Primary Arithmetic for Graded Schools - Forgotten Books

PRIMARY ARITHMETIC

FOR GRADED SCHOOLS

BY

SAMUEL HAMILT ON , PH.D.

AUTHOR OF“THE AND SUPERIN TENDENT

O F SCHOOLS, ALLEGHENY COUNTY . PA .

NEW YOR! CINCINNATI CHICAGO

AMERICAN BO O ! C OMPANY

QC

6 1 5 2 5 3

C

COPYRIGHT , 1 907, 1 909, BY

SAMUE L HAMILTON .

M d at Stationm’ Hall, London.

m . PRIH. AB.

W . P. I!

PREFACE

THIS Primary Arithmetic is intended to cover the workof the first four years . It is divided into three parts.

Part One includes the Work ordinarily done during the

first and second years.

Part Two includes the w ork of the third year . It is

devoted mainly to the presentation of the elementary factsand tables of arithmetic .

The text-book should be placed in the hands of the pupil

when he enters upon the work found in Part Two.

Part Three covers the work of the fourth year. Its pur

pose is to give a mastery of the fundamental operations, and,through the study of problems, to develop the ability to use

these Operations in a practical way.

The aim of this course is twofold : first, to give the child

mathematical skill ; second, to give himmathematical power.

T o these ends attention is inv ited to the following :

1 . T he prominence given to drill intended to give skill,

and the frequency of systematic rev iews.

2 . The Study of Problems intended to give mathematical

power.

3 . The plan which provides an easy treatment of each

subject before the complete treatment of it .

4 . T he easy steps in gradation .

5 . The emphasis given to business arithmetic .

6 . The appeal made to observation as a stimulus to

mathematical thought .

4 PREFACE

In many schools the unit of classification is the half y ear.

W ith this in V iew , the subject matter in the third and fourth

years has been separated into two parts . T he easy treat

ment of topics covers the first half of the year, and the

more complete treatment the second half.

SAMUEL HAMILTON .

Numbers to 5L iquid Measures

Halves, T hirds, FourthsComparisonNumbers 6 to 1 2Dry Measures

Reading and W ritingNumbers to 99

Roman N umbers to XX

Reading and W riting

Numbers to 9999Addition

SubtractionAddition and Sub tractionMultiplication by 3 and 4

Practical ProblemsDivision by 3 and 4Addition and Subtraction

of U. S. Money

Multiplication by 5 and 6

Division by 5 and 6DrillsSubtractionDrillsDryMeasures

Liquid Measures

Measures of W eight

Measures of LengthMeasures of SurfaceReview

F IRST HALF Y EAR

PAGES

7—1 4

1 2

1 3

1 5

1 6-24

1 9

25, 26

27

41 , 42

43—48

49-53

54

55-59

60, 61

62-66

67 68

69-72

73-75

76

77, 78

79

80

81

82

83 , 84

85

86

CONTENTS

PART I— FIRST AND SECOND YEARS

Addition

SubtractionPracticalProblemsMultiplication by 2

Division by 2Making ChangeThe Inch , the Foot, and

the Yard

Review

PART II — THIRD YEARSECOND HALF Y EAR

Reading and W ritingNumbers to

Roman Notation 87

Addition and Subtractionincluding Fractions 88—92

Review 93-96

Multiplication by 7 and 8 97-99

Div ision by 7 and 8 1 00, 1 01

Multiplication by Mixed

Numbers 1 02

Multiplication by 9 1 03 , 1 04

Division by 9 1 05

Division of United StatesMoney 106

Review 1 07, 1 08

Addition and Subtraction 1 09, 1 1 0

Review 1 1 1 — 1 22

Comparison 1 23

T ime Measures 1 24,1 25

Surface Measures 1 26

Rev iew 1 27-1 36

6 CONTENTS

PART III — FOURTH YEAR

FIRST HALF Y EARPAGES

Reading and W riting Numbers to

Addition and Subtraction1 39-141 ’

Multiplication by 1 0, 1 1

and 1 2 1 42-1 44

Division by 10, 1 1 , and

1 2

Review and Drills 1 47-1 52

Multiplication Table 1 53

Multipliers ending in 0 1 54, 1 55

Divisors ending in 0 1 56, 1 57

Multiplication by T WO-fig

ure Numbers 1 58, 1 59

Multiplication of Concrete

Numbers 1 60-1 62

ComparisonReview of Short Division 1 64

Long Division by T wo-figure Numbers 1 65-1 71

Review 1 72—1 76

Measures of T ime 1 77

Measures of ‘Veight 1 78

Measures of Length or

DistanceMeasures of Surface 1 80—1 82

SECOND HALF YEARPAGES

Reading and Writing Numbers to Billions

Re view and Drills

AAddition and Subtractionof Fractions and

Mixed Numbers 1 90-1 92

Multiplication by Three

figure Numbers 1 93-1 95

Parts of Numbers 1 96

Multiplication by Mixed

Numbers 1 97

Fractional Parts of a

Dollar 1 98

Long Divismn by Three

figure NumbersStudy of Problems of Two

Operations2 01 —208

Review 2 09

Combining Processes 2 1 0

Analysis2 1 1 , 2 12

Comparison 2 1 3 , 2 1 4

Bills

Review of Measures 2 1 7-2 1 9

T est Problems 220-229

Rev iew 230-232

FractionS,MixedNumbers 23 3-238Solids 2 39, 240

PRIMARY ARITHMETIC

PART I— FIRST AND SECOND YEARS

COUNTING NUMBERS TO TEN

HOW many books are therein this picture ?

Count the caps . Howmany more caps are therethan books ?

Count the bells . Howmanyare there ? Think that youhear them ring 1 , 2, 3 , 4.

How many ducks do you seein this picture ? Tell a storyabout them.

If Rob has as many

9 eeeee tops as you see in this picture, how many has he ?

8 FIRST AND SECOND YEAR [Oral

One day I saw seven eggs ina nest . How many are therein this one ?

Count the apples. How manymore apples are there than

Count the number of

birds that you see in thispicture.

Here are ten balls Q2 Q2 Q2these balls . Q2. Q2, Q2 Q ,

You have namedthemeither in words

naught one two three

0 1 2 3

Count

ten numbers and you can writeor in figures .

four five Six seven eight nine ten

4 5 6 7 8 9 1 0

Oral] NUMBERS To TWELVE 9

THE NUMBERS TWO AND THREE

1 . 1 ball and 1 ball are how many balls ?1 ball 1 ball 2 balls .When you unite 2 and 1 you add themand the answer

,

3 , is called the sum.

The Sign is read and or plus. The Sign is readequal or equals. 2 1 3 is read 2 plus 1 equals 3 .

2 . 1 1 2 1 top 2 cups 1 car

+ 2 + 1 + 1 + 2 tops + 1 cup + 2 carsSum

3 . John had 3 balls and lost one of them. Howmany balls had he left3 balls 1 ball 2 balls.

4 . How many more balls are 3 balls than 2 balls ?3 balls less 2 balls 1 ball .You have subtracted 2 balls from3 balls . The answer,

1 ball, is the difference or remainder.

The Sign is read minus or less . 3 2 1 is read3 minus 2 equals 1 .

5 . Subtract, beginning at the right3 3 3 2 1

l _3_ 2. l 1

Difference or remainder.

1 0 F IRST AND SECOND YEAR [Oral

THE NUMBER FOUR

g andg fi fi arek fl pa d f; $3

1 . Draw flags to Show the follow ingflags + 1 flag

= ? 4 flags— 1 flag

= ?

flags 2 flags 4 flags 3 flags

2 . Count the flags by 2 ’s. Two 2’

s

3 . How many times must 2 flags be taken to have4 flags ?

4 . 2 flags taken two times are flags .

7a:

n f

"

are

5 . How many times must 1 flag be taken to have4 flags . 4 times 1 flag flags .

6 . 2 x 2 flags flags .

The Sign x is read time or times .

Give answers, reading across the page

7 . 1 x l 2 x 1 1 x 2

8 . l x 3 1 x 4 4 x l

4 — 1 4 - 2

1 0 . 2 x 2 rings 3 x 1 box

1 1 . 1 x 3 balls 2 x 2 books =

1 2 . 4 x 1 pencil'

1 x 4 tables

om] NUMBERS To TWELVE 1 1

PRACTICAL WOR!

1 . Count the windows that you see in the picture.

2 . How many panes are there in each W indow ?

3 . Count the large trees on the school grounds.

4 . How many flower plots are there ?

5 . The porch has posts .

6 . Count the panels in the door.

7 . The glass In each w indow cost one dollar. How

much did all the glass cost ?

8 . Mary lives 2 miles from the school . If sheShould walk to and from the building, how manymiles would she walk every day

9 . James recited twice in the morning and twice inthe afternoon . How many times did he recite ?

1 0 . 2 books and 2 books books .

1 1 . 2 times 2 pencils pencils.

1 2 . 4 books less 1 book books .

1 2 FIRST AND SECOND YEAR [Oral

LIQUID MEASURES

For this exercisea set of liquid measures should be used .

1 . Fill the pintmeasure w ith waterand empty it intothe quart measure .

DO this a secondtime . You have

Shown that 2 pints equal a quart .

z . A quart is how many times a pint ? A pint iswhat part of a quart ?

3 . Show by measuring w ith the quart measure that4 quarts equal a gallon.

4 . A gallon is how many times a quart ? A quart iswhat part of a gallon ?

5 . How many times can the teacher fill Mary’s halfpint milk bottle from the pint measure ?

6 . Clare gets a pint of milk each morning and evening. HOW many pints does he get in two days ?

7 . Clare pays 2 cents for a pint of milk . How muchdoes he pay for 2 pints ?

8 . Raymond delivers, each day, 4 quart bottles ofmilk . How many gallons does he deliver ?

9 . Henry goes to the store for 2 quarts of molasses .How many pints does he get ?

Oral] NUMBERS To TWELVE 1 3

HALVES, THIRDS, AND FOURTHS

1 . Cutanapple into

2 equal parts . Whatis one part called ?

2 . Into how manyhalves can an apple be cut ? an orange ? a pie ?

One half of 1 is w ritten 5.1 o

3 .-

2Of 2 oranges orange 1

5of oranges

oranges .

4 . Cut an apple into 3equal parts . What is 1 partcalled ?

One third of 1 is written

5 . of 3 pennies of4 spl ints

6 . Cut an apple into 4 equalparts . Each part is named one

fourth,or one quarter.

One fourth of 1 is w ritten 1.

7 . How many fourths Of an apple make a wholeapple

8 . Write in figures : one half ; one third one fourth .

