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LIBRARY

OF THK

UNIVERSITY OF CALIFORNIA.

OF"

V

Accession 85969 Class

HEATH'S

PRIMARY ARITHMETIC

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HEATH'S

PRIMARY ARITHMETIC

BY

CHARLES E. WHITE

\\

AND

BRUCE M. WATSON

SYRACUSE, N.Y.

BOSTON, U.S.A.

D. C. HEATH & CO., PUBLISHERS

1901

COPYRIGHT, 1901,

BY D. C. HEATH & Co.

PREFACE

IN education, as in other affairs of life, there is a tendency, on the part

of many, to pursue good ideas to unreasonable extremes, and ofttimes to the

exclusion of other ideas quite as good.

This book has been prepared with the design of bringing together the

manifest advantages of the topically arranged text-book and the equally

manifest advantages of the so-called " spiral " plan.

Each subject is treated by itself as exhaustively as the scope and purpose

of tl$ book will warrant. At the same time each new subject introduced is

considered in all its relations with and bearing upon preceding subjects.

By the great abundance and variety of the drill work and problems

throughout the book, all subjects are kept in constant review, every principle

is applied in as many ways as possible, and the unity of the 'book is

preserved.

The order of subjects is determined by the law of dependence, the degree

of simplicity of the matter to be taught, and the relative importance of the

respective subjects in the business of life.

The development of the various principles and processes has been written

with great care and considerably in detail, with a view both to furnish the

teacher a definite plan for presenting the work and to help the student in

his efforts toward independent achievement.

Both the method and the matter of the book have been tested by actual

use in the schoolroom ; they are not in any sense an experiment.

Part I is a strictly primary arithmetic. The first few lessons are extremely

simple, yet they furnish an illustration of the logical steps in the develop-

ment of ideas of number. If any child begins the use of the book with

elementary notions of number already developed in his mind to a certain

point, the judicious teacher will be wise enough to begin where the child's

previously acquired knowledge stops.

The development work preceding each table is designed to give the child

a concrete understanding of the processes by which the table is made instead

of forcing him to memorize abstract results obtained by making arbitrary

combinations. But after a table has been thoroughly developed, the pupil

85969

VI PREFACE

should be drilled in all its combinations until he can give results instantly

without reference to the mental processes by which they may be obtained.

To this end the drill charts should be used daily until all results can be given

correctly without an instant's hesitation.

The problems following the tables were selected from lessons given by

scores of successful primary teachers, and it is believed that they are far

richer in variety of work and forms of statement than any list prepared by

a single individual.

Part II is an introduction to written arithmetic proper. The color work,

both here and in Part I, is introduced not merely to embellish the pages,

but rather to furnish the best means of illustration and practice in certain

arithmetical operations.

Much of the mental work in Part II may be used as supplementary to the

questions in Part I.

Definitions are given only when and where they are needed.

In the treatment of fractions the fact that a fraction is an expression of

division is kept prominent.

Throughout the book the authors have endeavored to insert whatever may

help the pupil to an understanding of principles ; to omit whatever is super-

fluous or may tend to confusion.

B. M. W.

SYRACUSE, February 8, 1901.

TABLE OF CONTENTS

PART I

PAGE

NOTATION AND NUMERATION 1

ADDITION 7

SUBTRACTION ............ 20

MULTIPLICATION ........... 31

DIVISION 42

PAET II

NOTATION AND NUMERATION ......... 75

Arabic . 77

Roman 80

Federal Money .82

ADDITION 83

SUBTRACTION 94

REVIEW PROBLEMS .......... 102

MULTIPLICATION ........... 104

DIVISION 113

REVIEW EXERCISES 124

REVIEW PROBLEMS 125

FACTORING 130

CANCELLATION 132

GREATEST COMMON DIVISOR ......... 134

LEAST COMMON MULTIPLE ......... 135

INDICATED OPERATIONS .......... 137

FRACTIONS 140

REDUCTION OF FRACTIONS . . . . * 143

ADDITION OF FRACTIONS . . . 152 '

SUBTRACTION OF FRACTIONS 154

SUBTRACTION OF MIXED NUMBERS 155

MULTIPLICATION OF FRACTIONS . . . . . . . .156

DIVISION OF FRACTIONS . . . . . . . . . . 161

COMPLEX FRACTIONS . . . . . . . . ... 166

THE THREE QUESTIONS OF RELATION ....... 167

ALIQUOT PARTS ........... 170

REVIEW OF FRACTIONS 172

DECIMAL FRACTIONS 176

To read Decimals . . . 179

To write Decimals .......... 180

REDUCTION OF DECIMALS ......... 182

vii

viii TABLE OF CONTENTS

PAGE

ADDITION OF DECIMALS ......... 184

SUBTRACTION OF DECIMALS 185

MULTIPLICATION OF DECIMALS 186

DIVISION OF DECIMALS 188

REVIEW OF DECIMALS 191

BILLS AND ACCOUNTS .......... 192

DENOMINATE NUMBERS .......... 194

Linear Measures 194

Surface Measures 196

Cubic Measures 199

Liquid Measures 200

Dry Measures 202

Avoirdupois Weight 203

Troy Weight 205

Apothecaries' Weight 205

Federal Money 206

Time 207

Miscellaneous Tables 208

REDUCTION OF DENOMINATE NUMBERS ....... 209

Descending 211

Ascending 212

REVIEW OF REDUCTION . 215

ADDITION OF COMPOUND NUMBERS 216

SUBTRACTION OF COMPOUND NUMBERS . . . . . . . 217

DIFFERENCE BETWEEN DATES . . . . . . . . 218

MULTIPLICATION OF COMPOUND NUMBERS . . . . ... 219

DIVISION OF COMPOUND NUMBERS 220

SURFACE MEASUREMENTS ......... 221

Plastering and Painting . . 223

Carpeting Rooms 224

Papering Walls . . . . . . . . . .227

Board Measure 227

VOLUME MEASUREMENTS . . . . . . . . . 228

Wood Measure . . . 231

Capacity of Cisterns 232

Capacity of Bins 232

PERCENTAGE 233

SIMPLE INTEREST ........... 238

TOPICAL REVIEW . . . . 241

Notation and Numeration 241

Common Fractions 241

Decimal Fractions .......... 242

Denominate Numbers 244

ANSWERS ............ 247

PRIMARY ARITHMETIC

PART FIRST

To THE TEACHER. For early work with numbers, a " counting

table" is almost a necessity, whatever text-book may be used.

It should be about two feet high, thirty inches wide, and six

feet to fourteen feet in length, according to the size of the class.

