 4 to 100; from 5
to 95.
3. Count by 7's from 1 to 99; from 3 to 94; from 6
to 97. Count by 8's from 1 to 97; from 3 to 99; from
6 to 94.
4. Count by 9's from 2 to 92 ; from 4 to 94 ; from 7 to 97.
5. Count by lO's from 4 to 94; by ll's from 5 to 93.
6. Count backward from 100 by 2's; by 3's; by 4's;
by 5's; by 6's; by 7's; by 8's; by 9's; by lO's; by ll's.
EXERCISES
244. Add and subtract rapidly :
Add in exercise 1, thus : " 46, 66, 73." Subtract in this way :
"45, 25, 17."
1. 45 66 82 43 54 75 96 88
28 42 69 37 38 24 52 43
2.
61
43
36
28
46
55
64
83
32
15
28
19
28
37
46
57
3.
72
67
94
65
48
86
42
74
29
58
18
26
39
47
19
38
4.
64
82
53
96
75
37
97
88
48
37
29
45
57
26
68
49
FIRST BOOK 261
5. A fanner who had 51 cows sold 17 of them. How
many had he left ?
6. A woman paid 56^ for a pound of tea and 39^ for a
pound of coffee. How much did both cost ?
7. From a barrel containing 50 gallons of paint, 18
gallons were sold. How much was left ?
8. Roy traveled 64 miles. He went 17 miles in a sleigh
and the rest of the way by train. How far did he go by
train?
9. There are 16 boys in the arithmetic class and 31
girls. How many pupils are there in the class ?
10. Oscar spent 54^ for valentines, and his brother spent
38^. How much did both boys spend?
How much more did Oscar spend than his brother?
WRITTEN SXBRCISSS
245. .Subtract and test:
Practice until you can do exercises 1-16 in less than 3^ minutes.
1. 2. 3. 4. 5.
$275.50 $589.72 $326.17 $603.00 $428.62
113.24 297.86 89.68 446.36 147.93
6. 7. 8. 9. 10.
$790.74 $235.40 $823.95 $361.33 $993.81
346.98 65.75 536.28 84.66 798.47
11. 12. 13. 14. 15.
$420.53 $706.04 $900.00 $640.30 $805.07
25.86 472.85 639.22 350.64 99.99
252 PROGRESSIVE ARITHMETIC
Add and test exercises 16-25 in less than 8 minutes :
16. 17. 18. 19. 20.
39,636 23,809 98,437 7,348 28,398
14,684 7,634 4,689 42,789 76,495
49,871 19,872 57,923 16 48,973
27,588 56,391 37 8,547 52,798
89,663 4,589 12,463 96,873 86,698
68,942 73,862 899 8,439 98,765
21. 22. 23. 24. 25.
$134.50 $896.38 $475.89 $563.47 $897.69
296.22 147.99 742.78 28.69 576.39
452.31 89.74 9.27 8.00 768.48
235.54 5.30 .63 .96 947.96
648.25 67.28 27.45 .08 678.89
379.86 795.89 638.03 89.76 836.78
523.75 427.76 277.54 798.65 458.99
. MULTIPLICATION
EXERCISES
246. 1. Count by 2's from to 100; by 3's to 99; by
4'sto96; by 5'sto 100.
2. Count by 6's from to 96 ; by 7's to 98 ; by 8's to 96 ;
by 9's to 108.
3. Count by lO's from to 120; by ll's to 132; by 12's
to 144.
♦• Count by 13's from to 52; by 14's to 42; by 15's
to 45; by 16'sto48.
M//f^
FIRST BOOK
253
MULTIPLICATION TABLE
A
247. Thoroughly review and memorize :
1x1= 1
Ix 2= 2
Ix 3= 3
IX 4= 4
2x1= 2
2x 2= 4
2x 3= 6
2x 4= 8
3x1= 3
3x 2= 6
3x 3= 9
3x 4 = 12
4x1= 4
4x 2= 8
4x 3 = 12
4x 4 = 16
5x1= 6
6x 2 = 10
5x 3 = 16
5x 4 = 20
6x1= 6
6 X 2 = 12
6x 3 = 18
6x 4 = 24
7x1= 7
7x 2 = 14
7x 3 = 21
7x 4 = 28
8x1= 8
8x 2 = 16
8x 3 = 24
8x 4 = 32
9x1= 9
9x 2 = 18
9x 3 = 27
9x 4 = 36
10x1 = 10
10 X 2 = 20
10 x 3 = 30
10 X 4 = 40 .
11x1 = 11
11 X 2 = 22
11 A 3 = 33
llx 4 = 44
12x1 = 12
12 X 2 = 24
12 X 3 = 36
12x 4 = 48
1x6= 5
Ix 6= 6
Ix 7= 7
Ix 8= 8
2x5 = 10
2x 6 = 12
2x 7 = 14
2x 8 = 16
3x5 = 16
3x 6 = 18
3x 7 = 21
3x 8 = 24
4 X 6 = 20
4x 6 = 24
4x 7 = 28
4x 8 = 32
5x5 = 26
5x 6 = 30
5x 7 = 35
6x 8 = 40
6x6 = 30
6x 6 = 36
6x 7 = 42
6x 8 = 48
7x5 = 36
7x 6 = 42
7x 7 = 49
7x 8 = 66
8x5=40
8x 6 = 48
8x 7 = 56
8x 8 = 64
9x5 = 46
9x 6 = 64
9x 7 = 63
9x 8 = 72
10x5 = 60
10 X 6 = 60
10 X 7 = 70
10 X 8 = 80
11x5 = 65
11 X 6 = 66
11 X 7 = 77
llx 8 = 88
12x5 = 60
12 X 6 = 72
12 X 7 = 84
12 X 8 = 96
1x9= 9
1x10= 10
1x11= 11
1x12= 12
2x9= 18
2x10= 20
2x11= 22
2x12= 24
3x9= 27
3x10= 30
3x11= 33
3x12= 36
4x9= 36
4x10= 40
4x11= 44
4x12= 48
5x9= 45
5x10= 50
6x11= 55
5x12= 60
6x9= 54
6x10= 60
6x11= 66
6x12= 72
7x9= 63
7x10= 70
7x11= 77
7x12= 84
8x9= 72
8x10= 80
8x11= 88
8x12= 96
9x9= 81
9x10= 90
9x11= 99
9x12 = 108
10x9= 90
10x10 = 100
10x11 = 110
10x12 = 120
11x9= 99
11x10 = 110
11 x 11 = 121
11 X 12 = 132
12x9 = 108
12x10 = 120
12 x 11 = 132
12 X 12 = 144
254 PROGRESSIVE ARITHMETIC
EXERCISES
248. Multiply, giving results instantly :
1.