9 . Find 5 Of 4 cents ; Q; Oi 3 cents ; of 2 cents .

1 0 . F1nd 12

- O i 2 ;

1 1 . Draw a circle showing halves ; another showing

thirds ; one Show ing fourths.

1 4 FIRST AN D SECOND YEAR [Oral

THE NUMBER FIVE

9

0 0w e

1 . Draw tops to Show the following4 tops + 1 top = ? 5 tops — 1 top = ?3 tops 2 tops 5 tops 3 topsI top + 4 tops 5 tops — 4 tops = ?

2 . Count by 1 ’s to 5 . 1 in 5, times .

3 . Give sums . Make problems2 1 3 2 4 1 1 4 2 3

3 4 1 2 1 3 2 0 1 2

Subtract . Make problems5 3 5 5 4 5 4 5 2

3 1 4 1 3 2 l 5

5 . Give at sight5 — 4 5 X 1

é of 4 % Of 3 aof z 2 x 2

6 . James spent 2 cents for a cake and 3 cents for anOrange . How many cents did he spend ?

7 . Mary had 5 chickens . She gave two to her cousin .

HOW many chickens had She left

Oral] NUMBERS To TWELVE

COMPARISON

1 . Which line is the shortest ? the longest ?a

2 . Which lines are shorter than 0 ?

3 . Which line is one half as long as b ?

4 . Which line is one fourthas long as d5 . A is how many times as

large as 06 . How many times larger

than O is B ?

7 . Are A , B,and 0 of the

same w idth ? Howmany squarecorners has each one ?

8 . Howmany sides Of A havethe same length

9 . HOW many Oblongs are there in B ?

1 0 . HOW many equal sides has thisfigure ? how many square corners ?

1 1 . What is the name of the figure ?How long is each side ?

1 2 . How many inches is it aroundthe square ?

1 3 . One inch is what part of two inches ?

1 4 . Two inches are what part of 4 inches ?

1 5

1 6 FIRST AN D SECOND YEAR [Oral

THE NUMBER SIX

1 . Show withmarbles the combinations that form6 .

5 marbles 1 marble 6 marbles 4 marbles3 marbles 3 marbles 6 marbles 1 marble2 marbles 4 marbles 6 marbles 3 marbles

2 . Add

2 l 2 4 3 5 3 4 0 2

4 5 3 1 3 1 2 2 6 2

3 . Fill in the blank spaces

5 2 4 3 3 3 2 1 6 1

6 5 6 6 5 4 6 6 6 5

4 . Subtract6 5 6 6 6 5 6 6 5

6 2 3 1 5 3 5 2 4 3

5 . Place Six marbles in two equal groups ; in threeequal groups

6 . Give answers at Sight

3 x 2 2 x 3 6 x 1 6 4

‘I-of 6 § of 3 i of 4 § Of 6

1 in 6,— times ? 9

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1 8 FIRST AND SECOND YEAR [Oral

THE NUMBER EIGHT

1 . Illustrate the combinations that make 8.

7 plums 1 plum 8 plums 7 plums5 plums 3 plums 8 plums 4 plums2 plums 6 plums 8 plums 6 plums

m9

z . Count t0 8 by 2’

s . ? x 2 = 8 ? ? x 4 = 8 ?

Add up, then down3 . 4 3 5 2 7 1 6 5 4

4 5 2 6 1 7 1 3 3

4 . 3 4 2 2 1 3 0 l 2

2 3 5 3 3 0 2 6 2

l l l 3 4 5 6 1

5 . Subtract8 8 6 8 8 7 8 8 8

3 7 3 1 6 5 8 5

6 . In 8 blocks,how many groups of 2 ’s are there ?

1 time 2 HOW many groups are there ?2 times 2 2 is contained in 4 times.3 times 2 2 is contained in 6 times .4 x 2 2 is contained in 8 times.

7 . Give answers at sight8 4-4 é of S

2 x 4 i of 8

l—‘OO

N

03

woo


DRY MEASURES

PINT Q UART PEC! BUSHEL

1 . Name articles that you can purchase by the peckor by the bushel .

2 . Why are these measures called dry measures

3 . The smallest dry measure shown in the pictureis called a pint . Fill a pint measure w ith sand and

empty it into the quart measure . DO this again . Isthe quart measure now full ? You have Shown that2 pints equal a quart .

4 . What part Of a quart is a pint ?

5 . Show by measurement, as in example 3, that8 quarts equal a peck . A quart is what part of a peek ?

6 . Show as before that 4 peeks equal a bushel. A

peek is what part of a bushel ?

7 . A bushel is how many times a peek ? how manytimes a quart

8 . Subtract :8 qt . 7 qt .

4 qt . 3 qt.

20 FIRST AN D SECOND YEAR [Oral

THE NUMBER NINE

Add

1 . 4 2 3 7 l 6 5 4 8 3

5 7 5 2 8 3 4 1 6

2 . From 9 take 8 ; take 7 ; 6 ; 5 ; 3 ; 2 ; 4 ; 1 ; 9.

3 . Draw and cut out a 3-inch square . Place yourruler at the edges and mark the inches.Fold the paper to Show 9 square inches.HOW many rows of square inches are

thereCount the row s Of square inches, thus1 time 3 square inches 1 x 3

2 times 3 square inches 2 x 3

3 times 3 square inches 3 x 3

4 . Find :§ Of 3 sq. inches. 3 x 3 = ?

% Of 6 sq . inches.

§ Of 9 sq. inches.

5 . Fill the blank spaces

+ 3 + 2 + 4 + 6 + 5 + 5 + 7 + 4 + 8

9 9 9 9 9 8 9 8 9

9 9 9 9 9 9 9 9

2 3 7 4

Oral] NUMBERS TO TWELVE 21

THE NUMBER TEN

Ten 1 ’s4 5

9

6 5F lve 2 s

2

8Two 5 ’s

1 3

9 7

1 . Show with blocks the combinations of 1 0

blocks 6 blocks 1 0 blocks 5 blocks9 blocks 1 block 1 0 blocks 8 blocks3 blocks 7 blocks 1 0 blocks 6 blocks

2 . Count to 1 0 by 1 ’s ; by 2’

s.

3 . Add :

2 4 3 3 9 6 5 1 8 7

8 6 5 7 l 4 5 9 2 3

4 . From 1 0 take 3 ; take 5 ; 7 ; 8 ; 4 ; 2 ; 9 ;

6 ; l .

5 . Arrange 1 0 blocks in two equal groups. How

many blocks are there in each group ? 2 x 5 blocks= ?

6 . Name the piece of money that has the same valueas ten pennies. 1 0 cents equal one dime .

7 . HOW many nickels equal 1 dime ?

8 . Find the cost of 2 oranges at5 cents each .

9 . 2 in 1 0, times. 5 in 1 0,— times.

4 in 1 0, times and over.

1 0. Take the number in the centerfromeach number outside the circle .


THE NUMBER ELEVEN

1 . W ith squares Show the combinations of 1 1

4 squares 7 squares 1 1 squares 8 squares5 squares 6 squares 1 1 squares 4 squares9 squares 2 squares 1 1 squares 7 squares

2 . Add

2 8 6 3 1 0 4 5 17 9

9 3 5 4 2 8 l 7 6 1 0

3 . Subtract1 1 1 1 1 1 1 1 1 1 1 1 9 1 1 1 1 1 1

9 1 3 6 2 5 8 4 8 7

4 . Give missing numbers

1 1

5 . 5 dollars 3 dollars 1 1 dollars .

The sign 3 may be used for the word dollar or dollars,and the sign 5! indicates cent or cents . $8 $3

6 . In 1 1 there are 4’

s and over.

In 1 1 there are 5’

s and over.

In 1 1 there are 3’

s and over.


THE NUMBER TWELVE

1 . With pencils Show the combinations thatmake thenumber 1 2 .

8 pencils 4 pencils 1 2 pencils 6 pencils2 pencils 1 0 pencils 1 2 pencils 9 pencils1 1 pencils 1 pencil 1 2 pencils 4 pencils9 pencils 3 pencils 1 2 pencils 5 pencils

2 . Count to 1 2 by 1 ’s ; by 2’

s ; by 3’

s ; by 4’

s ; by 6’

s.

3 . 1 2 is how many more than 8 ? 1 0 ? 7 ? 2 ? 6 ?

1 ? 4 ? 1 1 ? 9 ? 3 ? 5 ?

4 . Add

5 1 0 9

8 7 2 3

5 . Subtract

1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2

9 8 6 4 2 1 1 3 5 7 1 0

2 x 6

4 x 3

2 x & + 2 3 x 4

7. Multiply each numberthe circle by 2 .


DO! EN

1 . Draw 1 2 lines . Erase 4} ofthem. What is 4 of 1 2 ?

2 . Count the eggs that yousee in the basket .

3 . What name is sometimesgiven to 1 2 eggs ? to 1 2 pins ?to 1 2 lemons ?

1 2 things equal one dozen.

4 . How many oranges equal 4of a dozen ?

5 . What number is doubled to make 1 2 ?

6 . Make problems w ith4 x 3 cents 3 x 4 apples 2 x 6 games6 x 2 horses 5 x 2 dollars 2 x 4 cakes12Oi 1 2 peaches g» of 1 2 cars 1» of 1 2 apples

Subtract at Sight7 . 1 2 1 2 1 2 1 2 1 2 1 2

3 4 5 6 7 8

1 0 . Make problems w ith the above numbers .


READING NUMBERS1 . Read

1 4 24 55 48 51 64 70 91 40

1 5°

34 56 49 56 60 80 90 55

1 6 44 57 50 59 76 89 99 73

The right-hand figure in a number is called ones’

figure ; the second figure is called tens’ figure .

Point out the ones and the tens in each of the abovenumbers ; thus, 1 4 is 1 ten and 4 ones .

TABLE OF COMBINAT IONS IN ADDITION

In addition there are 45 different combinations offigures

,taken two at a time, and 1 7 different sums or

amounts . Use these combinations for drill frequently

Written] ROMAN NUMBERS 27

ROMAN NUMBERS TO TWENTY1 . The Romans wrote all numbers

up to 49 w ith the use of three letters

,I,V,X . I stands for 1 ; V

stands for 5 ; X stands for 1 0.

2 . This is how the Romans w rotetheir first twelve numbers :

1 2 3 4

I II III IV V VI

7 8 9 1 0 1 1 1 2

VII VIII IX XI XII

3 . Write the first twelve Roman numbers frommemory .

4 . Read the Roman numbers on the clock face.O n clock faces IIII is used for IV.