It should be surrounded by a slightly raised casing to prevent the

counters from falling off.

Toothpicks and shoepegs are very good to use as counters, on

account of their cheapness and convenience of handling.

1. Counters are in a pile in front of the pupils.

Take one counter.

Put another one with it. How many?

Put another with it. How many ?

So on until ten have been taken.

Take three counters ; seven counters ; five ; nine ;

six ; four ; ten ; eight.

Count the girls in the class.

Count the boys in the class.

How many fingers have you on your right hand?

On your left hand ?

i

PRIMARY ARITHMETIC

How many fingers have you on both hands ?

How many fingers and thumbs have you ?

Count ten with your eyes shut.

Give much drill on these numbers, using counters and other

objects.

2. Make the figures 1 , 2, 3, 4, 5, lo, ^ 8, C|.

Teacher place figure 1 on blackboard, and pupils take as many

counters. Teacher place figure 2 on the blackboard and children

take as many counters. So on with all the figures, one at a

time, the pupils each time taking as many sticks as the figure

means.

Teacher count out three, five, nine, seven, eight sticks, etc.,

and pupils make figures to represent them.

Make the figure to tell how many years old you are.

Make the figure to tell how many fingers you have.

Make the figure to tell how many hands and feet

you have.

Make the figure to tell the hour for coming to school.

Much drill should be given in this kind of work.

How many leaves on this

cherry branch ?

How many cherries ?

Make the figure that tells

how many leaves.

Make the figure that tells

how many cherries.

Make a stem holding 5 cher-

ries; 8 cherries; 10 cherries.

PRIMARY ARITHMETIC

How many roses in the

picture ?

How many rosebuds ?

What figure tells how

many roses ?

What figure tells how

many buds ?

Count the roses and buds

together.

How many parts has a wood-

bine leaf?

Make the figure.

How many leaves are there

on a c l ver stem ?

Make the figure.

Make two woodbine leaves.

Count the parts in the two leaves.

Count the red stripes in the flag.

Count the white stripes.

Make the figure that tells how

many red stripes.

Make the figure that tells

how many white stripes.

Count all the stripes.

Count the stars in the bot-

tom row.

How many colors in the flag ?

How many stripes below the blue field ?

How many red stripes below the blue field?

PRIMARY ARITHMETIC

Count the daisies in the

picture.

How many?

What figure tells how

many ?

Count the tall daisies.

Make the figure that tells

how many are not tall.

How many apples are in this picture ?

Make the figure that tells how many apples.

Count the red

apples.

Count the other

apples.

Make the figure

that tells how many

red apples.

How many pears are there in the picture ?

Make the figure that tells how many.

One, 1. Two, 2. Three, 3. Four, 4.

Five, 5. Six, 6. Seven, 7.

Eight, 8. Nine, 9. Ten, 10.

PRIMARY ARITHMETIC 5

3. Take ten sticks. m

Tie them in a bunch, thus, it

Count out ten such bunches and tie them up.

Call each bunch "a ten."

Put one bunch on the table. fj n

Put one stick beside it, thus, ml

How many sticks are there ? | |

Put another stick with it, thus, if If

How many sticks are there ? I J2

Take another ten and put three with it, iijjj

thus, if UHII

How many are there ? I 3

Go on in this way to nineteen.

What does the figure 1 stand for in the number 12?

In the number 13 ?

In 14, 15, 16, 17, 18, 19 ?

How many tens in 11 ? How many over ?

In 12, 13, 14, 15, 16, 17, 18, 19 ? '

4. Suppose we wish to write the number ten. We

will use 1 to stand for ten the same as in the other

numbers.

How many will there be over?

What shall we use to show that jj

there is none over ? *

We will use this figure, 0. Thus, I

The figure, 0, is called naught, and is used where

nothing belongs.

6

PRIMARY ARITHMETIC

Take two tens. How many sticks in all ?

To write twenty we use 2 to stand for two tens,

and to show that there is none over, thus,

Take two tens and one, thus,

How many ? Write it thus,

m

Make the figures for: jj

5. In the same manner as in the preceding lesson, develop

numbers to one hundred.

Write fifteen ; twenty ; eighteen ; fourteen.

Write twenty-five ; thirty-seven ; forty.

Write eighty-tw r o ; ninety-six ; seventy.

Write sixty-one ; forty-seven ; fifty.

Write seventy-nine ; twenty-one ; ninety.

Write forty-eight ; nineteen ; thirty-three.

Lay counters to make forty-two, thus,

Lay counters to make sixty-three.

Lay counters to make seventeen.

Count the desks in your room.

What number will the counters on the table make ?

PRIMARY ARITHMETIC 7

Count the hands in your schoolroom.

Write the number of books on the teacher's desk.

Count fifty forward and backward.

Read these numbers : 25, 21, 38, 45, 36, 28, 72, 64.

Write them in a column, so that the tens will be in a

vertical line.

Write them in words.

ADDITION

'6. Take one counter.

Take one more counter.

How many counters have you ?

How did you get two counters ?

One counter and one counter are how many counters ?

One stick and one stick are how many sticks ?

One book and one book are how many books ?

One boy and one boy are how many boys ?

One and one are how many ?

and are ?

One and one are ?

1 and 1 are ?

Write, 1 and 1 are 2.

Take two counters.

Put one more with them.

How many counters are there ?

How did you get three counters ?

Two counters and one counter are how many counters ?

PRIMARY ARITHMETIC

If the apples in the boy's hand be put with the apple

on the table, how many will there be on the table ? If

the one book be put on the three books, how many

books will there be in the pile ?

Make a number story about the two books and one

book.

Make a number story about the apples in the basket

and the apple on the table. About one marble and one

marble.

Two chairs and one chair are how many chairs ?

Two and one are how many ?

and * are ?

Two and one are ?

2 and 1 are ?

PRIMARY ARITHMETIC

9

In the same way teach three and one, four and one, and so on

to ten and one.

Have children write :

1

and

1

are

2

1

+ 1

= 2

2

and

1

are

3

2

+ 1

= 3

3

and

1

are

4

3

+ 1

= 4

4

and

1

are

5

4

+ 1

= 5

5

and

1

are

6

5

+ 1

= 6

6

and

1

are

7

6

+ 1

= 7

7

and

1

are

8

7

4-1

* 8

8

and

1

are

9

8

4-1

= 9

9

and

1

are

10

9

+ 1

= 10

10

and

1

are

11

10

+ 1

= 11

BLACKBOARD DRILL

Add the 1 to each of the other

numbers around the circle.

7. Take 1 counter. Take two more counters.

How many counters have you ?