5
7
8
2
11
6
3
10
5
6
4
3
9
4
6
7
9
11
2.
7
6
9
7
8
3
5
7
12
7
4
3
11
4
12
9
6
4
3.
8
5
11
8
6
4
11
12
5
6
7
6
8
10
9
8
6
8
4.
10
9
7
9
7
5
9
7
8
7
9
8
11
9
12
6
12
9
5.
12
10
9
11
10
8
11
11
12
8
10
12
10
12
10
11
12
12
6.
13
13
13
14
14
15
15
15
16
2
3
4
2
3
3
4
5
2
7.
16
17
18
20
20
20
24
25
25
3
2
2
3
4
5
2
3
4
8. What is the perimeter of a 12-foot square ?
9. If a horse travels 6 miles an hour, how far at that
rate will he go in 8 hours ?
10. If a window contains 6 panes of glass, how many
panes do 11 such windows contain?
11. How many quarts of milk are there in 12 cans, each
containing 8 quarts ?
FIRST BOOK 266
12. Find the cost of 2 lb. of beefsteak at 18^ a pound.
13. Find the cost of 2 collars @ 15^' of 3 ties @ 25^.
14. When sugar is sold at the rate of 16 pounds for $1,
how many pounds can be bought for $3?
15. Find how many square rods there are in a lot 9 rods
wide and 12 rods long.
16. At $3 an acre, how much will it cost to plow a field
containing 15 acres ?
WRITTEN SXERCISES
249. Multiply by 6, 7, 8, 9, 11, and 12:
1. 48 3.
269
5. $19.72
7. $476.25
2. 97 4.
848
6. $74.89
8. $638.63
Multiply :
9. 276 by 400
12.
89 by 2000
15.
6709 by 30
10. 742 by 600
13.
78 by 5000
16.
8524 by 90
11. 827 by 800
14.
99 by 7000
17.
9047 by 80
Multiply :
18. $8.97 by 16
21.
$74.39 by 49
24.
$4.56 by 394
19. $7.65 by 27
22.
$83.76 by 65
25.
$6.43 by 586
20. $9.84 by 38
23.
$68.92 by 78
26.
$8.39 by 759
Find products and test :
27. 237x456
31.
594 X 603
35.
689 X 508
28. 468x509
32.
706x498
36.
796x609
29. 608x258
33.
873 X 507
37.
857 X 786
30. 805x387
34.
908x702
38.
968 X 897
256 PROGRESSIVE ARITHMETIC
MEASURING
EXERCISES
250. 1. Find the number of inches in a yard ; in J yd. ;
in 1 yd. ; in | yd. ; in l^ yd. ; in lOj yd.
2. Draw a line . 1 yard long. Divide it into halves.
Mark off the feet. How many feet are there in ^ yd. ?
3. How many feet are there in 1 yd. 1 ft.? in 1 yd.
11 ft. ? in 1^ yd. ? in 3^ yd. ? in 5^ yd. ?
What is the distance 5^ yards called ?
4. How many rods are there in a mile ? in ^ mile ? in
J mile ? in I" mile ? in ^ mile ?
5. Give the table of measures of length.
6. How many square inches are there in a square foot ?
How many square feet are there in a square yard?
^ sq. ft. = sq. in. | sq. yd. = sq. ft.
7. Give the table of measures of volume.
f cu. yd. = cu. ft. 1^ cu. yd. = cu. ft.
8. Give the table of liquid measure ; of dry measure.
9. How many quarts are there in 1 gal. 2 qt. ? in 1^ gal. ?
in 2| gal. ? in 5 gal. 1 qt. ? in lO^ gal. ?
10. How many pints are there in a gallon ? in ^ gal. ? in
I gal. ? in 11 gal. ? in 12^ gal. ?
11. How many pecks are there in 1 bu. 2 pk. ? in 2^ bu. ?
inlfbu.? in2ibu.?
12. How many quarts are there in a bushel ? in f bu. ?
FIRST BOOK 257
WIUTTSN SXBRCISES
261. 1. How many feet 2. How many quarts are
are there in 5 yards 2 feet ? there in 5 bushels ?
Solution Solution
1 yd. = 3 ft. 1 bu. == 4 pk. ; 1 pk. = 8 qt.
5 yd. = 5 X 3 ft. =15 ft. 1 bu. =4 x 8 qt. =32 qt.
5 yd. 2 ft. = 15 ft. 4-2 ft. = 17 ft. 5 bu. = 5 x 32 qt. = 160 qt.
Finding the number of feet in 5 yards 2 feet is called
reducing 5 yards 2 feet to feet. Finding the number of
quarts in 5 bushels is called reducing 5 bushels to quarts.
Reduce :
3. 14 yd. 2 ft. to feet. 9. 3 bu. to quarts.
4. 5 yd. 1^ ft. to feet. lo. 2 lb. 5 oz. to ounces.
5. 8 gal. 2 qt. to quarts. ii. 3 mi. 20 rd. to rods.
6. 12 pk. 4 qt. to quarts. 12. 2f mi. to rods.
7. 11 gal. to pints. 13. 3 yd. to inches.
8. 5 sq. yd. 5 sq. ft. to sq. ft. 14. 1^ sq. yd. to sq. in.
15. Mt. Whitney is 14,502 feet high (above sea level).
How many feet less than 3 miles high is it ?
16. A can for maple sirup is 5 in. by 5 in. by 9j in. How
much more or less than a gallon (231 cu. in.) will it hold ?
253. Measuring time.
1. Write the present date. What time measures are
used in writing dates ? Name several smaller time measures.
FIRST PROO. AR. — 17
• <tk^^^^<i^^^ ^
258
PROGRESSIVE ARITHMETIC
2. How man y hands has a watcH ?
The smallest hand is called the
second hand.
3. How many little spaces does the
second hand move over while the
minute hand moves over one minute
space ?
How many seconds, then, equal one
minute ?
4. Leam this table of measures of time :
60 seconds (sec
.) = 1 minute (min.)
60 minutes
= 1 hour (hr.)
24 hours
= 1 day (da.)
7 days
= 1 week (wk.)
365 days
= lyear (yr.)
5. There are 12 months in a year. Name them.
6. Four of these months have 30 days each. All the
rest, except February, ha vis 31 days each.
February usually has 28 days, but once in four years it
has 29 days. The years in which February has 29 days are
called leap years. Leap years have 366 days.
Thirty days have September,
April, June, and November.