5 . Copy the follow ing numbers1 3 1 4 1 5 1 6 1 7 1 8 1 9 20

XIII XIV XV XVI XVII XVIII XIX

6 . Write in Roman numbers,9. Show what change

in the letters will make 1 1 .

7 . Write the Roman numbers from 1 to 20.

8 . What time is it by the clock in the picture ?

The Short hand is called the hour hand . The longhand is called the minute hand .

9 . Show the position of the hands at 30 minutesafter 9 at 30minutes after 1 0 at 30minutes after 1 1 .

28 FIRST AND SECOND YEAR [Oral and Written

ADDITION

State sums at sightb c d 3 f g h t ja

1 . 2 2 2 2 2 2 2 2 2 2

76 82 74 62 50 41 53 64 30 72

2 . Change the 2 above to 3 and add ; then to 42 2 2 2 2 2 2 2 2

85 65 75 55 45 63 73 93 43 83

4 . 3 3 3 3 4

59 49 69 79 49 38 48 88 78 58

5 . 2 3 2 6 2 5 2 5 2

4 2 O 3 2 3 2 4 3 5

3 4 3 1 O 4 1 1 0 3

6 . A boy spent 25 cents for a book and 1 2 centsfor a slate . How much did he spend for both ?

Write ones under ones and tens under25 cents tens. Add the right-hand column and

1 2 cents place the total, 7, underneath . Add the

37 cents second column and write the total un

derneath . The answer is 37 cents .

7 . Find the sumof

25 apples and 63 apples 24 boys and 1 5 boys37 cakes and 42 cakes 32 chairs and 26 chairs81 lemons and 1 7 lemons 47 books and 22 books42 balls and 24 balls 36 bats and 52 bats

Written] ADDITION

Adda b dc

1 . 20 30 40 50 60

30 1 0 1 0 20 1 0

2 . 3 1 2 1 23 32 1 2

1 2 32 1 3 23 33

3 . 42 44 44 43 1 4

2 1 23 24 34 44

Add upward ; test by adding downward4 . $45 $25 $35 $34 $42 $55

$1 4 $33 $54 $35 $45 $33

5 . $ 1 6 $45 $67 $72 $8 1 $83

$3 1 $54 $2 1 $25 $ 1 2 3 1 5

Only things having like names can be added.

b c da

6 . 1 7 boys 36 caps 56 balls 35¢

1 2 boys 2 1 caps 32 balls 24¢

a b

7. 1 2 girls 34 men1 0 girls 22 men23 girls 41 men

s. 1 4 cars 1 2 boxes32 cars 43 boxes22 cars 3 1 boxes

29

so FIRST AND SECOND YEAR [Written

ADDITION

1 . There are 54 houses On One street and 28 on an

other. HOW many are there on both streets ?Write ones under ones and tens under

54 houses tens. Add the ones’ column . The sum28 houses is 1 2 ones, or 1 ten and 2 ones . Write82 houses the 2 under the ones’ column and add

1 ten 2

The answer is 82 houses .the 1 ten to the tens’ column .

tens 5 tens 8 tens .

Add and testa b o d e f

2 . 36 47 42 54 48 35

25 24 39 36 34 27

3 . 46 1 9 29 1 8 38 1 7

3 6 24 1 0 36 1 7 46

4 . 1 9 2 1 32 23 3 1 42

1 4 1 9 4 1 5 43 1 6

3 1 2 I6 6 8 1 7

5 . 1 1 1 6 1 9 41 39 42

3 1 1 0 20 23 20 1 8

29 49 1 7 1 8 1 8 20

6 . 30 40 32 9 8 1 5

1 7 1 9 30 1 4 20 20

28 34 9 1 6 9 38

7 . Count by 3’

s to 36 ; to 75. By 4’s to 88 .

Written] ADDITION 3 1

ADDITION

1 . Thomas has $24 in the bank and $1 7 in hispocket . HOW many dollars has he ?

2 . A farmer sold 26 bushels of apples on Monday,3 5 bushels on Tuesday, and 30 bushels on Wednesday.

HOW many bushels did he sell in the three days ?

3 . On Tuesday a newsboy sold 28 morning papersand 44 even ing papers. How many papers did he sell ?

4 . A'

girl had 42 cents left after spending 25 centsfor ribbon and 1 0 cents for pins. HOW much moneyhad she at first ?

5 . Mrs. Jackson spent $24 for a suit, $3 1 for a coat,and $1 2 for a hat. HOW much did all cost ?

6 . Fred planted 29 potatoes in one row,3 1 in an

other, and 33 in a third row . HOW many potatoes didhe plant all together ?

7 . Ned spent 35¢ for a ball, 25¢ for a bat, and 1 0¢for car fare. HOW much did he spend ?

8 . The girls spent at the park , l5 ¢ for ice cream,

20¢ on the roller coaster, 35 ¢ in the picture gallery,

and 1 2 ¢ for popcorn . HOW much did they spend forall ?

9 . It took Mary 1 6 minutes to sweep and dust thelibrary

, 1 2 minutes for the dining room,and 2 1 minutes

for the parlor. HOW long did it take for the three rooms ?

1 0 . Edw in has 43 marbles, and Walter has 24 morethan Edw in . How many marbles has Walter ?

FIRST AN D SECOND YEAR

SUBTRACTION

1 . Mary has 9 cents . She spends 5 cents . HOWmany cents has she left ?

2 . A farmer had 7 cows. After selling a number hehad 4 left . HOW many did he sell ?

3 . Anna had 1 5 towels to iron . When she hadironed 9, how many were left to iron ?

4 . Lucy had 1 2 roses and gave Mary 5 roses. HOWmany roses had Lucy left ?

TABLE O F COMBINAT IONS IN SUBTRACTIONIn subtraction there are 45 difierent combinations of

figures,taken two at a time . Use these combination s

for drill frequently

34 FIRST AND SECOND YEAR [Written

PRACTICAL PROBLEMS

1 . David is 1 4 years Old andWalter is 7 years younger.

How Old is Walter ?

2 . Edna spent 35 cents for butter . She gave the clerka half-dollar. How much change should She receive ?

3 . A postal clerk sold 43 postal cards one week ,

and 67 the next. Week . How many more did he sell inthe second week than in the first week 9

4 . Aman lives 68 miles from the city and has traveled 24miles toward the city. HOW many miles has be

yet to travel

5 . Tom drove home 78 cow s and Ned 56 . HOW

manymore cows were there in Tom’

s herd than in Ned’s ?6 . Edna had 78 pieces in her doll’s dinner set, but 3 6

plates were broken . How many pieces remained ?

7 . Mr.Wilson’s farmcontains 76 acres of land , whichis 1 4 acresmore than his brother’s farm contains . HOWmany acres are there in his brother’s farm

8 . W illiamrode 27 miles o n his bicycle on Thursdayand 1 4 miles on Friday . HOW much farther did he ridethe first day than the second ?

9 . Make problems w ith :pupils pictures lamps books46 — 1 4 37 — 24 63 — 1 2 48 — 36 73 — 2 1

56 — 43 62 — 3 1 84 — 2 1 46 — 24 36 — 1 5

1 0 . 34 children were invited to ! ate’s party . Howmany of themwere absent, if only 22 Of them attended ?

Oral] MULTIPLICATION 35

MULTIPLICATION

1 . What is the cost of two 2-cent pencils ? 2 x 2 ¢

2 . HOW much Should you pay for three 2-cent apples ?four 2-Oent tops ? five 2-cent stamps ? Six 2-cent papers ?

3 . James counted 2¢ seven times ; thus, 2¢ 2¢ 2¢

and found that he had He couldhave said seven 2 ’

s are 1 4,or 7 x 2 1 4.

4 . Write in two other forms : 8 x 2 = 1 6 ; 2

n ine 2 ’s = 1 8 ; 1 0 x 2 = 20.

2 2g5 . Build the table of 2 ’

s thus :2 2 2 2

Write the sum of each column 2 2 2 2 2

beneath it . Look at each column . 2 2 2 2 2 2

See how many 2 ’

s it contains . Say,

6 x 2 1 2 etc .

6 . Find products5 x 2 caps 8 x 2 plums 9 x 2 birds 4 x 2 cups6 x 2 dolls 3 x 2 hats 7 x 2 birds 2 x 2 hats

7 . Memorize the table . Table of 2 ’s

8 . Multiply each number outside the circle by 2 .

36 FIRST AND SECOND YEAR [Oral and Written

1 . How many are two 7’s ? two 1 0’s ?

2 . Write these two problems in two other ways.

3 . How many are two 34 ’

s ? This may be written34 34 68

, or 34

34 The sumof two 34’

s is 68.

68, sum.

4 . A Shorter process for finding two 34’s is bymu ltiplication ; written thus, 34 Write the multi

X 2 plier 2 under the68 right-hand figure

Of the number to bemultiplied, which is 34. Beginningat the right , say 2 x 4= 8. Write 8 in ones

’ place inthe answer. 2 x Write 6 in tens’ place in the

answer. The result is 68 . Test by addition, 34 34 68 .

Multiply,and test by addition

a b c d e f

5 . 23 54 53 64 71 62

2 2 2 2 2 2

6 . 40 81 94 70 63 53

2 2 2 2 2 2

7 . 93 72 62 53 82 91

2 2 2 2 2 2

s . 44 32 83 24 84 74

2 2 2 2 2 2

N O TE — Teachers who desire to proceed from this point w ith the

work of multiplication, will find the tables of 3’

s, 4'

s, and 5’

s on pages

5 5—60, 69.

Oral and Written] DIVISION 37

DIVIDING BY 2

1 . [I I/ I/ Count the splints by 2’

s.

How many times must two splints be taken to have1 0 splints ? 1 0 spl ints contain 2 splints times .

2 . 6 contains 2 times . 8 contains 2times . 1 2 contains 2 times .

3 . Into how many groups of two each may 1 0 bedivided ? 1 0 divided by 2 equals 5 , written1 0 2 5, or The Sign is read divided by .

5

Read, and give answers :

4 . 4 -2 .

5 . 22 ; 221 2 ; 2L6 ; 22 2

6 . Divide 24 by 2 .

2 is contained in 2 tens, 1 ten time ;write 1 in tens ’ place . 2 is contained in

1 2 4 ones,2 times ; write 2 in ones

’ place .

The answer is 1 2 .

Find the answers :a

7 . 222

8 .

9 .

1 0 .

FIRST AND SECOND YEAR [Oral and Written

MA! ING CHANGESecure toy money, or make circles from cardboard to repre

sent the different pieces.

Appoint storekeepers and purchasers, and have the counting

done in the schoolroom. Consult “Market Report” for prices.

1 . Hattie’s purchase . 2 . John ’s purchase .