How did you get three counters ?

One counter and two counters are how many counters ?

One apple and two apples are how many apples ?

One and two are how many ?

Take two counters. Take two more counters.

How many counters have you?

10

PRIMARY ARITHMETIC

How did you get four counters ?

Two counters and two counters are how many

counters ?

Two boards and two boards are how many boards ?

Two sheep and two sheep are how many sheep ?

Two and two are how many ?

Take three counters. Take two more counters.

How many counters have you ?

How did you get five counters ?

Three counters and two counters are how many

counters ?

Three books and two books are how many books ?

Three trees and two trees are how many trees ?

Three and two are how many ?

In a similar way teach the entire table of twos.

Have children write :

1

and

2

are

3

1

+ 2

= 3

2

and

2

are

4

2

+ 2

= 4

3

and

2

are

5

3

_l_ 2

= 5

4

and

2

are

6

4

_l_ 2

= 6

5

and

2

are

7

5

+ 2

= 7

6

and

2

are

8

6

i 2

= 8

7

and

2

are

9

7

i 2

Q

8

and

2

are

10

8

_j_ 2

= 10

9

and

2

are

11

9

+ 2

= 11

10

and

2

are

12

10

_j_ 2

= 12

PRIMARY ARITHMETIC 11

Make a number story about 3 dolls and 2 dolls.

Another child give the answer.

Make a number story about 7 red roses and 2 white

roses. Give the answer.

Make a story about 6 and 2, 7 and 2, etc.

and are ?

Six and two are ?

6 + 2 = ?

c^ ^ ^

V^^ ^V BLACKBOARD DRILL

b( C\ \

) LL Add the 2 to each of the other num-

^ ^ T 4

T

\ / bers quickly.

/ ^- ^o

I

8. Take 1 counter. Take 3 more counters.

How many counters have you ?

How did you get 4 counters ?

One counter and three counters are how many

counters?

One stick and three sticks are how many sticks ?

One marble and three marbles are how many mar-

bles?

One cat and three cats are how many cats ?

One and three are how many ?

Take two counters. Take three more counters.

How many counters have you ?

How did you get five counters ?

12

PRIMARY ARITHMETIC

Two counters and three counters are how many

counters ?

and are how many dots ?

Two cows and three cows are how many cows ?

Two and three are how many ?

In a similar ,way, teach all the table of threes.

Make a number story about 2 red cherries and 3 red

cherries. Another child give the answer.

Make a story about 8 green leaves and 2 green leaves.

Make a number story about 2 boys and 5 boys.

Make a number story about 7 dollars and 3 dollars.

About 9 and 3.

Have children write :

1

and

3

are

4

1

+ 3 =

4

2

and

3

are

5

2

1 O

-f- o

5

3

and

3

are

6

3

+ 3 =

6

4

and

3

are

7

4

4-3 =

7

5

and

3

are

8

5

+ 3 =

8

6

and

3

are

9

6

+ 3 =

9

7

and

3

are

10

7

+ 3 =

10

8

and

3

are

11

8

+ 3 =

11

9

and

3

are

12

9

+ 3 =

12

10

and

3

are

13

10

4-3 =

13

In a similar manner teach the entire table of Addition, giving

much drill with both concrete and abstract work, as you proceed,

to fix the tables in the minds of the children.

Vary the work, sometimes the teacher doing the work and

pupil telling what she did, and the result.

Have children make questions.

PRIMARY ARITHMETIC

13

9.

BLACKBOARD DRILL

Add the 3 to each of the other num-

bers quickly.

TABLE OF ADDITION

1+1= 2

1+2= 3

1+3= 4

1+4= 5

1+ 5= 6

2 + 1= 3

2+2= 4

2+3= 5

2+4= 6

2+ 5= 7

3 + 1= 4

3+2= 5

3+3= 6

3+4= 7

3+ 5= 8

4 + 1= 5

4+2= 6

4+3= 7

4+4= 8

4+ 5= 9

5 + 1= 6

5 + 2= 7

5 + 3= 8

5 + 4= 9

5+ 5=10

6+1= 7

6+2= 8

6+3= 9

6+4=10

6+ 5 = 11

7 + 1= 8

7 + 2= 9

7+3=10

7+4 = 11

7+ 5 = 12

8 + 1= 9

8+2=10

8+3 = 11

8+4 = 12

8+ 5=13

9 + 1 = 10

9+2=11

9+3 = 12

9 + 4=13

9+ 5=14

io + i=n

10+2 = 12

10+3 = 13

10+4=14

10+ 5=15

1 + 6= 7

1 + 7= 8

1+8= 9

1 + 9 = 10

1+10=11

2+6= 8

2+7= 9

2+8=10

2+9 = 11

2+10=12

3+6= 9

3+7 = 10

3+8 = 11

3 + 9 = 12

3 + 10=13

4+6=10

4 + 7=11

4+8=12

4 + 9 = 13

4+10=14

5 + 6 = 11

5+7=12

5+8 = 13

5+9 = 14

5+10=15

6+6 = 12

6 + 7 = 13

6+8 = 14

6+9 = 15

6+10=16

7 + 6 = 13

7 + 7 = 14

7 + 8 = 15

7 + 9 = 16

7 + 10=17

8 + 6 = 14

8+7 = 15

8+8=16

8 + 9 = 17

8 + 10 = 18

9 + 6 = 15

9 + 7 = 16

9 + 8 = 17

9+9=18

9+10=19

10 + 6 = 16

10 + 7 = 17

10 + 8 = 18

10+9 = 19

10 + 10=20

14 PRIMARY ARITHMETIC

Give three answers to each question below :

1. ?-

h?

= 10

9.

9 _

f-?

= 12

2. ?H

h?

= 17

10.

9 _

h?

= 15

3. ?H

h ?

= 9

11.

9 _

h?

= 21

4. ?-

h?

= 20

12.

9 _

h?

= 11

5. ?H

-?

= 14

13.

9 _

h?

= 8

6. ?H

_ 9

rr

14.

?-

h?

= 6

7. ?H

_ 9

= 16

15.

?-

h?

= 18

8. ?H

_ 9

= 13

16.

?H

h?

= 19

ADDITION DRILL CHART

This chart contains all additions which result in sums no

larger than 20. It should be copied on the blackboard, and

6

5

6

10

2

8

3

3

2

'7

7

7

1

5

4

2

4

1

9

1

5

7

2

4

5

10

4

3

6

7

10

5

2

5

7

3

2

4

4

4

3

1

5

6

8

6

2

3

2

1

10

4

6

7

8

3

1

9

3

8

1

3

1

6

1

9

9

4

6

9

2

10

8

6

9

10

3

1

5

3

5

7

8

1

8

6

5

2

10

2

10

8

9

4

10

7

8

7

10

9

4

10

5

9

9

6

9

8

8

7

children should recite the sums every day until they can do so

without making an error. Vary the drill. Begin at different

PRIMARY ARITHMETIC

15

places and go through the entire chart to the place of beginning.