All the rest have thirty-one,
Save February, which alone
Has twenty-eight ; and one day more
We add to it one year in four.
253,Q ^duce and e xplain each reductioQ ^fV
FIRST BOOK
WRITTEN EXERCISES
1. 5f min. to seconds. 4. 16 wk. 3 da^to days.
2. 3 hr. 20 min. to minutes. 5. 2^ hr. to seconds.
3. 2 yr. 15 da. to days. 6. 3 da. 12 hr. to hours.
7. A watch gained 2 minutes during September. How
many seconds did it gain a day ?
8. A horse trotted a mile in 2 min. 12 sec. How many
feet did the horse trot per second ?
254. Measuring weight.
1. Name things sold by the pound ; by the ounce.
2. The butcher sells meat by the pound. He buys it
by the hundred pounds, or hundredweight.
How do you think cattle,
hogs, and sheep are sold ?
3. The dairyman often
buys bran and feed by the
hundredweight.
The dealer buys such
things in larger quantities,
by the 2000 pounds, or ton.
Mention other articles ^^
sold by the ton.
4. How many himdredweight are there in a ton ?
5. Iron ore, iron, and steel (except iron and steel in bars)
are sold by a larger ton of 2240 poimds, called a long ton.
^^^
260 PROGRESSIVE ARITHMETIC
6. Learn this table of measures of weight :
16 ounces (oz.) = 1 pound (lb).
100 pounds = 1 hundredweight (cwt.)
20 hundredweight = 1 ton (T.)
2240 pounds = 1 lo»g ton (L.T.)
WRITTEN EXERCISES
255. Reduce, and explain each reduction :
1. 4 lb. 8 oz. to ounces. 4. 7f T. to cwt.
2. 12j cwt. to pounds. 5. -^^ T. to ounces.
3. 3 T. 375 lb. to pounds. 6. 5 cwt. 80 lb. to lb.
Find the cost of :
7. 2i T. of hay at $11.60 per ton.
8. 2 T. 6 cwt. of bran at $1.20 per cwt.
9. 32 T. of coal at $4.50 per ton.
10. 7| cwt. of beef at $ 10.40 per cwt.
11. 145 cwt. of bar iron at $2.05 per cwt.
12. 200 long tons of steel rails @ $28.
256. Measuring land.
1. What is the area of a building lot 30 ft. by 150 ft. ?
2. A square, each of whose sides is 1 rod long, is called
a square rod (sq. rd.).
3. What, then, is the area of a pasture lot 10 rods by
16 rods ? of a garden 20 rods by 8 rods ?
160 square rods is called an acre (A.).
FIRST BOOK
261
4. Tell in acres the area of the pasture lot mentioned in
exercise 3 ; the area of the garden.
5. What is the area in acres of a peach orchard 40 rods
square ? of a cotton field 80 rods long and 60 rods wide ?
WRITTEN EXERCISSS
267. 1. Several years ago Mr. Taylor bought the tract
of land 160 rods square, shown
in this map with its corners
marked © . How much did the
land cost him at $25 an acre?
*yy/A /*"( '''// '^y^ ''
y/A
'V\ .^ -^^ I
-'^^'^"^ ■ - "^^^
'-:tHax"[£"-:
^ l>«*4^4it .
2. When the roads on the
east and west sides were laid
out, each 4 rods wide, half the
width of each was taken from
Mr. Taylor's land. How many
acres less had he than before ?
3. Mr. Taylor sold the north half of his farm, between
the roads, to Mr. Holden, at $45 an acre. How much did
he receive for that part of his farm ?
4. Later he sold the southwest quarter, 78 rd. by 80 rd.,
to Mr. Hall, at $65 per acre, and the southeast quarter to
Mr. Lee at $75 per acre. How much did he receive for
each of these farms ?
5. Mr. Lee's com field is 80 rd. by 46 rd. ; his meadow,
60 rd. by 32 rd. ; and the lot for buildings, garden, etc.,
20 rd. by 32 rd. Find the number of acres in each part.
262
PROGRESSIVE ARITHMETIC
6. Before Broadway, State St., and Pearl St. were laid
out, Mr. Adams paid $120 an acre for a piece of land
26| rd. by 24 rd., shown i i
here with the corners 1 "
marked ©.
Find the cost of the -
land.
e — BROADWAY
-^
PEARL
How much did
7. When the streets
and the alley were laid
^ out, Mr. Adams divided
"t^e land left into lots,
J each 40 ft. by 132 ft.,
> except A and B.
^ Ale sold four 40-foot lots at $150 each,
he receive for them ?
8. Later he sold eight 40-foot lots at $15 a front foot,
and still later five more at $22 a front foot. How much
did he receive from these sales ?
9. He sold lot B, 36 ft. by 132 ft., at $.30 a square foot.
How much did he receive for lot B ?
10. Later, one man offered him $60 a front foot for lot
A, which is 76 ft. wide ; and another man offered him $5000
for the lot. Which was the better offer, and how much ?
11. When Broadway was paved, the owner of lot C had
to pay for a strip of pavement 40 ft. by 39 ft. Find the
expense to him at $2.25 per square yard.
12. Find the cost of paving the alley, 12 ft. by 396 ft.,
at $1.75 per square yard.
c
FIRST BOOK 268
FRACTIONS
268. 1. What is a fraction ? Write a fraction.
2. Write the fraction that stands for 3 of the 4 equal
parts of 1 ; 5 of the 6 equal parts of 1.
3. The fraction ^ stands for 7 of the 8 equal parts of 1.
In this fraction 7 is called the numerator^ and 8 the
denominator; 7 and 8 are called the terms of the fraction.
4. What is the numerator of the fraction f? the de-
nominator ? What are the terms of the fraction ? -^
5. What are the terms of l? of |? of |? y ^-^^^ '
_ _ ^ ^ — -^ ^'^ ^ -"^
259. <:R6guciDfif fractions to lower or higher t ermsr>v^-y f
% Cr
1. How many tenths of this oblong are shaded? how
many fifths ? Then 3-% = ?
Which fraction has the smaller, or lower,
terms, inr or f ?
Changing ^ to the equal fraction f is called reducing -^
to lov^er terms.
2. What number will exactly divide both terms of ^?
What fraction is obtained by dividing the terms of ^^ by 2 ?
Then how may ^^ be reduced to lower terms ?
3. Can you reduce f to lower terms ?
Then ^^^ reduced to lowest terms is f .
4. Reduce to lowest terms :f;f;f;|;|;i^;A.
5. Look at the oblong and tell the number of tenths in f .
Changing f to -^^ is called reducing f to Mgher terms.
x^
264 PROGRESSIVE ARITHMETIC
6. Multiply both terms of f by 2. To what fraction
does this change f? Then how may f be reduced to
tenths?