Sugar, 1 0¢ The storekeeper, Fire crackers, 1 5¢Butter, 1 5¢ when making the Torpedoes

, 5¢

Potatoes,l2¢ change , places the Matches

,2¢

Cost, 37¢ coins as he counts, Rockets, 20¢

1 ¢ thus :1 ¢ 1 ¢

ChangeChange, Ch

1 ¢

1 0¢ange

1 ¢

50¢ 5¢

3 . Willie boughtmeat for 30¢ andmilk for 4 Howmuch change should he receive from

Make change from 50¢ for :

4 . Oranges for l5¢, lemons for pears for 512.

5 . Popcorn for taffy for nuts for

6 . Rice for tapioca for prunes for

7 . Potatoes for bread for turnips for

8 . Plums for sugar for pepper for

9 . Celery for lettuce for spinach for

1 0 . Corn for seed for apples for

Oral] LENGTH 39

MEASURING LENGTH

For this exercise the teacher should secure a foot rule and a yard

stick.

1 . Examine a foot rule . Observe that it is dividedinto 1 2 equal spaces . Each Space is called one inch .

A foot rule is therefore 1 2 inches long.

2 . The follow ing represents a foot rule,although it

is only one fourth the real length . Count the numberof inch spaces .

3 . Cut from cardboard a foot rule and mark the

inches on it .

4 . With the rule draw a line 1 inch long ; 4 incheslong.

5 . HOW many inches equal of a foot g. of a foot ?

1. Of a foot ?

6 . Draw an oblong 1 2 inches long and 8 inchesw ide . How many inches is it around the Oblong

7 . Draw a 2-inch square . How many inches is itaround the square ?

8 . Measure a yard stick W ith your foot rule . ThisShow s that there are 3 feet in a yard .

9 . Mark off W ith the yard stick on the blackboard aline 1 foot in length ; 2 feet in length ; 1 yard in

length .

1 0 . How many feet equal 2 yards ? of a yard

40 FIRST AND SECOND YEAR [Written

REVIEW

1 . Aman paid 3 80 for 2 cows. HOW many dollarsdid each cost ?

2 . A family bought 48 pints Of milk in a month .

How many quarts did they buy ?

3 . How much w ill 2 lb. of tea cost at 40¢ a pound ?

4 . How many 2-cent stamps can be bought for 64cents ?

5 . Eva paid 86 cents for 2 yards Of linen. Whatwas the cost Of 1 yard ?

6 . If Ruth takes 2 piano lessons every week, howmany does She take in 44 weeks ?

7 . A girl is 1 4 years old . Her brother is tw ice asold . How Old is her brother ?

8 . How many pints are there in 44 quarts ?

9 . If a clerk earns 3544 a month , how much w ill heearn in 2 mon ths ?

1 0 . Dick has 68 cents . He gives 35 cents to ! ate .

HOW many cents has he left ?1 1 . If molasses costs 1 4 cents a pint, how much w ill

a quart cost ?

Find the cost of

1 2 . 2 pieces of soap at 1 0 cents a piece.

1 3 . 2 pounds of butter at 24 cents a pound.

1 4 . 2 dozen lemons at 1 2 cents a dozen .

1 5 . 2 yards of muslin at 1 1 cents a yard.

42 THIRD YEAR [Oral and Written

1 6 . Add 1 to 1 000. The sum is one thousand one,

written 1 001 .

Write i n figures

1 7 . One thousand two. 20 . One thousand seven .

1 8 . One thousand nine . 2 1 . One thousand eight .

1 9 . One thousand six. 2 2 . One thousand three .

The first figure on the right is called the ones’ figure ;

the next is called the tens’ figure ; the next is called

the hundreds’ figure ; the next is called the thousands’

figure. The tens are always read as so many ones .

Thus, 1 625 is read, 1 thousand, 6 hundred, 25 . In

25,the 2 tens are read as 20.

Read,then w rite

a b

2 3 . 1 025 2040

2 4 . 1 1 25 2 1 41

2 5 . 1 1 39 3005

26 . 201 4 4020

Write as one number

2 7 . 6 hundreds,4 tens

,8 ones .

28 . 8 thousands, 5 hundreds, 3 tens, 3 ones .



3 1 . 9 thousands, 4 hundreds, 0 tens, 5 ones .

Oral and Written] ADDITION 43

ADDITION( Review pages 28 to 3 1 )

1 . Count from 2 to 1 00 by 2 ’s.



4 . Count from4 to 1 00 by 4’s.

5 . Count from 1 to 1 01 by 4’s .

6 . Add the number in the cen

ter to each number outside the circle .

7 . Add 3 to each of the follow ing numbers ; then 4 ;then 5 :

24 34 44 55 65

36 46 56 66 76

47 67 27 38 58

Find sums . Test by adding downwards :a b c d e

6 . 23 32 42 45 51

1 3 23 32 51 42

43 43 44 54 1 4

9 . 44 2 1 53 32 3 1

55 32 32 24 24

33 1 2 43 3 2 32

The process of uniting two or more numbers to formone number is called addition.

The numbers united are called addends .

The answer in addition is called the sumor amount .

44 THIRD YEAR [Written

ADDITION1 . Add 234

,359, and 266.

234 2 hundreds 3 tens 4 ones359 3 hundreds 5 tens 9 ones266 2 hundreds 6 tens 6 ones859 7 hundreds 1 4 tens 1 9 ones .

1 9 ones7: 1 ten and 9 ones. Write the 9 in ones’

place and carry the 1 ten to tens’ place . 1 4 tens 1

ten 1 5 tens . Write the 5 in tens’ place and carry

the 1 to hundreds’ place . 7 hundreds 1 hundred8 hundreds .

Write fromdictation,then add and test

a b c d e

2 . 234 230 1 01 23 1 301

326 325 304 405 226

434 265 376 568 304

3 . 405 304 604 400 291

304 349 787 697 743

296 200 342 345 456

4 . 623 344 23 509 20

5 593 906 5 1 02

340 25 25 820 67

5 . 708 93 1 68 7 423

55 67 834 751 92

634 8 436 534 899

Written]

Add rapidly

i"

Write from dictation,then add

qmb—‘O

QO

CR

Q

a

2 . 305

79

6

394

3 . 562

9

645

834

4 . 390

59

508

74

380

b

tO

CJT

CD

OO

ml—‘m

wCD

CJT

O'D

O

N

O'D

OO

Q

b

542

67

500

9

807

58

6

526

300

5

794

896

25

l—‘Qo

o

ml-P

CJI

OO

NJ

QA

O

CID

CJ'R

CJT

CJO

GD

ND

l—‘Q

ADDITION

ADDITION

f g h

9 8 7

0 5 2

2 6 7

6 1 6

6 3 8

9 8 1

2 7 3

4 3 7

c d

740 8

90 48

708 600

502 540

60 536

547 67

44 25

782 981

29 6

330 306

57 27

8 407

901 92

l—lNJ

CJ'l

l-P

mto

q

cb

s’o

45


ADDITION1 . Find the sumof 2430, 4307, and 68.

2430 2 thousands 4 hundreds 3 tens 0 ones4307 4 thousands 3 hundreds O tens+ 7 one s68 O thousands 0 hundreds 6 tens 8 ones

6805 6 thousands 7 hundreds 9 tens 1 5 ones .

1 5 ones 1 ten 5 ones . 1 ten 9 tens 1 0 tensor 1 hundred . 1 hundred 7 hundreds 8 hundreds.4 thousands 2 thousands 6 thousands .

Write from dictation, then adda b c d e

2 . 23 378 298 1 008 603

604 49 342 49 2798

3068 3067 6781 706 6987

3 . 1 304 2004 4987 3740 6425

3050 9 609 4020

6000 50 807 4203 205

200 674 5002 6001 1 347

4 . 6870 5475 64 2 1 3006

2 2681 370 2 1 02 2904

3078 5004 4274 3478 799

2690 79 5007 9 6094

Written] ADDITION 47

ADDITIONWrite fromdictation , then add

1 . Twenty-five two hundred twen ty-fiv e ; threehundred fifty.

2 . Four hundred two ; seventy-three ; n ine ; fivehundred Sixty.

3 . Four thousand twenty ; Six hundred Six ; five .

4 . Six hundred n inety ; ten ; three hundred ; twothousand four.

5 . TW O hundred eighty ; n ineteen ; Six

thousand.

e. 230 65 + 1 00 405.

7 . 300 9 25 500.

8 . 6555 1 02 1 00¢

9 . 3 42 + 8 504 3 1 05 + $3 .

1 0 . 24 pt . 1 20 pt . 7 pt. 36 pt .

1 1 . 1 000 qt . 1 4 qt . 1 3 5 qt . 1 0 qt.

1 2 . 1 74 pk . 1 30 pk . 5 pk . 800 pk.

1 3 . 1 200 in . 1 0 in . 1 00 in . 20 in .

1 4 . 60 dimes 4000 dimes 4 dimes 300 dimes.

1 5 1 6 . 1 7 1 8

2000hours 1 370minutes 40 gallons 409 days1 46 hours 234minutes 209 gallons 3090 days9 hours 30minutes 2900 gallons 9 days

3 472 hours 605minutes 4 gallons 374 days


ADDITION

Read and solve

2465 3642 461 2 5534 6342

4756 3254 432 1 41 32 3536‘7

4234 351 2 2435 1 543 2453

5243 2453 32 1 5 41 23 423 1

63 1 4 1 355 2652 1 623 3245

9

7664 2845 6246 3 664 4554

7 . 6050 4004 1 804 4536 61 43

S. 3652 4630 5672 3867 5468

9 . 4876 6724 41 1 6 3442 41 62

1 0. 3640 4466 7201 404 1 62‘7

1 1 . A carpenter had 23 men and hired 1 3 more.

How many had he then ?

1 2 . Mr. Jones deposited 3 1 23 in a bank on Monday ;3 232 on Tuesday ; and 3 32 1 on Wednesday . Howmuch did he deposit in the three days ?

1 3 . A ship sailed 223 miles the first day, 320 milesthe second, and 23 1 miles the third. How many milesdid it sail ?

1 4 . A farmer raised 230 bushels Of wheat, 1 22 bushels of corn , 1 1 2 bushels Of oats , and 323 bushels of rye .

How many bushels of grain.

did he raise ?

1 5 . Mrs . Foster bought a bedroom set of furniture for3 1 25, a piano for 3 350, curtains for 3 52, pictures for

3 1 28, and a rug for 3 23 . HOW much did they all cost ?


SUBTRACTION

1 . From 83 subtract 35 .

83 8 tens 3 ones, or 7 tens 1 3 0 1 168

35 3 tens 5 ones48 4 tens 8 ones.