Change the order, going sometimes to right, and to left, and some-

times up -or down. Vary concert and individual recitation with

and without the pointer. Sometimes pupils use the pointer.

Use the chart persistently.

10. To THE TEACHER. Pupils need drill on this kind of work

till they can give results instantly.

1 . How many boys are 5 boys and 3 boys ?

2. Three eggs and 4 eggs are how many eggs ?

16 PRIMARY ARITHMETIC

3. How many are six tops and 3 tops ?

4. How many are 8 hens and 7 hens ?

5. Two cats and four cats are how many cats ?

6. Five books and two books are how many

books ?

7. Four hats and six hats are how many hats ?

8. Eight slates and nine slates are how many?

9. 3 chairs and 5 chairs are how many chairs ?

10. Six balls and three balls are how many balls ?

11. Five and two are how many ?

12. Nine and three are how many ?

13. How many are four and four?

14. May had three cents, and I gave her 8 cents ;

how many cents did she have then ?

15. John found 4 eggs in one nest and six in another ;

how many eggs did he find ?

16. James had 7 cents and found 4 more ; how many

cents did he then have ?

17. Make a number story about 3 birds and 6 birds.

4 men and 6 men. 5 and 2.

11. 1. A boy saw 6 squirrels in one tree and 4 in

another. How many squirrels did he see ?

2. 5 oranges + 3 oranges = ? 7 pins + 9 pins = ?

6 + 7 = ?

3. Henry had 5 cents, John 4, and George 8. How

many cents did they all have ?

4. A wagon carried 7 women, 5 men, and 3 chil-

dren. How many persons did it carry?

PRIMARY ARITHMETIC

17

5.

3+2+4=?

22.

8 + 5 = ?

6.

2+7+5=?

23.

3+8+1+1=?

7.

4 + 8+2=?

24.

4+6+9=?

8.

6+5+3=?

25.

2+3+6+4=?

9.

9+2+5=?

26.

8+2+2+6=?

10.

6+1+4=?

27.

18 + 3 = ?

11.

6+1+5=?

28.

28 + 3 = ?

12.

5+6+1=?

29.

48 4- 3 = ?

13.

7 + 24-8 = ?

30.

69 + 5 = ?

14.

l4_2 + 3 + 9 = ?

31.

49 4. 10 + 1 = ?

15.

6+3+1+8=?

32.

95 + 5 = ?

16.

1+2+4+8=?

33.

7 4. 8 + 5 = ?

17.

18.

19.

20.

l4_9 + 2 + l = ?

54-2 + 3 + 9 = ?

6+4+8=?

6+3+4=?

34.

35.

Add by fives from

to 20.

Add by threes

from to 30.

21.

6+1+6+2=?

36. Count by 2's from to 40.

37. Count by 4's from to 40.

38. Count by 6's from to 48.

39. Count by 7's from to 35.

40. Count by 8's from to 48.

From 1 to 21.

From 2 to 30.

From 5 to 42.

From 5 to 47.

From 6 to 54.

5

41. Make a number story about 5 swallows, 9

swallows, and 3 swallows.

.

42. Make a number story about 5, 3, and 8.

12. 1. Eight boys and 5 boys are how many boys?

2. Seven eggs and three eggs are how many eggs?

18

PRIMARY ARITHMETIC

3. 9 tops and three tops are how many tops?

4. 6 cats and 2 cats are how many cats ?

5. 7 books and 5 books are how many books ?

6. 10 hats and 4 hats are how many hats ?

7. 10 slates and 1 slate are how many slates ?

8. How many chairs are 8 chairs and 3 chairs?

9. How many balls are 10 balls and 6 balls?

10. How many dogs are 6 dogs and 5 dogs?

11. 11 days and 4 days are how many days?

12. Seven apples and 4 apples are how many apples?

13. 11 balls and 5 balls are how many balls?

14. 8 cows and 3 cows are how many cows ?

15. 11 and 5 are how many?

16. 10 and four are how many?

17. How many are 11 and 6 ?

18. John spent 3 cents for candy, 5 cents for a top,

and 6 cents for marbles. How much did he spend in all ?

19. A man had three cows in one field, four in an-

other, and seven in another. How many did he have in

all ? Make a picture of the fields using dots for cows.

20. 9 -f 4 = ?

28. 5+ 7 = ?

36. 7 + 9 = ?

21. 8 + 5 = ?

29. 4+ 8 = ?

37. 8 + 10 = ?

22. 6 + 2 = ?

30. 4+ 9 = ?

38. 2 + 5 + 3 = ?

23. 9 + 2 = ?

31. 5 + 10 = ?

39. 4 + 6 + 7 = ?

24. 6 + 2 = ?

32. 8+ 5 = ?

40. 9 + 1 + 5 = ?

25. 6 + 3 = ?

33. 9+ 6 = ?

41. 8 + 2 + 3 = ?

26. 9 + 4 = ?

34. 8+ 7 = ?

42. 9 + 9 + 2 + 1 = ?

27. 5 + 5 = ?

35. 8+ 8 = ?

43. 1+2+3+4 + 5 = ?

PRIMARY ARITHMETIC 19

13. 1. George picked O O Q ^ rom on ^ tree >

O C O O O from another tree, and Q Q Q

O O O fr m an ther tree. How many did he pick

in all?

2. There were

one row, 4 in another, and 9 in another. How many

trees were there in all ?

3. A girl earned 8 cents, found 5 cents, and had

3 cents given to her. How many cents had she ?

4. A cat caught X^X^fe V^Xjf*' in the

and %^%/%/%/%/^%/<%/ in

the field. How many did she catch in all ?

5. A gardener gave Ned ^ ^ ^ }, Nell K K

[X) ^), and Will as many as the other two. How

many fVs did he give all ?

6. Frank ate three plums, gave Charles nine, and

had four left. How many plums had he at first ?

7. I saw on the lawn 10 sparrows, 6 robins, and

4 orioles. How many birds did I see in all ?

8. A boy paid 2 dollars for shoes, 1 dollar for a

hat, 5 dollars for a coat, and 9 dollars for books. How

much did he pay for all ?

9. A boy caught 10 fish, and his sister 9. How

many fish did both catch?