7. How may ^ be reduced to sixths? ^ to ninths?
J to eighths? f to tenths?
8. Reduce to twelfths :i;i^;i;i;f;f;f.
Multiplying or dividing both terms of a fraction by tJie
same number does not change its value.
EXERCISES
260. 1. Change J to eighths ; to tenths ; to twelfths ; to
sixteenths ; to twentieths ; to twenty-fourths.
2. Change f to sixths; to ninths; to twelfths; to fif-
teenths ; to eighteenths ; to twenty-fourths ; to thirtieths.
3. Reduce to twentieths: J; ^; ^; |; f ; j^^; f ; ^.
4. Reduce to twenty-fourths * f ; |- ; f ; A ; -g^.
5. Reduce to hundredths: i; |; f ; ^V; ^ttJ Ai H-
Reduce to lowest terms :
6. -^ 10. ^ 14. fi 18. A^^ 22. e
7. 3^ 11. if 15. if 19. ^ 23. H
8. t\ 12. 1^ 16. If 20. 3^ 24. ^
9- A 13- jl_ _ 17. if ^21. ^^^ 25. If
261. !6educing integers and mixed n«nihftr» f<^ frartin^gp
1. Which is less, the numerator of f or the denominator ?
the numerator or the denominator of f ? of |? of f ?
A fraction whose numerator is less than its denominator
is called a proper fraction.
FIRST BOOK 266
2. Which is less, for 1? ^orl? fori? fori?
A proper fraction is less than 1.
3. How does the numerator compare with the denomi-
nator in f? inf? inf? in |? in f ?
A fraction whose numerator is equal to or greater than
its denominator is called an improper fraction.
4. How does f compare with 1? f with 1? f ? f ? f ?
An improper fraction is equal to or greater than 1.
5. How many fourths are there in 1 ? in 2 ? in 3 ? in 3
and J? in3i? in 5 and |? in 5f ?
6. How many fifths are there in 3 ? in 3f ? in 5f ?
7. Reduce 2 to halves ; 4 to thirds ; 3 to fifths.
8. Reduce 2^ to halves ; 4f to thirds ; 3f to fifths ; 5^ to
sixths ; 4f to eighths ; 6^^^ to tenths.
EXERCISES
262. Reduce to an improper fraction :
1. 71 4, 2f 7. 8| 10. 7| 13. 10^
2. 5J 5. 3^ 8. 6f 11. 4^^ 14. 12f
. 3. 4f 6. 9i 9. 5| 12. 83^ 15. llj
WRITTEN EXERCISES
263. 1. Reduce 27 to halves ; to thirds ; to fourths.
2. Change 32 to a fraction whose denominator is 3 ; 5 ; 8.
Reduce to an improper fraction :
3. 25^ 5. 19| 7. 34| 9. 48x% n. 26^1
4. 43| 6. 27f 8. 18^ 10. 35^ 12. 14^
266 PROGRESSIVE ARITHMETIC
264. Reducing improper fractions to integers or mixed
numbers.
1. How many half dollars does it take to make $ 1 ?
Then how many dollars are there in 4 half dollars ? in
7 half dollars? in 10? in 13?
2. Find the value in dollars of 8 quarter dollars ; of $ f ;
of 9 quarter dollars; of $|; of $^; of $-V^; of $^^-.
3. Whatisthe value off? |? |? f? ^? ^?
The value of a fraction is the quotient of its numerator
divided by its denominator.
4. Change to an integer: f; ^; ^; ^; ^.
5. Reduce to a mixed number: ^; ^3^; ^ ] ^-^-\ ^; ^.
6. Tell how to reduce- an improper fraction to an integer
or a mixed number.
EXERCISES
265. Reduce to an integer or to a mixed number :
1- 1
*• ¥
7. y
10. ^
13. ^
2- f
5- ¥
8. e
11. ¥
"• ^
3. f
6 ¥
9- ^
12. ^
15. fl
WRITTEN EXERCISES
266. Reduce to an integer or a mixed number :
1. -^ 4. ^ 7. ifi 10. ^^ 13. ^
2. ¥ 5- ¥ 8- H^ 11- W "• W
3. ^ 6. ^ 9. W 12. ^ 15. W
FIRST BOOK
267
267. Adding and subtracting fractions.
1. Compare the denominators of J and f ; of ^ and ^^.
The fractions j% and -^ have a common denominator.
2. What must be done to fractions that have different
denominators before they can be added or subtracted?
3. Reduce | and J to fractions having a common de-
nominator ; f and ^ ; J and f ; ^ and J.
Add I and ^; f and ^. Subtract | from f ; ^ from J.
EXERCISES
268. Give answers :
1- i + f 4- l-i V. f -J 10. § + | + J
2- Hi 5. i-i 8. I +f 11. l-l + f
3. i-i 6. i + i 9. ^^-f 12 i + i-,^
13. Count by 2|'s from to 50, thus : " 2|, 5, 7^," etc.
Count back by 2|^'s from 50 to in this way : "50, 47^,
45," etc.
14. Count by 3^'s from to 50 and back ; count by 4j's
from to 42 and back.
Add and subtract :
15. 7i
5i
16. 5i
2f
17. 6|
4|
20. If the hole in this iron plate is
Y^ square, how wide is the plate ?
21. How far is the hole from the
right end of the plate?
268
PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
269. 1. Add I, f , and t^^-
What must be done before these fractions can be added ?
Can they all be reduced to tenths? to twentieths? to
fortieths ?
f + f + ru= Why is it better to reduce
i..g. + ^8^ + 14 = .| T = ii^ the fractions to twentieths than
to fortieths ?
By what number must the terms of f be multiplied to
reduce the fraction to twentieths ? the terms of f ? of ^jj ?
Observe that the common denominator is a multiple of
each of the given denominators, 4, 5, and 10.
Do as the signs indicate :
3. l + f 6. fl-e 9- H + U 12- f-f + f
Add and subtract :
14. 43^ 15. 363^ 16. 84| 17. 75x^2 18- 97^^
27| 19| 51^ 38ii 23M
19. How long is this anvil ?
The top is 3f wide, and
ifaft*
20
the square hole is l^^'' from each
side. How wide is the hole?
21. A 135-pound anvil after several years' use weighed
132^^ pounds. Find the loss of weight due to wear.