Since 5 ones cannot be taken from 3 ones, take 1 ten1 0 ones) from the 8 tens (leaving 7 tens) and add

it’

to the 3 ones, making 1 3 ones . 1 3 ones less 5 onesequal 8 ones. 7 tens (remaining) less 3 tens equal 4 tens .

Before subtracting, the work may be expressed thus :We think : “ 5 from 1 3 leaves 8 ; 3 from 7

7 1 3

leaves 4 ; 48 . 8 3

Test — 48 35 83 .3 5

The process of finding the difference between two

numbers is called subtraction .

The number from which we subtract is called the

minuend ; the number subtracted is called the subtra

hend ; the result is called the difference or remainder.

Subtract, and test each result :b da c

2 . 63 92 84 57

27 69 39 38

3 . 48 74 81 63

29 47 29

4 . 55 80 3 1

1 9 27 1 8

Written] SUBTRACTION 51

Subtract and testa b c d f

1 . 769 81 9 346 665 749 864

374 568 94 374 298 539

2 . 332 748 552 1 75 729 534

1 40 339 429 68 549 360

3 . Make,solve

,and test 200 problems like the above.

4 . From 803 subtract 576.

7 9 1 3

8 03 7 hundreds 9 tens 1 3 ones5 76 5 hundreds 7 tens 6 ones

2 2 7 2 hundreds 2 tens 7 ones.

Take 1 hundred from 8 hundreds ; this leaves 7 hundreds . 1 hundred equals 1 0 tens . Take 1 ten from 1 0

tens ; this leaves 9 tens . 1 ten and 3 ones are 1 3 ones .803 then is equal to 7 hundreds, 9 tens, and 1 3 Ones .1 3 ones — 6 ones= 7 ones ; 9 tens — 7 tens = 2 tens ; 7hundreds 2 hundreds 5 hundreds. Answer

,227.

Read,then subtract and test

C b c d e

5 . 8404 7604 5041 5202 701 1

3625 4896 1 979 1 824 4583

6 . 7024 8401 5401 8704 4087

3767 4574 251 9 6247 1 069

7 . Subtract 1 87 from9234 ; then take 1 87 from eachsuccessive remainder, until the final remainder is 7364.

52

6 9 10

THIRD YEAR

SUBTRACTION

1 . From700 take 264.

700 6 hundreds 9 tens 1 0 ones2 64 2 hundreds 6 tens 4 ones4 3 6 4 hundreds 3 tens 6 Ones

a

2 . 500

1 54

300

263

604

1 60

609

285

706

567

2042

1 01 2

701 8

4009

b

600

247

700

288

809

341

501

209

801

560

41 06

201 4

5080

3 1 07

0

900

678

600

327

701

202

303

1 80

704

395

5001

301 4

9001

3082

d

400

1 97

800

561

902

720

806

1 99

560

297

801 2

5707

8304

501 2

6

800

372

200

1 81

606

408

903

287

601

269

7020

2904

4400

3870

[Written


SUBTRACTIONSubtract

a. b c d e

1 . 6432 7244 6475 7994 8641

41 76 5371 3879 3877 1 282

2 . 453 1 4351 4234 2432 21 34

1 522 1 543 1 235 1 344 1 545

3 . 5423 42 1 5 3254 3524 823 1

2545 1 567 1 565 1 566 4743

4 . 4253 323 1 5453 81 2 1 641 4

1 464 1 865 1 974 3642 3892

5 . 41 2 boys and 325 girls were enrolled in a school .How many more boys than girls were enrolled ?

6 . Harry has 42 chickens . After he has fed 1 5 Of

them, how many ch ickens remain to be fed ?

7 . John ’s home is 1 32 miles from New York,and

Mary’s hOme is 341 miles fromNew York . HOW manymiles farther fromNew York does Mary live than John ?

8 . The perimeter or distance around a dining tableis 28 feet and that of the library table is 2 1 feet .

Find the difierence in the perimeters .

9 . An automobile ran 3 1 2 miles one week and 1 45miles the next week. HOW many more miles did the

automobile run the first week than the second week ?


ADDITION AND SUBTRACTION1 . In the Central School, there are 398 pupils ; in

the Garfield School , 1 045, and in the Holmes School,

2306. How many pupils are there in the three schools ?

2 . Mr. Adams’s home cost 3 4370, and Mr. Boyd ’s cost

$3745. Find the difference in the cost of their homes .

3 . John lives 5906 feet from his school, and Thomaslives 21 94 feet nearer the school than John . HOW far

does Thomas live from the school ?

4 . Bertha counted the people in four parades. In the

first there were 208 ; in the second, 890 ; in the third,1 506 and in the fourth

,1 781 . How many were there

in all ?

5 . In two city schools, boys parade as soldiers . In

the first school there are 1 790 boys ; in the secondschool 279 boys less than in the first. HOW manyboys are there in the second school ?

6 . A merchant sold for the fourth Of July, 3706small flags

,1 71 2 larger flags

, and 1 9 flags for flagpoles. HOW many flags did he sell ?

7 . In counting the steps to school,Joseph took 1 370

,

and Harvey took 940 less than Joseph . HOW manysteps did Harvey take ?

8 . A street-car conductor collected 1 03 fares on the

first trip, 72 on the second trip, 1 76 on the third trip,

and 39 on the fourth trip . How many fares did hecollect ?

Oral] MULTIPLICATION 55

MULTIPLYING BY 3

1 . Count by 2 ’

s to 36 ; by 3’

s to 36.

2 . HOW many are or two 3’

s?

or three 3 ’

s ? or four 3 ’s ? 3

3 . Three 3’

s are five 3’

s are3 3

Six 3’

s are n ine 3 ’

s are3 3 3

3 3 3 34 . How many are l x 3 ? 5 x 3 ?

3 3 3 3 3

5 . Build the table of 3’

s to 1 2 x 3 thus : 3 3 3 3 3 3

Write the sumOf each column beneath it. 3 3 3 3 3 3 3

Look at each column and say, 1 x 3 3

2 x 3 = 6 ; 3 x etc.

6 . 3 x 8= 8 x ? 3 x 5= 5 x ? 9 x 3 = 3 x ?

Table of 3 ’s 7. Memorize the table.

66 THIRD YEAR [W ritten

MULTIPLYING BY 3

1 . Multiply 65 x 3 .

3 x 5 ones 1 5 ones, or 1 ten

Multiplicand 65 and 5 ones. Write the 5 ones inMultiplier 3 ones’ place . 3 x 6 tens 1 8 tens ;Product 1 95 1 8 tens + the 1 ten of the 1 5 ones

1 9 tens. The answer is 1 95 .

We think : 3 times 5 : 1 5 ; 3 times65 6= 1 8 ; Product 1 95.

The number multiplied is called the1 95 multiplicand . The number show ing how

many t imes the multiplicand is taken is

Test . 65

65

called the multiplier.

called the product .

The result in multiplication is

Multiply, and test each product by addition

2 . 4

0

5

3

3 . 1 35

3

1 . 236

3

5 . 209

3

s . 1 32

3

75

3

1 05

3

409

3

1 46

3

1 45

3

d

6

0

6 74

3 3

2 1 6 308

3 3

237 258

3 3

284 1 67

3 3

0298 276

3 3

53 THIRD YEAR [Oral

MULTIPLYING BY 4

1 . Count by 4’s to 1 2 ; to 24 ; to 36 ; to 48.

2 . How many are 4 4, or two 4

’

s ? 4 4 4, or

three 4’

s ? or four 4’

s ? 4

3 . Five 4’s are six 4’

s are

4 1:4 . How many are 2 x 4? 4 x 4 ? 5 x 4 ?

4 4 4 4


s to 1 2 x 4 thus 4 4 4 4 4

Write the sumof each column beneath it. 4 4 4 4 4 4

Look at each column and say, 1 x

2 x 4= 8 ; 3 x 4= 1 2 ; etc .

6 . 4 x 8= ? x 4 9 x 4= 4 x ? 6 x 4= ? x 6

7 . Memorize the table . Table of 4’s

Give products .

Give products at sight5 7 9 1 1 1 2

4 4 4 4 4

4 x 5 3 x 8 4 x 1 0

3 x 6 4 x l2 3 x 2

4 x 1 1 4 x 2 3 x 1 0

Oral and Written] MULTIPLICATION 59

PRACTICAL PROBLEMS

1 . Emma has 4 pieces of ribbon of 1 0 yards each .

How many yards has she in all ?

2 . How many lemons are there in 4 dozen ?3 . How far can you ride in 4 hours ill a carriage

that travels on an average of 4 miles an hour ?

4 . How many pecks are there in 1 1 bushels5 . At 1 0¢ a quart, how much w ill 1 gal . oil cost ?

6 . How many days are there in 4 weeks ?

Multiply, and test by additiona b c d

7 . 1 65 238 369 748

4 4 4

8 . 293 687 574

4 4 4

9 . 786 934 867

4 4 4

1 0 . 91 5 846 739

4 4 4

1 1 . 886 995 774

4 4 4

Give products at sight

1 2 . 4 x 20 4 x 50 4 x 80 4 x 25 4 x l7

1 3 . 4 x 30 4 x 60 4 x 90 4 x l5 4 x l8


PRACTICAL PROBLEMS

Make the requiredchange w ith toymoney,or w ith paper markedasmoney. Make otherproblems from the list .

1 . Jane’s slip reads“ 2 waists, 2 collars 5 The collectorreceives from her ahalf dollar, and in making the change , says“ 35 cents ” ; then gives5 cents, and says, “ 40

cents ” ; then gives adime

,and says, “ 50

cents .

2 . Mrs. Brown’s slip reads 1 pair lace curtains

2 counterpanes How much change shouldshe receive from

3 . John ’s slip reads : 1 fancy shirt 1 5 2 collars5 2 handkerchiefs Make the change from 50

4 . Carrie’

s slip reads : “ 6 napkins 6 2 tablecloths20 3 towels Return the change from fifty cents.

5 . Mother’s slip reads 1 dozen towels 1 2 9 nap

kins 2 pillow slips Find change from 50 cents.

6 . Mary’s slip reads : 1 wrapper 35 if, 1 waist 1 5 14”

Give the change out of a half dollar.

W ritten] MULTIPLICATION 61

PRACTICAL PROBLEMS

1 . If a sail maker uses 1 8 yards of cloth in amainsail, how many yards would he require for 3 such sails ?

2 . If it takes Helen 24minutes to hemstitch a collar,how many minutes w ill it take for 4 collars ?

3 . Aman bought 4 lots at $475 each . How muchdid they cost ?