LIBRARY

OF THK

UNIVERSITY OF CALIFORNIA.

OF"

V

Accession 85969 Class

HEATH'S

PRIMARY ARITHMETIC

s

3

o

e

t

HEATH'S

PRIMARY ARITHMETIC

BY

CHARLES E. WHITE

\\

AND

BRUCE M. WATSON

SYRACUSE, N.Y.

BOSTON, U.S.A.

D. C. HEATH & CO., PUBLISHERS

1901

COPYRIGHT, 1901,

BY D. C. HEATH & Co.

PREFACE

IN education, as in other affairs of life, there is a tendency, on the part

of many, to pursue good ideas to unreasonable extremes, and ofttimes to the

exclusion of other ideas quite as good.

This book has been prepared with the design of bringing together the

manifest advantages of the topically arranged text-book and the equally

manifest advantages of the so-called " spiral " plan.

Each subject is treated by itself as exhaustively as the scope and purpose

of tl$ book will warrant. At the same time each new subject introduced is

considered in all its relations with and bearing upon preceding subjects.

By the great abundance and variety of the drill work and problems

throughout the book, all subjects are kept in constant review, every principle

is applied in as many ways as possible, and the unity of the 'book is

preserved.

The order of subjects is determined by the law of dependence, the degree

of simplicity of the matter to be taught, and the relative importance of the

respective subjects in the business of life.

The development of the various principles and processes has been written

with great care and considerably in detail, with a view both to furnish the

teacher a definite plan for presenting the work and to help the student in

his efforts toward independent achievement.

Both the method and the matter of the book have been tested by actual

use in the schoolroom ; they are not in any sense an experiment.

Part I is a strictly primary arithmetic. The first few lessons are extremely

simple, yet they furnish an illustration of the logical steps in the develop-

ment of ideas of number. If any child begins the use of the book with

elementary notions of number already developed in his mind to a certain

point, the judicious teacher will be wise enough to begin where the child's

previously acquired knowledge stops.

The development work preceding each table is designed to give the child

a concrete understanding of the processes by which the table is made instead

of forcing him to memorize abstract results obtained by making arbitrary

combinations. But after a table has been thoroughly developed, the pupil

85969

VI PREFACE

should be drilled in all its combinations until he can give results instantly

without reference to the mental processes by which they may be obtained.

To this end the drill charts should be used daily until all results can be given

correctly without an instant's hesitation.

The problems following the tables were selected from lessons given by

scores of successful primary teachers, and it is believed that they are far

richer in variety of work and forms of statement than any list prepared by

a single individual.

Part II is an introduction to written arithmetic proper. The color work,

both here and in Part I, is introduced not merely to embellish the pages,

but rather to furnish the best means of illustration and practice in certain

arithmetical operations.

Much of the mental work in Part II may be used as supplementary to the

questions in Part I.

Definitions are given only when and where they are needed.

In the treatment of fractions the fact that a fraction is an expression of

division is kept prominent.

Throughout the book the authors have endeavored to insert whatever may

help the pupil to an understanding of principles ; to omit whatever is super-

fluous or may tend to confusion.

B. M. W.

SYRACUSE, February 8, 1901.

TABLE OF CONTENTS

PART I

PAGE

NOTATION AND NUMERATION 1

ADDITION 7

SUBTRACTION ............ 20

MULTIPLICATION ........... 31

DIVISION 42

PAET II

NOTATION AND NUMERATION ......... 75

Arabic . 77

Roman 80

Federal Money .82

ADDITION 83

SUBTRACTION 94

REVIEW PROBLEMS .......... 102

MULTIPLICATION ........... 104

DIVISION 113

REVIEW EXERCISES 124

REVIEW PROBLEMS 125

FACTORING 130

CANCELLATION 132

GREATEST COMMON DIVISOR ......... 134

LEAST COMMON MULTIPLE ......... 135

INDICATED OPERATIONS .......... 137

FRACTIONS 140

REDUCTION OF FRACTIONS . . . . * 143

ADDITION OF FRACTIONS . . . 152 '

SUBTRACTION OF FRACTIONS 154

SUBTRACTION OF MIXED NUMBERS 155

MULTIPLICATION OF FRACTIONS . . . . . . . .156

DIVISION OF FRACTIONS . . . . . . . . . . 161

COMPLEX FRACTIONS . . . . . . . . ... 166

THE THREE QUESTIONS OF RELATION ....... 167

ALIQUOT PARTS ........... 170

REVIEW OF FRACTIONS 172

DECIMAL FRACTIONS 176

To read Decimals . . . 179

To write Decimals .......... 180

REDUCTION OF DECIMALS ......... 182

vii

viii TABLE OF CONTENTS

PAGE

ADDITION OF DECIMALS ......... 184

SUBTRACTION OF DECIMALS 185

MULTIPLICATION OF DECIMALS 186

DIVISION OF DECIMALS 188

REVIEW OF DECIMALS 191

BILLS AND ACCOUNTS .......... 192

DENOMINATE NUMBERS .......... 194

Linear Measures 194

Surface Measures 196

Cubic Measures 199

Liquid Measures 200

Dry Measures 202

Avoirdupois Weight 203

Troy Weight 205

Apothecaries' Weight 205

Federal Money 206

Time 207

Miscellaneous Tables 208

REDUCTION OF DENOMINATE NUMBERS ....... 209

Descending 211

Ascending 212

REVIEW OF REDUCTION . 215

ADDITION OF COMPOUND NUMBERS 216

SUBTRACTION OF COMPOUND NUMBERS . . . . . . . 217

DIFFERENCE BETWEEN DATES . . . . . . . . 218

MULTIPLICATION OF COMPOUND NUMBERS . . . . ... 219

DIVISION OF COMPOUND NUMBERS 220

SURFACE MEASUREMENTS ......... 221

Plastering and Painting . . 223

Carpeting Rooms 224

Papering Walls . . . . . . . . . .227

Board Measure 227

VOLUME MEASUREMENTS . . . . . . . . . 228

Wood Measure . . . 231

Capacity of Cisterns 232

Capacity of Bins 232

PERCENTAGE 233

SIMPLE INTEREST ........... 238

TOPICAL REVIEW . . . . 241

Notation and Numeration 241

Common Fractions 241

Decimal Fractions .......... 242

Denominate Numbers 244

ANSWERS ............ 247

PRIMARY ARITHMETIC

PART FIRST

To THE TEACHER. For early work with numbers, a " counting

table" is almost a necessity, whatever text-book may be used.

It should be about two feet high, thirty inches wide, and six

feet to fourteen feet in length, according to the size of the class.