FIRST BOOK 269
270. Finding parts of numbers.
EXERCISES
Find:
1. I of 48 4. 3^ of 70 7. fof56 lo. j*'^ of 120
2. I of 55 5. T^<y of 90 8. I of 64 u. ^ of 108
3. I of 72 6. ^ of 84 9. I of 96 12. ^ of 144
13. How many minutes are there in ^ of an hour?
14. A boy who had 80 cents spent ^ of it on the Fourth
of July. How many cents did he spend ?
15. How many quarts of oats had Mr. Gould fed his
horse when he had fed him -| of a bushel?
WRITTEN EXERCISES
271. Find:
1. I of $2.68 4. I of 392 7. | of 4984
2. I of $4.92 5. ^ of 860 8. jV of 6396
3. I of $6.88 6. 3^ of 948 9. ^^ of 8076
10. Find the cost of f A. of land at $136 A.
11. Mr. Harmon set out 228 tomato plants, and Mr.
Gage I" as many. How many plants did Mr. Gage set out ?
12. Find the cost of f of a ton of coal at $6.25 a ton.
13. A farmer stored 384 bushels of potatoes, and ^ of
them decayed. How many bushels decayed ? How many
did not decay?
14. I paid $4632 for a house and sold it for ^ of the
cost. For how much did I sell it ? How much did I lose ?
270 PROGRESSIVE ARITHMETIC
273. Multipljring by a mixed number.
EXERCISES
Multiply :
1. 9by7i 3. 10 by 4^. 5. 24 by 2^ 7. 16 by 2f
2. 8by9j 4. 12by5i «• 15 by 3f 8. 20 by 3f
9. Find the cost of 2| pounds of cheese @ 14^.
10. When eggs are worth 20^ a dozen, how much must
be paid for 3j dozen ?
11. Mr. Ford bought 2^ bushels of corn at 40^ a bushel.
How much did the corn cost ?
WRITTEN EXERCISES
273. Multiply:
1. 78 by 6| 4. 225 by 47| 7. 576 by 146|
2. 84by9| 5. 464by56| 8. 768 by 325^
3. 96by8f 6. 680by89jV »• 948 by 478^^
Find the cost of :
10. 12| gallons of vinegar @ $.28.
11. 25f acres of land @ $ 96. .
12. 37f tons of hay @ $ 15.50.
13. 44|- yards of silk @ $ 1.12.
14. A dressmaker bought a piece of velvet containing
24f yards at $ 2.25 a yard. Find the cost.
15. If an express train runs at the rate of 48 miles an
hour, how far will it run in 23^^^ hours ?
y^
FIRST BOOK rs;d^ oV^^^ ^"^-^
274^^c^l nding the whole when one or more parts are give fl)
1. If 3 oranges cost 9 cents, how much will 1 orange
cost ? 4 oranges ?
2. If 3 fourths of a cake cost 9 cents, how much will 1
fourth of it cost ? 4 fourths, or the whole cake ?
3. If f of the cost of a top is 9 cents, how much is \ of
the cost ? f , or the whole cost ?
4. If f of a number is 9, what is J of it ? what is the
number ?
5. If f of a number is 10, what is ^ of it ? what is the
number ? If f of a number is 8, what is the number ?
EXERCISES
275. 1. If f of a number is 15, what is the number?
2. 12 is f of what number ?
3. 18 is f of what number?
4. 20 is \ of what number ?
5. 24 is f of what number ?
6. Helen spent f of the money she had for a fan. If
the fan cost 40 cents, how much money had she at first ?
7. If f of the number of pupils in the fourth grade are
girls and there are 25 girls, how many pupils are there ?
8. FinH^thp oc\>^t of a pound of mustard, '^ \ o f a pound
costs 24<5entS.^j '-'f -^-^"^ r^^-L^^:>t .'."^^T i. /v^ :.v . -'? tfLs- nvO<^-'^
9. Mr. Hay bought f of a bushel of corn for 30 cents.
At that rate how much would a bushel cost ?
10. Elmer weighs 55 pounds, and his weight is \^ that of
Henry. How much does Henry weigh ?
272 PROGRESSIVE ARITHMETIC
WRITTEN EXERCISES
\l 276. 1. Mr. Day has $278 in the bank, and this is f of
all the money he has. How much money has he ?
; ' ^^^ i of his money = $ 278 -s- 2, or $ 139.
His money =3 times $139, or $417.
$417
2. Find the c oal of a horse, if f of the cost was $135.
} s. How much is a ton of coal worth when f T. costs $ 3.75 ?
j y 4. A man owning a mill offered to sell f of his interest
" -for $7675. At that rate how much was the mill worth?
5. - J£ \ of the cost of a farm was 3S2964. find the cost.
6. Mr. Stone paid $2.25 for f of a bushel of grass seed.
. How much was a bushel worth at the same rate ?
. Vt^'^^^^7. Jf ^ of thft gflrriaon of a. fort rftnftivftd wnnnda and
< \^' -^''*d85 soldiers were wounded, how many were in the fort?
277.'v J'inding wto part one' num Wis-JOfanotheP
1. What part of the whole oblong is 1
vertical colunrn of squares ? 2 columns ?
How many squares are there in the ob-
long? how many are shaded? What pait
of the oblong is shaded ?
Then 8 squares is what part of 20 squares '^
8 is ^, or f , of 20.
2. How many squares of the oblong are light? What
part of the oblong is light ? Then 12 is what part of 20 ?
12 is Ji or f , of 20.
FIRST BOOK 273
3. How many squares are there in 2 horizontal rows ?
What part of the oblong is 2 rows ?
Then 10 is what part of 20?
4. What part of the oblong is 3 horizontal rows ? Then
15 is what part of 20 ?
5. What part of 24 is 8? 9? 12? 16? 18? 20? 22?
EXERCISES
. 278. What part of:
1. 15 is 5? 5. 18 is 12?
2. 16 is 4? 6. 30 is 20?
3. 18 is 6? 7. 36 is 18?
4. 12 is 9? 8. 40 is 25? .
13. What part of 100 is 10? 20? 25? 30? 40? 45? 50?
60? 70? 75?' 80? 90?
14. What part of $1 is 10^? 20)^? 25^? 50^? 75^?
15. Mr. Boyd feeds his horses 12 quarts of oats per day.
What part of a bushel does he feed them each day ?
16. What part of an hour is 15 minutes ? 20 minutes ?
30 minutes ? 45 minutes ?
17. Robert lives 80 rods from the schoolhouse. What
part of a mile does he have to walk in going to school ?
18. What part of an acre is there in a lot that is 10 rods
long and 8 rods wide ?
19. Mr. Gay bought 500 pounds of bran. What part of
a ton did he buy? How much did it cost at $16 a ton?
FIRST PROG. AR. — 18
9.