4 . Mr. Home made 3 payments of $645 each forhis house . What was the cost of his house

5 . If each pupil in a school of 658 has 4 books,how

many books have they all6 . A drover bought 3 horses at $235 each . HOW

much did he pay for all7 . A farmer sold 276 sheep at $4 a head . How

much did he receive for all ?

8 . If a train runs 476 miles in a day, how far can

I travel on it in 3 days ?

9 . A ship sailed 364 miles each day . HOW far didit sail in 4 days ?

1 0 . A car carries 60 persons . How many personsw ill 4 such cars carry ?

1 1 . How many acres are there in 4 farms,if each

farm contains 1 75 acres ?

1 2 . At 1 5 each , how much w ill 3 paintings cost ?

1 3 . How many boys are playing soldier, if there are4 row s and 1 6 boys in each row


DIVIDING BY 3

1 . Count by 3’

s to 9 ; to 1 8 ; to 30 ; to 36.

2 . HOW many times does 6 contain 3 ? I"

3 . Show by separating into groups1 2 contains 3 times 1 5 contains 3 times1 8 contains 3 times 21 contains 3 times

4 . Give quotients at sight9 — 3 1 8 —3

5 . Divide each number outs ide thecircle by 3 .

6 . Find :

§ of 27 g~ of 30 %=oi 36 -} oi 1 5

fi oi 1 2 § of 1 8 % 0f 2 1 § oi 33

7 . Compare 6 and 2 ; thus : 6 is 3times 2. 2 is 3

5 oi 6.

The number divided is called the dividend .

The number by which we divide is called the divisor.

The answer in division is called the quotient .

Divide and testc ea b d

3 . 3224 3286 3230 am9 . 3 2393 3 2363 3 2339 32933 3 2303

1 0 . 321 50 32660 32693

Oral and Written] DIVISION 63

1 . The sign is read divided by .

2 . means that we are to find how manytimes 3 13 is contained in 24 thus :

Find quotients

3 . 82 days + 2 days

4 . 1 86 hours 3 hours

8 times.

9 . 1 89 years 3 years1 0 . 244 roses 2 roses

5 . 422minutes 2 minutes 1 1 . 664 cents 2 cents

6 . 448 feet 2 feet

7 . 249 inches + 3 inches

8 . 622 dollars + 2 dollars

1 2 . 336 quarts + 3 quarts

1 3 . 1 44 gallons —z-2 gallons

1 4 . 428 pints + 2 pints

1 5 . 3 means that we are to find one third of

thus : 4 of 24¢ equals or

Find quotients1 6 . 224 days+ 2

1 7 . 333 cents + 3

1 8 . 2 1 6 dollars 3

1 9 . 622 birds -z 2

20 . 326 inches + 2

2 1 . 2 1 9 hours + 3

2 2 . 444 roses 2

2 3 . minutes 2


REMAINDER IN DIVISION

1 . Divide 263 by 3 .

Divisor 3 263 Dividend 26 tens 3 8 tens, and 2 tens87 Q uotient (20 ones) remaining . Write

Remainder ? the 8 tens in the tens’ place .20 ones 3 ones 23 ones . 23 ones 3 7 ones, and2 ones remaining. Q uotient 87 remainder 2 .

We think : 3 in 26,8 times

,and 2 remaining ; 3 in 23,

7 times, and 2 remaining.

”

Q uotient 87 ; remainder 2 .

Test . If the answer is correct, then 3 x 87, or 261 ,2,the remainder, w ill equal 263 , the dividend.

Divide and test by 2 ; by 3a b c d e

2 . 265 864 786 624 7368

3 . 71 3 2 1 9 265 758 2457

4 . Compare 1 2 2 and 4 of 1 2 ; 1 2 3 and 4 of 1 2.

Tofind 4 of any number, divide the number by 2 .

Tofind 4 of any number, divide the number by 3 .

How many area b c

5 . 4 of 240men ? 4 of 1 71 balls ? 4 of 7484 ?

6 . 4 of 71 7 feet ? 4 of 2 1 6 mi. ? 4 of 3927 ?

7 . 4 of 435 yd. ? 4 of 384 bu. ? 4 of 8064 ?

8 . 4 of 759 gal ? 4 of 902 in. ? 4 of 2 1 60 ?

9 . 4 of 285 pk. ? 4 of 405 ft. ? 4 of 8 2754 ?


DIVISION1 . Walter had 48 baskets of fruit . He sold an equal

number to 4 different buyers . How many baskets dideach buy

No. of baskets . 4 of 48 baskets : 1 2 baskets.1 2 No . of baskets to each .

2 . Mary has 45 cents . How many 3 cent orangescan she buy w ith hermoney ?

3 cost of 1 orange1 5 times

,or 1 5 oranges.

3 . Aman divided property valued at 369 equallyamong his 3 children . How much did each receive ?

4 . Mr. Bellearned 3 96 in 3 months . What were hismonthly wages

5 . Find the cost of 1 bushel of wheat, if 4 bushelscost 280 cents .

6 . If a girl sews 4 buttons on each pair of gloves,how many pairs has she finished when she has used468 buttons

7 . A farmer having 96 hogs sold one third of them.

How many did he sell ?

8 . In a car containing 639 baskets of peaches, one

third were spoiled . How many baskets were spoiled ?

9 . How many pound boxes can be filled from 1 64

quarter pounds of candy ?

1 0 . When molding costs 1 5 if a yard, how much w ill1 foot of it cost ?

1 ft . 4 of a yard ; 1 ft. will cost 4 of 1 5 or 5 cents.

Oral and Written] UN ITED STATES MONEY

UNITED STATES MONEY

United States money is written in dollars and cents .

A period named a “ decimal point ,” is placed to

the right of dollars . After the point, cents are writtenin two places . Thus

, 5 dollars and 25 cents isw ritten

1 . Read :

In addition and subtraction of Un ited States money,the p oint must be written under the p oint, dollars underdollars, and cen ts under cents.

Read and add2 .

Add across and in columns :

3 .

4 . 3 3 3 3

5 . 2 34+

Read and find difierencesa b c d e

6 .

7 .

8 . Add and 1 0 . Add and

9 . Add 35 and 1 1 . Add and


UNITED STATES MONEYRead and add :

a b e

1 .

2 .

3 3 3 3

3 3 3 3

3 3 3

3 3 3

Subtract and test

o

ur

uh

y

a b

7 .

8 .

9 .

c

35

1 0.

MULTIPLICATION

MULTIPLYING BY 5

1 . Count by 5’s to 1 0 ; to 30 ; to 45 ; to 60.

2 . HOW much are two 5-cent pieces ? 2 x

3 . Howmuch are three 5-cent pieces ? 3 x 5

4 . Tell the value of four 5-cent pieces ; of 5 such

pieces ; of 6, 7, 8, 9, 1 0, 1 1 , 1 2 .

5 . How many 5’s are there in 1 0 ? in 20 ? ill 30 ?60 ? 25 ? 35 ? 45 ? 50 ? 1 5 ?

6 . Multiply each of the outsidenumbers by 5 . Change the numberW ithin the circle to 4 and multiply ;then to 3 ; to 2 . Build the table of 5 ’

s

as you built the table of 4’

s.

7 . Memorize the table .

8 . Supply the missing Table Of

numbers :

2 x 5= ? 5 is ? of 1 0

4 x ?= 20 ? is -51—of 20

5 x 5 = ? 25 is ? x 5

? x 5 = 35 ? is 4 of 35

9 x ?= 45 4of 45 is ?

9 . Give products : 8 x 5 ;9 x 5 ; 3 x 5 ; 5 x 5 ; 7 x 5 ; 6 x 5 ; 1 2 x 5 .

1 0 . What is the difference in value between3 x $5 and 5 x $3 ? 7 x 5 hats and 5 x 7 hats ?

6 x $5 and 5 x $6 ? 2 x 4 books and 4 x 2 books ?


MULTIPLICATION OF DOLLARS AND CENTS

1 . Multiply by 3 .

In multiplying dollars and cents, place

3the decimal point in the product directlyunder the decimal point in the multiplicand . Write the dollar sign before thenumber of dollars .

2 . Multiply by 4. 3 . Multiply 7011 by 3 .

70¢

4 3

2 1 0¢ (Why ?)Multiply :

a b c d

4 . 3

2 4 3 5

5 . 74¢

4 5 3 4

6 . 22¢ 49¢ 26¢ 95¢

3 5 4 5

7 . How much w ill 3 peeks of peaches cost at 65¢ apeck

8 . A messenger boy delivers 4messages at 45¢ each .

How much does he earn for his companv

9 . May gets per week in a department store.Find her wages for 4 weeks.

W ritten] PROBLEMS FOR REVIEW 71

PRACTICAL PROBLEMS

1 . How many seats are there on

each side of the car ?

2 . How many are two times 1 1seats ?

3 . The conductor collected 75 fareson the first trip and 87 fares on the re

turn trip . How many fares did hecollect ?

4 . The fare is 5 cents . How muchmoney did he collect on both trips ?

5 . A lady paid for herself and 5

children. She gave the conductor 2.

half dollar. How much change shouldshe receive ?

6 . Each seat w ill accommodate two persons . Howmany persons can be seated in the car ?

7 . The conductor earns in a day. How

much does he earn in 5 days ?

8 . The motorman is paid a day . How muchdoes he earn in 5 days ? How much more does he earnin a day than the conductor ?

9 . The line is 8 miles long. How far does a car run

in making 5 round trips ?

1 0 . On one trip each seat was occupied. and 5 persons had to stand. Find the amount of the fares for

the trip.


MULTIPLYING BY 6

1 . Count by 6’s to 1 2 ; to 24 ; to 48 ; to 60 ; to 72 .

Build the table of 6 ’

s.

2 . How many 6’s are there in 1 2 ? in 1 8 ? 24 ? 36 ?48 ? 54? 60 ? 66 ? 72 ?

Table of 6’s 3 . Memorize the table .

4 . Compare in two ways :Thus 6 is 3 more than

3 ; 6 is i c 3 .

6 and 3 1 2 and 3

6 and 4 1 2 and 4

6 and 5 1 2 and 5

4 and 2 1 6 and 4

5 . Multiply each number outside

the circle first by 3 , then by 4, thenby 5, then by 6.

Multiply by 6 ; by 5 ; by 4 ; by 3a b c

6 . 243 567 1 49

7 . 679 295 293

8 . 978 869 687

9 . 207 890 903

1 0 . Give products at sight

6 x 40 5 x 20 6 x 80

6 x 70 5 x 35 5 x 32

6 x 90 5 x 41 4 x 71


DIVIDING BY 6

1 . How many times is 6 contained in 1 2 ? in 1 8 ?

in 24 ? in 48 ? 60 ? 54 ? 36 ? 66 ? 42 ? 72 ?