It should be surrounded by a slightly raised casing to prevent the

counters from falling off.

Toothpicks and shoepegs are very good to use as counters, on

account of their cheapness and convenience of handling.

1. Counters are in a pile in front of the pupils.

Take one counter.

Put another one with it. How many?

Put another with it. How many ?

So on until ten have been taken.

Take three counters ; seven counters ; five ; nine ;

six ; four ; ten ; eight.

Count the girls in the class.

Count the boys in the class.

How many fingers have you on your right hand?

On your left hand ?

i

PRIMARY ARITHMETIC

How many fingers have you on both hands ?

How many fingers and thumbs have you ?

Count ten with your eyes shut.

Give much drill on these numbers, using counters and other

objects.

2. Make the figures 1 , 2, 3, 4, 5, lo, ^ 8, C|.

Teacher place figure 1 on blackboard, and pupils take as many

counters. Teacher place figure 2 on the blackboard and children

take as many counters. So on with all the figures, one at a

time, the pupils each time taking as many sticks as the figure

means.

Teacher count out three, five, nine, seven, eight sticks, etc.,

and pupils make figures to represent them.

Make the figure to tell how many years old you are.

Make the figure to tell how many fingers you have.

Make the figure to tell how many hands and feet

you have.

Make the figure to tell the hour for coming to school.

Much drill should be given in this kind of work.

How many leaves on this

cherry branch ?

How many cherries ?

Make the figure that tells

how many leaves.

Make the figure that tells

how many cherries.

Make a stem holding 5 cher-

ries; 8 cherries; 10 cherries.

PRIMARY ARITHMETIC

How many roses in the

picture ?

How many rosebuds ?

What figure tells how

many roses ?

What figure tells how

many buds ?

Count the roses and buds

together.

How many parts has a wood-

bine leaf?

Make the figure.

How many leaves are there

on a c l ver stem ?

Make the figure.

Make two woodbine leaves.

Count the parts in the two leaves.

Count the red stripes in the flag.

Count the white stripes.

Make the figure that tells how

many red stripes.

Make the figure that tells

how many white stripes.

Count all the stripes.

Count the stars in the bot-

tom row.

How many colors in the flag ?

How many stripes below the blue field ?

How many red stripes below the blue field?

PRIMARY ARITHMETIC

Count the daisies in the

picture.

How many?

What figure tells how

many ?

Count the tall daisies.

Make the figure that tells

how many are not tall.

How many apples are in this picture ?

Make the figure that tells how many apples.

Count the red

apples.

Count the other

apples.

Make the figure

that tells how many

red apples.

How many pears are there in the picture ?

Make the figure that tells how many.

One, 1. Two, 2. Three, 3. Four, 4.

Five, 5. Six, 6. Seven, 7.

Eight, 8. Nine, 9. Ten, 10.

PRIMARY ARITHMETIC 5

3. Take ten sticks. m

Tie them in a bunch, thus, it

Count out ten such bunches and tie them up.

Call each bunch "a ten."

Put one bunch on the table. fj n

Put one stick beside it, thus, ml

How many sticks are there ? | |

Put another stick with it, thus, if If

How many sticks are there ? I J2

Take another ten and put three with it, iijjj

thus, if UHII

How many are there ? I 3

Go on in this way to nineteen.

What does the figure 1 stand for in the number 12?

In the number 13 ?

In 14, 15, 16, 17, 18, 19 ?

How many tens in 11 ? How many over ?

In 12, 13, 14, 15, 16, 17, 18, 19 ? '

4. Suppose we wish to write the number ten. We

will use 1 to stand for ten the same as in the other

numbers.

How many will there be over?

What shall we use to show that jj

there is none over ? *

We will use this figure, 0. Thus, I

The figure, 0, is called naught, and is used where

nothing belongs.

6

PRIMARY ARITHMETIC

Take two tens. How many sticks in all ?

To write twenty we use 2 to stand for two tens,

and to show that there is none over, thus,

Take two tens and one, thus,

How many ? Write it thus,

m

Make the figures for: jj

5. In the same manner as in the preceding lesson, develop

numbers to one hundred.

Write fifteen ; twenty ; eighteen ; fourteen.

Write twenty-five ; thirty-seven ; forty.

Write eighty-tw r o ; ninety-six ; seventy.

Write sixty-one ; forty-seven ; fifty.

Write seventy-nine ; twenty-one ; ninety.

Write forty-eight ; nineteen ; thirty-three.

Lay counters to make forty-two, thus,

Lay counters to make sixty-three.

Lay counters to make seventeen.

Count the desks in your room.

What number will the counters on the table make ?

PRIMARY ARITHMETIC 7

Count the hands in your schoolroom.

Write the number of books on the teacher's desk.

Count fifty forward and backward.

Read these numbers : 25, 21, 38, 45, 36, 28, 72, 64.

Write them in a column, so that the tens will be in a

vertical line.

Write them in words.

ADDITION

'6. Take one counter.

Take one more counter.

How many counters have you ?

How did you get two counters ?

One counter and one counter are how many counters ?

One stick and one stick are how many sticks ?

One book and one book are how many books ?

One boy and one boy are how many boys ?

One and one are how many ?

and are ?

One and one are ?

1 and 1 are ?

Write, 1 and 1 are 2.

Take two counters.

Put one more with them.

How many counters are there ?

How did you get three counters ?

Two counters and one counter are how many counters ?

PRIMARY ARITHMETIC

If the apples in the boy's hand be put with the apple

on the table, how many will there be on the table ? If

the one book be put on the three books, how many

books will there be in the pile ?

Make a number story about the two books and one

book.

Make a number story about the apples in the basket

and the apple on the table. About one marble and one

marble.

Two chairs and one chair are how many chairs ?

Two and one are how many ?

and * are ?

Two and one are ?

2 and 1 are ?

PRIMARY ARITHMETIC

9

In the same way teach three and one, four and one, and so on

to ten and one.

Have children write :

1

and

1

are

2

1

+ 1

= 2

2

and

1

are

3

2

+ 1

= 3

3

and

1

are

4

3

+ 1

= 4

4

and

1

are

5

4

+ 1

= 5

5

and

1

are

6

5

+ 1

= 6

6

and

1

are

7

6

+ 1

= 7

7

and

1

are

8

7

4-1

* 8

8

and

1

are

9

8

4-1

= 9

9

and

1

are

10

9

+ 1

= 10

10

and

1

are

11

10

+ 1

= 11

BLACKBOARD DRILL

Add the 1 to each of the other

numbers around the circle.

7. Take 1 counter. Take two more counters.

How many counters have you ?