50 is 30?
10.
48 is 36?
11.
60 is 48?
12.
75 is 50?
274 PROGRESSIVE ARITHMETIC
279. Finding the cost when the price can be expressed as
an easy fraction of a dollar.
1. How much will 12 hats cost at $1 each? at $.50?
What part of $ 1 is $ .50 ? Then what part of the cost
of 12 hats at $1 is the cost of the same number at $.50?
An easy way to find the cost of 12 hats at $ .50 each is
to find ^ of the cost at $1 each.
2. From the cost of 16 yards of cloth at $1 a yard, find
the cost at $.25, or $J, a yard; at $1.25, or $1 4-$ J, a yard.
From the cost at $ J a yard, find the cost at $.75, or $f,
a yard.
3. What part of $1 is $.20? How much will 15 books
cost at $.20 each? at $1.20 each?
EXERCISES
280. In a similar way find the cost of :
1. A dozen handkerchiefs at 25^ each.
2. 24 to'wels at 50^ each.
3. 40 napkins at 75^ each.
4. 1 case of eggs (30 doz.) at 20^ a dozen.
5. 44 yards of carpet at $1.25 per yard.
6. 15 baskets of plums at 40^ per basket.
7. 35 pounds of tea at 60^ per pound.
8. 30 hammocks at $1.20 each.
9. 14 yards of silk at $1.50 per yard.
10. 25 pounds of choice candy at 40^ per pound.
11. 70 gallons of maple sirup at $1.10 per gallon.
FIRST BOOK 275
WRITTEN EXERCISES
281. 1. Mr. Hopkias bought 236 bushels of oats at $ .25
a bushel. How much did they cost him ?
At $1 a bushel 236 bushels of oats would
4)$236 ^^ ^236. ($ .25 = $ J.)
*^^ At $ J a bushel the oats cost J of $236, or $ 59.
2. A grocer bought 400 pounds of butter at 25 cents
per pound. Find the cost.
3. At a fair 3248 50-cent tickets were sold in one day.
Find the gate receipts for that day.
4. A farmer sold a load of hops weighing 2880 pounds
at $ .20 a pound. How much did he receive for them ?
5. An orchard yielded 840 bushels of peaches. How
much were they worth at $1.50 per bushel?
6. How much will a boy earn in 28 days at $ .75 per day ?
7. A car contained 175 barrels of apples. How much
were they worth at $1.40 per barrel?
8. A cargo of lemons consisting of 25,000 boxes was
bought for $1.60 per box. Find the cost of the cargo.
9. Thirty olive pickers and an overseer received $50 a
day. If each picker received $1.50 per day, how much did
the overseer receive ?
10. Find the cost of this lot at
$ .80 per square foot.
11. Find the cost of sending 30,000 pounds of oranges
from California to New York at $1.25 per hundredweight.
276
PROGRESSIVE ARITHMETIC
282. Comparing fractions.
1. Into how many small squares is
the oblong divided ?
What part of the oblong is each small
square ?
The oblong is also divided into halves and mXo fourths.
Point to \ of the oblong ; to |^ of it ; to ^ of it.
2. How many fourths are there in ^ ?
Compare ^ with \ in this way : " ^ is 2 times J."
Whatpartof ^is J?
Compare J and \ in this way : " i is ^ of J.''
3. How many eighths are there in J? What part of
iisi?
^ is times \.
i is of |.
4. How many eighths are there in J? What part of \
is ^ ? Compare J with \ ; \ with \.
EXERCISES
283. By observing this oblong compare :
1. ^ with ^ 3. \ with ^
2. yV with ^ 4. yV with \
Draw oblongs, and by dividing them properly, compare :
5. ^ with ^ 9. ^ with 3^^ 13. \ Avith ^
6. \ with ^ 10. -^ with ^ 14. ^^ with \
7. J with ^ 11. ^ with ^ 15. ^ with ^
8. ^ with ^ 12. ^ with \ 16. -^ with ^
FIRST BOOK 277
DIVISION
EXERCISES
284. Give quotients at sight :
1. 48-5-3 5. 42H-14 9. 99-i-ll i3. 72-!- 6
2. 63-^7 6. 88-i-Il 10. 84-8-12 i4. 30-i-15
3. 50-!-2 7. 34-i-17 11. 26-!- 13 15. 28-i-14
4. 32-8-8 8. 60-!-12 12. 32-S-16 i6. 39-!-13
17. Write " 72 divided by 8 " in these three ways :
(1) Use the division sign, -^ .
(2) Use a curved line between 8 and 72.
(3) Use a fraction whose terms are 72 and 8.
Read, using the words " divided by " ; answer carefully :
18. ^^= 23. 12 in. )96 in. ^^ 45 ft.
19. 140bu.-i-7= 24. 12 )132 ft. ^
20. 7 )140 days 25. 108in.-!-12= 29. ^-^
3 ft.
21. 7 da.)14 da. 26. 144 in. -s- 12 in. =
72 pk.
22. 120^-«-40^= 27. 48 oz. -«- 16 oz. = 30. -^-^
Answer carefully, reading across the page :
31. 3 )6 yd. -H yd. 3 )7 yd. 4 )13 gal.
2 yd. -I- ^ yd. — yd. — gal.
32. 4qt. )8qt.-H qt. 4 qt. )9 qt. $5)$22
2 -h i
278 PROGRESSIVE ARITHMETIC
33. We find J of 17 pecks by dividing 4 )17 pk.
17 pecks by 4. — pk.
34. We find how many times 17 pecks 4 pk. )17 pk.
contains 4 pecks by dividing 17 by 4.
Tell what each indicated division means ; then answer :
35. 2 )27 qt. 39. 2 pt. )31 pt. $47 $47
36. 4)39 bu. 40. 4 pk. )50 pk. *^* ~2~' "$2
37. 5 )41 mi. 41. 3 ft. )62 ft. 44. 420min.^60
38. 16 )36 lb. 42. 12 in. )30 in. 45. 300 sec. h- 60 sec.
Find the cost of 1 article at the rate of :
46. 3 for 25^ 48. 8 for 50^ so. 3 for 50^
47. 4 for 25^ 49. 8for$l 51. 12 for $1
WRITTEN EXERCISES
285. 1. Reduce 101 in. to feet and inches; 75 in. to feet.
Solutions
12 m. )101 in. 12 in. )75 in.
8, 5 in. remainder 6^^
101 in. = 8 ft. 5 in. 75 in. = 6^^ ft. = 6J ft.
Reduce :
2. 46 ft. to yd. and ft. 5. 200 in. to ft.