2 . Give answers60 4— 6 48 —z— 6

— 0 f 35 % Of 42

6254 6g )

3 . Divide each number by 6480 600 624 540 366

720 61 8 246 726 61 "

4 . Complete— and — over. 50

45 — 6 = — and — over.

5 . Divide by 5 and give remainders ; then by 6 :843 864 63 1 7235 8697

675 293 845 461 8 3 256

93 1 787 569 8627 43 67

6 . Compare in two w ays : 8 1 8 and $3 ; $36 and $6 ;35 books and 5 books ; 24 hats and 4 hats ; 42 lemonsand 7 lemons ; 45 fl and

7 . Find the cost of6 oranges at 1 8¢ a doz. 40 pears at 4¢ each .

36 apples at 2 each . 1 8 eggs at 1 0 a doz.

8 . At 3 apiece,how many oranges can you buy for

l8¢ ? for for for


PRACTICAL PROBLEMS

1 . Find the cost of 5 yards of cloth at .75 a yard.

2 . Four boys deposited in the school bank as follow s : and What was theentire deposit ?

3 . Julia went to the store w ith a twenty-dollar bill .

She paid 75 cents a yard for 6 yards of oilcloth, andfor a rug. How much had she left ?

4 . A box contains 360 oranges . If of them are

bad,how many good ones are there in the box ?

5 . At 36 cents a dozen, how much w ill 5 dozenoranges cost ?

6 . At 24 cents a dozen,how much w ill 6 dozen

oranges cost ? How much change should a lady receiveafter paying for the oranges w ith a two-dollar bill ?

7 . Make a problemw ith : and

5.

8 . John paid a bill of and had remaining. How much had he at first ?

9. If there are 28 lines on each page of a book, howmany lines are there on 9 pages ?

1 0 . A furniture dealer paid $624 for tables at $6each . How many did he buy ?

1 1 . Jack has collected 250 post cards and pastes 5 on

each page of his album. How many pages do they fill

1 2 . How many lamps, at 5 each, can be bought for83 How much money will remain ?


DRILLS IN ADDITION

Add rapidly,finding 3 answers in 1 minute.

a b c d

1 . 2345 3256 4325

3253 5433 2534

1 43 2 2345 3523

2564 4356 2456

73 1 6 51 34 5346

2 . 2434 3245 65 1 3

3256 1 452 3245

51 45 541 6 53 1 4

4253 2533 2425

3242 3254 5253

3 . 6325 6436 6546

4264 2462 3562

2633 6354 6255

1 462 5633 5364

6326 3265 4534

4 . Give sums at sight

37 + 26 59 + 1 7

1 9 4- 28 49 4-26 39 » 58 47 4-47


SUBTRACTION

From 804 take 365 .

1 . We cannot take 5 ones from 4 ones.

7 9 1 4 We cannot take 6 tens from0 tens .8 0 4 Take 1 hundred from 8 hundreds ; this3 6 5 leaves 7 hundreds . 1 hundred equals 1 04 3 9 tens. Take 1 ten from 1 0 tens, leaving

9 tens. 1 ten and 4 ones are 1 4 ones.804 therefore is equal to 7 hundreds, 9 tens, and 1 4ones . Subtracting, the difierence is 439.

Subtracta b c d e

2. 6304 7065 6401 801 4 4706

3 1 68 1 474 3 1 62 6202 2 1 65

3. 4060 8305 8560 6070 4904

2976 601 2 3574 4304 1 060

4. 61 05 7805 6099 3940 6303

2 1 66 4991 481 4 2 1 08 1 494

5. 81 1 0 4444 6222 83 1 4 81 96

4884 2666 4879 6070 7246

6 . 61 62 3 1 1 0 5641 41 32 61 1 2

3 1 04 2904 32 1 2 1 841 3897

7 .

between 9630 and 2709.

Find the difference between 8904 and 1 996 ;


DRILLS IN SUBTRACTION

Subtract, finding 5 remainders in 1 minutea c d

1 . 5434 3254 4203 6043

3565 2435 1 564 2564

2 . 4360 3204 3204 201 0

2654 1 605 1 3 1 6 1 51 6

3 . 3 1 05 401 0 6302 3051

1 046 2505 2603 2 1 03

4 . 6035 6501 1 045 3060

2456 2436 556 2065

5 . 1 405 2601 3561 6306

656 1 654 1 456 2501

6 . 6702 2041'

6020 503 1

3026 1 554 1 61 5 1 025

7. 61 03 301 4 203 1 6072

2005 2245 1 505 4003

8 . 5203 6203 41 06 2435

1 546 5204 3502 1 543

W ritten] MULTIPLICATION AND DIVISION 79

DRILLS IN MULTIPLICATION AND DIVISION

Multiply and divide each number by 2, 3 , 4, andb d f

1 . 468 456 273 3 32 634 804

2 . 684 654 372 233 436 972

3 . 236 564 732 548 364 729

4 . 632 542 41 2 485 1 84 908

5 . 846 452 2 1 4 854 41 8 890

Multiply and divide each number by 6, 5, 4, and 3

6 . 426 848 408 798 249 284

7 . 264 844 840 897 942 428

8 . 624 853 480 789 429 842

9 . 1 65 790 981 679 257 91 2

1 0 . 561 970 1 89 796 725 1 92

Multiply and divide each number by 2, 4, 6, and 5 :

1 1 . 456 295 2 1 7 51 3 665 537

1 2 . 654 925 1 72 1 35 656 357

1 3 . 546 529 91 8 1 50 250 640

1 4 . 237 592 1 89 51 0 520 460

1 5 . 372 71 2 891 566 502 604

Multiply and divide each number by 3,5,6, and 4 :

1 6 . 206 666 270 474 228 924

1 7 . 620 246 720 276 282 492

1 8 . 457 426 372 822 249 742

1 9 . 475 642 723 726 846 952

so THIRD YEAR I'

Oral

DRY MEASURES

1 . Name some dry articles purchased by the pint ; bythe quart ; the peck ; the bushel.

2 . Secure some sand or grain, and show by actualmeasurements the number of pints in a quart ; the number of quarts in a peek ; the number of pecks in a

bushel .3 . Memorize this table

4 . 1 bu. pecks ; 1 pk quarts.

5 . How many quarts equal 1 bushel ?

6 .1} pk. quarts ; 12“ pk . quarts.

7 . At 1 0¢ per quart, find the cost of 8 quarts of

cherries.

8 . At 6 14per quart, find the cost of 1 peck of hazelnuts.

9 . A horse eats l2peck of oats 3 times a day. How

many bu shels does it eat in 6 days ?

1 0 . 2 1 pk . quarts ; 1 6 qt . pecks .

1 1 . James bought 1 4 bushels of tomatoes . Howmany pecks did he buy ?

1 2 . If I buy —12bushel of cherries

,how many quarts

should I get ?

82 THIRD YEAR [om

MEASURES OF WEIGHT

1 . Tell how the follow ing articles are sold

Butter, eggs, milk . cheese, coal, oil.

2 . Give the tables ofliquid measures and drymeasures .

The smallest w eightin the picture is calledan ounce w eight . Thelargest weight is a six

teen-ounce weight, and

is called a pound w eigh t.

Any article that the

pound weight balancesis said to weigh just one

pound .

A lady’s purchase at the store is balanced byweight . What is the w eight of her package

6 oz . + 4 oz . + 6 oz . lb.

’

1 0 oz . + l2 oz . + 1 0 oz .= lb .

i lb. oz . % lb .= oz . lb .

How many 2 oz. packages weigh 1 pound ?

Oral] MEASURES 83

MEASURES OF LENGTH OR DISTANCE

1 . Examine a foot rule .2 . Into how many parts do the long marks divide

the rule ?

3 . The distance between any two of these marks iscalled one inch .

4 . Count the inches in a foot.

5 . Place the rule on a paper or on the blackboardand mark off a line 1 2 inches long .

6 . A line 1 2 inches long is called one foot.

7 . Short distances are measured in inches orfeet.8 . 6 inches is what part of a foot ?

9 . Draw a line 4} ft . in length . How many inches

long is the line ?1 0 . Draw a line ft. in length . How many inches

long is this line ?1 1 . Without the aid of a r ule, draw a line 1 2 inches

in ' length ; 6 inches in length ; 2 feet in length .

1 2 . Place the rule on the lines in problem 1 1 and

observe how much too long or too short they w eredrawn .

Pupils should practice this kind of work until they can esti

mate length quite accurately.

length of a foot rule .

THIRD YEAR [Oral and W ritten

MEASURES OF LENGTH OR DISTANCE1 . Measure the top of your desk in feet and inches.2 . 1 ft. inches ; 2; ft . inches .

3 . Some articles are sold by a measure 3 times theName some of them.

4 . Draw a line on the blackboard 3 feet in length .

5 . The line you have drawn is one yard long.

6 . A piece of cloth is 6 yards long. How manyfeet is it in length ?

Copy and fill in the blanks7 . 3 6 in . ft.

8 . 3 ft . yd .

9 . 2 ft .— in .

1 o. 60 in .= ft .

1 1 . 1 8 ft . yd.

1 2 . 3 ft . in.

Change :

1 9 . 2 ft . and 3 in . to inches.

20 . 3 ft . and 4 in . to inches.

2 1 . 4 yd . and 1 ft . to feet.

2 2 . 6 yd . and 2 ft . to feet.

2 3 . 27 in . to feet and inches.

2 4 . 1 6 ft . to yards and feet.

m. to yards.

ft . to yards.

in . to feet.

in . to feet.

yd . to feet .

yd. to feet.

Oral] MEASURES 85

MEASURES OF SURFACE

One inch

1 . Measure this figure w ith your rule. How long isit ? how W ide ?

2 . What is a square inch ? How does the entire figure difier from one square inch ?A figure having square corners and longer than it is

w ide is called an oblong.

3 . Cut from paper an oblong 1 inch w ide and 4 incheslong

,and fold it to show the number of square inches in

it . Do the same w ith an oblong 2 inches w ide and 4

inches long.

4 . An oblong is 5 inches long and contains 1 5 squareinches. Draw the oblong to show the width and the

number of square inches.

5 . An oblong has 24 square inches . It is 6 incheslong . Draw the figure on paper. Fold it to show eachsquare inch.

6 . An oblong 6 inches long and 3 inches w ide w illmake an oblong inches long and 1 inch w ide .

7 . Show that a square containing 9 square inches is3 inches on each side.