How did you get three counters ?

One counter and two counters are how many counters ?

One apple and two apples are how many apples ?

One and two are how many ?

Take two counters. Take two more counters.

How many counters have you?

10

PRIMARY ARITHMETIC

How did you get four counters ?

Two counters and two counters are how many

counters ?

Two boards and two boards are how many boards ?

Two sheep and two sheep are how many sheep ?

Two and two are how many ?

Take three counters. Take two more counters.

How many counters have you ?

How did you get five counters ?

Three counters and two counters are how many

counters ?

Three books and two books are how many books ?

Three trees and two trees are how many trees ?

Three and two are how many ?

In a similar way teach the entire table of twos.

Have children write :

1

and

2

are

3

1

+ 2

= 3

2

and

2

are

4

2

+ 2

= 4

3

and

2

are

5

3

_l_ 2

= 5

4

and

2

are

6

4

_l_ 2

= 6

5

and

2

are

7

5

+ 2

= 7

6

and

2

are

8

6

i 2

= 8

7

and

2

are

9

7

i 2

Q

8

and

2

are

10

8

_j_ 2

= 10

9

and

2

are

11

9

+ 2

= 11

10

and

2

are

12

10

_j_ 2

= 12

PRIMARY ARITHMETIC 11

Make a number story about 3 dolls and 2 dolls.

Another child give the answer.

Make a number story about 7 red roses and 2 white

roses. Give the answer.

Make a story about 6 and 2, 7 and 2, etc.

and are ?

Six and two are ?

6 + 2 = ?

c^ ^ ^

V^^ ^V BLACKBOARD DRILL

b( C\ \

) LL Add the 2 to each of the other num-

^ ^ T 4

T

\ / bers quickly.

/ ^- ^o

I

8. Take 1 counter. Take 3 more counters.

How many counters have you ?

How did you get 4 counters ?

One counter and three counters are how many

counters?

One stick and three sticks are how many sticks ?

One marble and three marbles are how many mar-

bles?

One cat and three cats are how many cats ?

One and three are how many ?

Take two counters. Take three more counters.

How many counters have you ?

How did you get five counters ?

12

PRIMARY ARITHMETIC

Two counters and three counters are how many

counters ?

and are how many dots ?

Two cows and three cows are how many cows ?

Two and three are how many ?

In a similar ,way, teach all the table of threes.

Make a number story about 2 red cherries and 3 red

cherries. Another child give the answer.

Make a story about 8 green leaves and 2 green leaves.

Make a number story about 2 boys and 5 boys.

Make a number story about 7 dollars and 3 dollars.

About 9 and 3.

Have children write :

1

and

3

are

4

1

+ 3 =

4

2

and

3

are

5

2

1 O

-f- o

5

3

and

3

are

6

3

+ 3 =

6

4

and

3

are

7

4

4-3 =

7

5

and

3

are

8

5

+ 3 =

8

6

and

3

are

9

6

+ 3 =

9

7

and

3

are

10

7

+ 3 =

10

8

and

3

are

11

8

+ 3 =

11

9

and

3

are

12

9

+ 3 =

12

10

and

3

are

13

10

4-3 =

13

In a similar manner teach the entire table of Addition, giving

much drill with both concrete and abstract work, as you proceed,

to fix the tables in the minds of the children.

Vary the work, sometimes the teacher doing the work and

pupil telling what she did, and the result.

Have children make questions.

PRIMARY ARITHMETIC

13

9.

BLACKBOARD DRILL

Add the 3 to each of the other num-

bers quickly.

TABLE OF ADDITION

1+1= 2

1+2= 3

1+3= 4

1+4= 5

1+ 5= 6

2 + 1= 3

2+2= 4

2+3= 5

2+4= 6

2+ 5= 7

3 + 1= 4

3+2= 5

3+3= 6

3+4= 7

3+ 5= 8

4 + 1= 5

4+2= 6

4+3= 7

4+4= 8

4+ 5= 9

5 + 1= 6

5 + 2= 7

5 + 3= 8

5 + 4= 9

5+ 5=10

6+1= 7

6+2= 8

6+3= 9

6+4=10

6+ 5 = 11

7 + 1= 8

7 + 2= 9

7+3=10

7+4 = 11

7+ 5 = 12

8 + 1= 9

8+2=10

8+3 = 11

8+4 = 12

8+ 5=13

9 + 1 = 10

9+2=11

9+3 = 12

9 + 4=13

9+ 5=14

io + i=n

10+2 = 12

10+3 = 13

10+4=14

10+ 5=15

1 + 6= 7

1 + 7= 8

1+8= 9

1 + 9 = 10

1+10=11

2+6= 8

2+7= 9

2+8=10

2+9 = 11

2+10=12

3+6= 9

3+7 = 10

3+8 = 11

3 + 9 = 12

3 + 10=13

4+6=10

4 + 7=11

4+8=12

4 + 9 = 13

4+10=14

5 + 6 = 11

5+7=12

5+8 = 13

5+9 = 14

5+10=15

6+6 = 12

6 + 7 = 13

6+8 = 14

6+9 = 15

6+10=16

7 + 6 = 13

7 + 7 = 14

7 + 8 = 15

7 + 9 = 16

7 + 10=17

8 + 6 = 14

8+7 = 15

8+8=16

8 + 9 = 17

8 + 10 = 18

9 + 6 = 15

9 + 7 = 16

9 + 8 = 17

9+9=18

9+10=19

10 + 6 = 16

10 + 7 = 17

10 + 8 = 18

10+9 = 19

10 + 10=20

14 PRIMARY ARITHMETIC

Give three answers to each question below :

1. ?-

h?

= 10

9.

9 _

f-?

= 12

2. ?H

h?

= 17

10.

9 _

h?

= 15

3. ?H

h ?

= 9

11.

9 _

h?

= 21

4. ?-

h?

= 20

12.

9 _

h?

= 11

5. ?H

-?

= 14

13.

9 _

h?

= 8

6. ?H

_ 9

rr

14.

?-

h?

= 6

7. ?H

_ 9

= 16

15.

?-

h?

= 18

8. ?H

_ 9

= 13

16.

?H

h?

= 19

ADDITION DRILL CHART

This chart contains all additions which result in sums no

larger than 20. It should be copied on the blackboard, and

6

5

6

10

2

8

3

3

2

'7

7

7

1

5

4

2

4

1

9

1

5

7

2

4

5

10

4

3

6

7

10

5

2

5

7

3

2

4

4

4

3

1

5

6

8

6

2

3

2

1

10

4

6

7

8

3

1

9

3

8

1

3

1

6

1

9

9

4

6

9

2

10

8

6

9

10

3

1

5

3

5

7

8

1

8

6

5

2

10

2

10

8

9

4

10

7

8

7

10

9

4

10

5

9

9

6

9

8

8

7

children should recite the sums every day until they can do so

without making an error. Vary the drill. Begin at different

PRIMARY ARITHMETIC

15

places and go through the entire chart to the place of beginning.