3. 95 qt. to gal. and qt. 6. 110 pk. to bu.
4. 220 min. to hr. and min. 7. 134 qt. to gal.
FIRST BOOK 279
Reduce :
8. 125 qt. to pk. and qt. ii. 110 ft. to yd.
9. 177 mo. to yr. and mo. 12. 126 qt. to pk.
10. 1000 oz. to lb. and oz. 13. 156 hr. to da.
14. If a train runs 500 miles in 12 hours, how many
miles does it run per hour ?
15. A barrel of flour weighs 196 pounds. How much
does a quarter of a barrel of flour weigh ?
Find the weight of J barrel of flour.
16. 17. 18.
1|00 )75|60 2|00)8|40 2|00)9l60
75TV^ = 75f 4^ = 4i 4M§ = 4f
Divide :
19. 570 by 100 23. 420 by 200 27. $1250 by 1000
20. 350 by 100 24. 960 by 200 28. $7500 by 3000
21. 720 by 100 25. 1200 by 500 29. 5000 T. by 2000
22. 2440 by 100 26. 1500 by 800 30. 2500 lb. by 2000 lb.
Reduce :
31. 210 sec. to minutes. 34. 1800 rd. to miles.
32. 440 min. to hours. 35. 2840 lb. to cwt.
33. 500 sq. rd. to acres. 36, 5500 lb. to tons.
37. Express 875^ as dollars and cents.
38. Find the cost of 3000 lb. of hay at $12.50 per ton.
39. Find the value of a farm 120 rods long and 110 rods
wide at $56 an acre.
280 PROGRESSIVE ARITHMETIC
WSITTEH EXERCISES
286. I. Divide 4572 by 48.
-V ^ -1
95i
48)4572 4^72 + 48 = 95, with a remainder of 12.
432 12 + 48=if = i-
252 The quotient is 95j.
240 Test the answer by multiplying 48 by 94 J.
12
Divide and test:
2. 1737 -J- 18 6. 1356 + 32
10. 1534-5- 16
3. 4319 H- 56 7. 2922-54
11. 3900 •<- 84
4. 6226-5-66 8. 5848-5-72
12. 2676-5-132
5. 2976-5-36 9. 1652-5-24
13. 5388-5-144
14. If 28 boys weigh 2114 pounds, what is their average
weight?
15. A bushel of wheat weighs 60 pounds. How many
bushels of wheat are there in a car that contains 37,520
pounds of wheat?
Divide :
16. 189,175 by 235 21. 389,672 by 536
17. 407,886 by 471 22. 406,224 by 496
18. 288,750 by 750 23. 727,155 by 585
19. 166,957 by 427 24. 555,111 by 333
20. 311,812 by 548 25. 780,781 by 409
FIRST BOOK
281
WRITTEN EXERCISES
287. This electric
railway connects two
towns 7 miles apart.
1. If the cars
run from one town
to the other in 15
minutes, how many
miles per hour do
they run ?
2. Each steel rail
is 30 feet long and
weighs 65 pounds per
yard. How much does 1 rail weigh ?
3. Find the cost of all the rails at $28 per long ton.
4. The ties are 10 inches wide and the spaces between
them 14 inches wide. How many are there per mile ?
5. Find the cost of ties for a mile of track at 60^ each.
6. There are 44 poles for every mile of track. How
many feet apart are the poles ?
7. Find the cost of the poles at $2.75 each.
8. How many posts 1 rod apart are required for both
fences? Find their cost at 18^ each.
9. How many pounds of wire are required for both
fences, if 15 feet of wire weigh a pound?
10. The copper trolley wire weighs 2128 pounds per
mile. Find its cost at 16^ per pound.
: dci--
4,
282 rv/ PROGRESSIVE ARITHMETIC
^
yr\y DECIMAL FRACTIONS
A \ 288. 1. When anything is divided into 10 equal parts,
\, what is each part called?
One tenth may be written in these two ways: 3^^ and .1.
The period before the figure 1 is called the decimal point.
Read: ^^) .3; y^^; .5; .6; .9; &.
Write in two ways : 2 tenths ; 4 tenths ; 7 tenths.
2. If each tenth of anything is divided into 10 equal
parts, into how many equal parts will the whole thing be
divided ?
• When anything is divided into 100 equal parts, what is
each part called ?
One hundredth may be written in these two ways : ^^
and .01.
Read: xoxrJ '03; rinrJ -O* 5 ijinrJ '25; oirJ -oO; .37;
.06; .18; .45; .09; .75.
Write in two ways : 8 hundredths ; 15 himdredths ; 35
hundredths ; 4 hundredths ; 62 hundredths.
3. If each hundredth of anything is divided into 10 equal
parts, into how many equal parts will the whole thing be
divided ?
When anything is divided into 1000 equal parts, what is
each part called ?
One thousandth may be written in two ways : xinnr ^^d
.001.
Read: ttAttt; -003; j^h) -019; M^\ .225; .007;
.045; .372; .608; .250; .009; .075.
Write in two ways: 5 thousandths; 25 thousandths;
FIRST BOOK 283
452 thousandths; 8 thousandths; 50 thousandths; 86
thousandths ; 999 thousandths.
4. How many thousandths are there in 1 hundredth?
hundredths in 1 tenth ? tenths in 1 unit ?
Fractions that express tenths, hundredths, thousandths,
etc., are called decimal fractions, or decimals.
Other fractions are called common fractions.
5. Read these decimals :
.1 .01 .001 .111
.3 .03 .003 .333
How many figures are needed to express tenths ? hun-
dredths? thousandths?
What does 1 mean when it stands in the first place at
the right of the decimal point? in the second place? in
the third?
What does 3 mean when it stands in tenths' place ? in
hundredths' place ? in thousandths' place ?
6. One and 1 tenth may be written, 1.1; 1 and 1 hun-
dredth, 1.01; 1 and 1 thousandth, 1.001.
Write : 5 and 7 tenths ; 23 and 9 hundredths ; 247 and
139 thousandths; 4 and 56 hundredths; 17 and 8 thou-
sandths ; 9 and 24 thousandths.
Read, using the word and between the integer and the
decimal, but not elsewhere: 3.4; 5.9; 8.25; 19.07; 6.146;
25.037; 30.002.
7. A number expressed by an integer and a decimal is
called a mixed number, or a mixed decimal.
C I
289. Read:
1. .5
4. .04
2. .8
5. .85
3. .24
6. .005
284 PROGRESSIVE ARITHMETIC
EXERCISES
7. .325 10. 6.4
8. .032 11. 3.08
9. .430 12. 7.875
Write each of the following in another form :
13. ^ 16. .11 19. .27 22. 3^
"• T^ 17. .011 20. .016 23. 43^
IS- Tinnr 18- -111 21. .375 24. Sj^^^y^
Write as decimals :
25. 6 tenths ; 2 hundredths ; 3 thousandths.