Change the order, going sometimes to right, and to left, and some-

times up -or down. Vary concert and individual recitation with

and without the pointer. Sometimes pupils use the pointer.

Use the chart persistently.

10. To THE TEACHER. Pupils need drill on this kind of work

till they can give results instantly.

1 . How many boys are 5 boys and 3 boys ?

2. Three eggs and 4 eggs are how many eggs ?

16 PRIMARY ARITHMETIC

3. How many are six tops and 3 tops ?

4. How many are 8 hens and 7 hens ?

5. Two cats and four cats are how many cats ?

6. Five books and two books are how many

books ?

7. Four hats and six hats are how many hats ?

8. Eight slates and nine slates are how many?

9. 3 chairs and 5 chairs are how many chairs ?

10. Six balls and three balls are how many balls ?

11. Five and two are how many ?

12. Nine and three are how many ?

13. How many are four and four?

14. May had three cents, and I gave her 8 cents ;

how many cents did she have then ?

15. John found 4 eggs in one nest and six in another ;

how many eggs did he find ?

16. James had 7 cents and found 4 more ; how many

cents did he then have ?

17. Make a number story about 3 birds and 6 birds.

4 men and 6 men. 5 and 2.

11. 1. A boy saw 6 squirrels in one tree and 4 in

another. How many squirrels did he see ?

2. 5 oranges + 3 oranges = ? 7 pins + 9 pins = ?

6 + 7 = ?

3. Henry had 5 cents, John 4, and George 8. How

many cents did they all have ?

4. A wagon carried 7 women, 5 men, and 3 chil-

dren. How many persons did it carry?

PRIMARY ARITHMETIC

17

5.

3+2+4=?

22.

8 + 5 = ?

6.

2+7+5=?

23.

3+8+1+1=?

7.

4 + 8+2=?

24.

4+6+9=?

8.

6+5+3=?

25.

2+3+6+4=?

9.

9+2+5=?

26.

8+2+2+6=?

10.

6+1+4=?

27.

18 + 3 = ?

11.

6+1+5=?

28.

28 + 3 = ?

12.

5+6+1=?

29.

48 4- 3 = ?

13.

7 + 24-8 = ?

30.

69 + 5 = ?

14.

l4_2 + 3 + 9 = ?

31.

49 4. 10 + 1 = ?

15.

6+3+1+8=?

32.

95 + 5 = ?

16.

1+2+4+8=?

33.

7 4. 8 + 5 = ?

17.

18.

19.

20.

l4_9 + 2 + l = ?

54-2 + 3 + 9 = ?

6+4+8=?

6+3+4=?

34.

35.

Add by fives from

to 20.

Add by threes

from to 30.

21.

6+1+6+2=?

36. Count by 2's from to 40.

37. Count by 4's from to 40.

38. Count by 6's from to 48.

39. Count by 7's from to 35.

40. Count by 8's from to 48.

From 1 to 21.

From 2 to 30.

From 5 to 42.

From 5 to 47.

From 6 to 54.

5

41. Make a number story about 5 swallows, 9

swallows, and 3 swallows.

.

42. Make a number story about 5, 3, and 8.

12. 1. Eight boys and 5 boys are how many boys?

2. Seven eggs and three eggs are how many eggs?

18

PRIMARY ARITHMETIC

3. 9 tops and three tops are how many tops?

4. 6 cats and 2 cats are how many cats ?

5. 7 books and 5 books are how many books ?

6. 10 hats and 4 hats are how many hats ?

7. 10 slates and 1 slate are how many slates ?

8. How many chairs are 8 chairs and 3 chairs?

9. How many balls are 10 balls and 6 balls?

10. How many dogs are 6 dogs and 5 dogs?

11. 11 days and 4 days are how many days?

12. Seven apples and 4 apples are how many apples?

13. 11 balls and 5 balls are how many balls?

14. 8 cows and 3 cows are how many cows ?

15. 11 and 5 are how many?

16. 10 and four are how many?

17. How many are 11 and 6 ?

18. John spent 3 cents for candy, 5 cents for a top,

and 6 cents for marbles. How much did he spend in all ?

19. A man had three cows in one field, four in an-

other, and seven in another. How many did he have in

all ? Make a picture of the fields using dots for cows.

20. 9 -f 4 = ?

28. 5+ 7 = ?

36. 7 + 9 = ?

21. 8 + 5 = ?

29. 4+ 8 = ?

37. 8 + 10 = ?

22. 6 + 2 = ?

30. 4+ 9 = ?

38. 2 + 5 + 3 = ?

23. 9 + 2 = ?

31. 5 + 10 = ?

39. 4 + 6 + 7 = ?

24. 6 + 2 = ?

32. 8+ 5 = ?

40. 9 + 1 + 5 = ?

25. 6 + 3 = ?

33. 9+ 6 = ?

41. 8 + 2 + 3 = ?

26. 9 + 4 = ?

34. 8+ 7 = ?

42. 9 + 9 + 2 + 1 = ?

27. 5 + 5 = ?

35. 8+ 8 = ?

43. 1+2+3+4 + 5 = ?

PRIMARY ARITHMETIC 19

13. 1. George picked O O Q ^ rom on ^ tree >

O C O O O from another tree, and Q Q Q

O O O fr m an ther tree. How many did he pick

in all?

2. There were

one row, 4 in another, and 9 in another. How many

trees were there in all ?

3. A girl earned 8 cents, found 5 cents, and had

3 cents given to her. How many cents had she ?

4. A cat caught X^X^fe V^Xjf*' in the

and %^%/%/%/%/^%/<%/ in

the field. How many did she catch in all ?

5. A gardener gave Ned ^ ^ ^ }, Nell K K

[X) ^), and Will as many as the other two. How

many fVs did he give all ?

6. Frank ate three plums, gave Charles nine, and

had four left. How many plums had he at first ?

7. I saw on the lawn 10 sparrows, 6 robins, and

4 orioles. How many birds did I see in all ?

8. A boy paid 2 dollars for shoes, 1 dollar for a

hat, 5 dollars for a coat, and 9 dollars for books. How

much did he pay for all ?

9. A boy caught 10 fish, and his sister 9. How

many fish did both catch?

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