^ 26. 12 and 25 hundredths ; 14 and 125 thousandths.
i I 27. 100 and 4 hundredths; 1000 and 1 thousandth.
EeSucing decimals to common fractionsy
; WRITTEN EXERCISES
1. Reduce .2 to a common fraction ; also .75.
•2 = ^ = i -75 = ^ = 1
Reduce to a common fraction in its lowest terms :
2.
.4
8.
.60
14.
.06
20.
.005
3.
.6
9.
.80
15.
.200
21.
.250
4.
.8
10.
.50
16.
.500
22.
.025
5.
.20
IX.
.32
17.
.020
23.
.750
6.
.25
12.
.05
18.
.050
24.
.400
7.
.40
13.
.04
19.
.002
25.
..800
FIRST BOOK 286
^ = ^=•5 H = A = .3
29l CTteducing c ommo n fractions to rfecimflTS^
EXERCISES
1. Reduce ^ to a decimal ; also ^.
1 _ 5 .
2 ""TO ■
Reduce to tenths and write as a decimal :
3. f 5. ^ 7. if 9. H
Reduce to hundredths and write as a decimal :
10. i 12. J 14. /^ 16. ^^%
11- i 13. I 15. ^ 17. /^
Reduce to thousandths and write as a decimal :
18. i 20. f 22. 2^ 24. ^2^
19. i 21. J 23. ^ 25. -^^
292. Adding and subtracting decimal fractions.
WRITTEN EXERCISES
1. Add 1.125, 4.27, and 6.075.
. Units are written in one column, tenths in
another, etc. When this is done, the decimal
points stand in a column.
^■.' Adding and placing the decimal point imder
the other decimal points, the sum found is
11.470; but since tVA^tW; we write 11.47.
286 PROGRESSIVE ARITHMETIC
Add:
2. 4.7 and 3.8 7. 45, 3.5, 10.05
3. 6.75 and 2.63 8. 3.6, 4.82, 5.756
4. 4.235, 6.41, 2,567 9. 34.704, .436, 2.47
5. 3.625, 1.05, 3.385 lo. 17.205, .495, 3.7
6. 24.63, 0.75, 61.006 ii. 3.3, 4.03, 6.003, .667
12. Subtract 2.34 from 5.8.
5.80 The minuend 5.8 has fewer decimal
2.34 places than the subtrahend 2.34. But since
3.46 Y^iF = T(r(^f *^^ minuend may be written 5.80.
Subtract :
13. 1.56 from 2.5 is. 3.822 from 25.4
14. 7.405 from 9.64 16. 5.218 from 6.434
17. From 10 subtract: 7.5; 2.5; 6.67; 1.625.
18. From 100 subtract: 4.8; 44.8; 63.75; 33.33.
Add or subtract as indicated :
19. 3.1 ft. + 2.48 ft. 22. 1.1 gal. +99.9 gal.
20. 6.75 in. -4.37 in. 23. 10 in. -4.75 in.
21. 28.72 yd. + 3.58 yd. 24. 3.205 A. +4.375 A.
25. A man who had a farm of 120.75 acres sold 44.37
acres of it. How many acres had he left ?
26. Edward rode 439.4 miles on the train in going from
New York to Buffalo, and 535.9 miles in going from Buffalo
to Chicago. How many miles did he ride ?
FIRST BOOK
287
BILLS
293. 1. Mr. Charles H. Thompson bought the following
articles at Mr. A. B. McLaurin's grocery store :
Apr. 20, 5 lb. of butter @ $.27;
Apr. 21, 3 qt. of beans @ $.06,
and 2 pk. of potatoes @ $ .25 ;
Apr. 24, 3 doz. oranges @ $.35.
How much did Mr. Thompson owe the grocer for butter ?
for beans ? for potatoes ? for oranges ? for all ?
2. When Mr. Thompson bought the oranges he asked
how much he owed. The grocer then made this bill:
New York, O^Jiv. 2^, 190^.
Mv. &/m»^.
886 €. ^vxt&e/ntA ^t.
»0Uflljt (A A. B. McLAURIN, 205 Third Ave.
Dealer in Staple and Fancy Groceries,
terms: &citA.
a^.
^0
6(^. (^utteA. .27
/
36
//
2/
3 cft. i-ea/yi^ .06
f8
//
//
2^
2 ^k.^^Mx^toe^ .26
3 clxx^. <y[yOuruf&^ .36
/
60
06
3
08
Find whether $3.08 was the correct amount, or footing.
3. When the bill was paid, Mr. McLaurin receipted it by
writing below it, " Received payment '' and his name.
288 PROGRESSIVE ARITHMETIC
W8ITTKH JUUCttdSES
394. Suppose that you own a store and have sold the
following goods to several customers (your classmates or
others). Make out a bill to each, and present it for pay-
ment. If found correct, and paid, receipt it.
1. 2 pairs of scissors @ 7of; 16 papers of tacks @ 4^ ;
4 planes @ 80^; 3 hammers @ 65^.
2. 3 chisels @ 45^; 2 screwdrivers @ 55^; 4 augers,
11^, 14^, 17^, 20^; 6 bits @ 20^.
3. 3 wrenches @ 25^; 2 pairs of pliers @ 45^; 8 dozen
bolts @ 24^; 2 lawn mowers @ $4.75.
4. 2 tents @ $8.25; 4 rubber blankets @ $2.75; 2
camp stoves @ $5.50.
5. 2 fishing rods, $2.50; 2 reels, 75^; 100 yd. fish Une
@ 40^ per 25 yd. ; 5 doz. trout flies @ 35^.
Make out and foot bills for the following sales :
The seller may be a merchant known to you ; the buyer, one of
your classmates.
6. 5 doz. oranges @ 35^; 8 doz. bananas @ 15^; 12 qt.
peanuts @ 5^.
7. 9 collars @ 15^; 6 pairs cuffs @ 25^; 4 ties @
50JZJ; 6 shirts @ $1.50; 18 handkerchiefs @ 20^.
8. 1 couch @ $25; 6 chairs @ $1.75; 6 chairs @ $4.25.
9. 3 hoes @ 25^; 2 rakes @ 35^; 1 spade, 75^; 2
shovels C«i 65^; 75 ft. hose @ 15^.
10. 85 yd. carpet @ $1.25; 24 yd. linoleum @ $1.35.
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