86 THIRD YEAR [Oral and W ritten

REVIEW

1 . Count by 6’s from 1 to 97 from2 to 98.

2 . Count by 7’s from 1 to 99 ; from 2 to 1 00.

3 . Count by 8’

s from 1 to 97 ; from 2 to 98 .

4 . Count by 9’

s from 1 to 82 ; from 2 to 1 01 .

5 . Express in words : 41 1 2 ; 9487 ; 91 1 1 .

6 . How many pints are there in 4 gallons ?

7 . How many quarts are there in 5 bushels ?

8 . How many inches are there in 3 yards ?

9 . How much time is there between A.M . and

1 0 . A train leaves the station at A.M. and returnsin 4 hours and 25 minutes. Give the position of the

hands of the clock at the time of its return .

1 1 . A message is sent from the telegraph office whenthe clock shows A.M. The clock show s A .M.

when the answer is received. How much time haspassed ?

1 2 . The weight of four boys is as follow s : 6412lb.,

73 lh., 5912 lb.,and 78 lb. W hat is their total weight ?

1 3 . A man asked $ 1 75 for a horse, but sold it for1 5 less. How much did he receive for it ?

1 4 . A train leaves the station at o ’clock A.M . It

takes 45 minutes to reach Irw in. Give the position of

the hands of the clock at the time it reaches Irwin .

1 5 . How many pints are there in 48 gallons ?

Oral and Written] NUMBERS TO 99999 87

READING AND WRITING NUMBERSIn reading large numbers, separate them by commas

into groups of three figures each , beginning at the right .

Each group is called a period and has ones’ place

,

tens’ place , and hundreds

’ place . The last period to theleft may con tain only one or two figures ; as,

Beginning at the right,the places in are called

ones, tens, hundreds , thousands, tens of thousands. Thenumber is read ,

“ 24 thousand, 205.

Copy,point OE into periods

,and read

1 . 45268 65283 25834

2 . 39371 94736 93687

3 . 20905 1 81 1 0 60009

ROMAN NUMERALS

1 . W rite the Roman numerals from 1 1 to 1 9. Place

X before each . This gives the numerals from 2 1 to 29.

2 . XXX 30. L 50. XL 40.

Write the numerals from 3 1 to 40 from41 to 50.

3 . LX 60. LXX 70. LXXX 80.

Write the numerals from 50 to 70.

4 . C 1 00. CC 200. XC 90. XCIX 99.

Write the numerals from 70 to 1 00.

W rite 2 1 0, 290, 299, 300, 349, 235, 341 .

Read XCII, CIX,CCXL, CCXCIX .


ADDITION AND SUBTRACTION OF U. S. MONEY

Read and add

2 .

a b c d

1 .

.75 286 37 903 . 8692 1 93

4 . 630 1 8

5 . 84

Subtracta

6 . 3 1

b c d e

7 . 486 35

Find the difierence between

8 . and 1 1 . and

9 . and 1 2 . and

1 0 . and 1 3 . and


THIRDS

1 . How many thirds are there inthe oblong ? How many thirds are

there in one of anything ? in 1 yard ?How many feet are there in 1 yard ? What part of ayard is 1 foot ? What part of a yard is 1 2 inches ?How many thirds are there in 2 oranges ?

Add

2 . g, or 2

a b c d e

44 63 511: 84 9424 14 4 54 773

84 732

;94 7 1 2

1 04 64 5 84 841 24 84 84 64 91

Find the missing number

5 . 84 94 7 1 54 84

1 14 1 44 1 24 1 84 1 14

e. 74 84 94 1 84 1 7g3 54 — 4g 54 94

7 . I rubbed out 24 inches from a line 54 inches long.

How long was the part remaining ?

Oral and Written] FRACTIONS 91

FOURTHS

1 . Into how many parts has thesquare been divided ? Give the nameof. each part. What is the difierencebetween a quarter and a fourth of 8 1 ?

of 1 pie ? of 1 apple ? Into how manyfourths can any object be divided ?

4+4+4= how many fourths ? 4 gal . +4Find the sum

2 . 43

4 . 64 gal. + 4 gal . 6 . 84bu . + 4 bu.

3 . 64+ 4 5 . 34 pk . + 24 pk . 7 . 74 hr. + 14 hr.

Add

a d e f

8 . 24 34 1 04 1 2434 84 74 9

ii 99: 84 8%

9 . 1 1 g 534: 2051;1 44 4 64 8

274 i 1 7 3 14

Complete1 0 . 1 2 . 1 4 .

1 1 . 1 3 . 1 5 . 4: 64

Find the difference1 6 . 84 7 1 9 . 94 84 2 2 . 1 94 741 7 . 1 64— 54 20 . 1 64 74 2 3 . 1 64

— 8

1 8 . 234 74 2 1 . 1 24 1 1% 2 4 . 1 44“ 7

92 THIRD YEAR [W ritten

PRACTICAL PROBLEMS

1 . A dealer sold 24 tons of coal at one time and 34tons at another time . How many tons did he sell

2 . From a barrel containing 3 14 gallons, 25 gallonswere sold . How many gallons remained

3 . A dairyman sold in one month 1 8754gallons ofmilk . He sold 250 gallons less the next month . Howmuch did he sell the second month

4 . A farmer picked potatoes as follow s : 23 bu,

244bu ., and 1 14 bu. How many bushels did he pick ?

5 . After selling 564bu. of the potatoes, how manybushels remained

6 . 74 yards of silk w ere cut from a piece containing1 84yards . How many yards remained

7 . A dressmaker used 54yards of cloth for a skirtand 24yards for a waist . How many yards did she usefor both ?

8 . Mr. Miller owned 304acres of land . He kept 244acres and sold the remainder at $48 an acre . Howmuch did he receive for the part sold ?

9 . Find the weight of 4 baskets of butter containing 354 lh .

,1 8 lb .

,224 lb .

,and 1 6 lb .

, respectively .

1 0 . Harry made 84 gallons of lemonade and sold 7gallons . How much was unsold ?

1 1 . Find the distance around a room that is 1 84 ft.long and 1 6 ft . wide .

W ritten] FUNDAMENTAL PROCESSES 93

REVIEW

Add the products, and show how to test answers

1 . 5 x 201 2 . 5 x 25 3 . 4 x 65 4 . 3 x l26‘

4 x 201 3 x 25 2 x 65 4 x 1 26

Find the difference between the products

5 . 5 x 80 6 . 6 x 72 7 . 6 x 96

3 x 80 4 x 72 3 x 96

9 . Add the quotients

4 of 75 4 of 246

4 of 90 4 of 225

4 of 60 4of 1 64

Find the sum in the shortest way

1 0. 1 46 1 1 . 235 1 2 . 946 1 3 . 809

1 46 235 946 809

1 46 235 946 809

1 46 235 946 809

1 46 235 946 809

Find the sumof the quotients in the shortest way

1 4 . 1 5 . 1 6 . 484 -5 4 1 7 .

525 4- 5

525 4-5 484 4-4 396

484 -4 4

484 4 -4

THIRD YEAR [W ritten

REVIEWDivide and test

1 . 5 . 1 44 4-6 9 . 375 4-5

2 . 6 . 1 0 .

3 . 7 . 1 1 .

4 . a. 1 2 . 3 96

1 3 . 30 6 1 4 . 62420 1 2

Find the sum in the shortest way1 5 . 348 1 6 . 462 1 7. 564 1 8 . 879

348 462 564 879

348 462 564 879

348 462 564 879

348 462 564 879

Find the sumof the quotients in the shortest way1 9 . 20 . 2 1 .

936 4-6

936 4-6

2 2 . 25¢ times 5¢ of

Compare as in No. 22

2 3 . 35¢ and 2 7. 42 yards and 6 yards.

24 . 60¢ and 28 . 44 and $4.

2 5 . 54¢ and 2 9 . 72 pounds and 6 pounds

26 . 60 pints and 6 pints. so. 1 pound and 4 ounces .


PRACTICAL PROBLEMS

1 . At 28 miles per hour, how far can a train run in

6 hours ?

2 . When butter is worth 32 cents per pound, howmuch w ill 6 pounds cost ?

3 . At 80¢ each, how much w ill 2 doz . books cost ?

4 . A barrel of flour weighs 1 96 pounds . After selling of it, how much remains ?

5 . Find the cost of 5 pounds of steak at 1 8 cents

per pound .

6 . There are 1 6 ounces in a pound . How manyounces are there in 6 pounds ?

7 . A grocer bought 6 gallons of vinegar at 20 cents

per gallon, and sold it at 5 cents per pint. How muchdid he make ?

8 . Find the cost of 6 bn . of. nuts at 90¢ per bushel .

9 . How many inches equal 5 feet and 4 inches ?

1 0 . How many quarts equal 6 gallons and 2 quarts ?

1 1 . When 6 tons of coal cost 3 30, how much w ill1 ton cost ?

1 2 . John buys 5 baskets of grapes for 90 How

much is that a basket ? How much do 2 baskets cost ?

1 3 . If Frank prints 42 cards in 6 minutes on hisprinting press , how many cards does he print in 1

minute ? in 2 minutes ?

1 4 . Mary has 40 cents, and Jane has 6 times asmuch . How much more money has Jane than Mary


REVIEW

1 . Count by 5’s from0 to 1 00.

2 . Count by 6’s from0 to 1 20.

The Sign followed by a price means “at so much

a unit . Thus, 3 lb . steak 1 5 means 3 lb . steakat 1 5 ¢ a pound ;

“ 6 doz . buttons 20 means6 doz . buttons at 2015 a dozen .

”

Find the amount of each of the following3 . 3 lb . steak

4 . 6 bu. potatoes 48 f.

5 . 6 lb . sugar

6 . 5 cans tomatoes 1 2A

7 . 6 doz . eggs

Find the cost of8 . 5 sheep 3 1 3 . 6 hats

9 . 6 bureaus 1 4 . 5 books 3

1 0 . 6 cows 3 48 . 1 5 . 6 lamps 3

1 1 . 6 rugs 1 6 . 6 wagons 3 85.

1 2 . 5 vases 1 7 . 5 horses 3 1 75 .

1 8 . Add 45 and 56, thus : 45 and 50are 95 ; 95 and

6 are 1 01 .

Add in the same way :

1 9 . 35 and 48 2 3 . 78 and 64 2 7 . 1 9 and 96

20 . 1 8 and 25 24 . 84 and 76 28 . 78 and 97

2 1 . 20 and 46 25 . 93 and 42 29 . 87 and 46

2 2 . 81 and 72 2 6 . 48 and 75 so. 96 and 41

98 THIRD YEAR [Oral and W ritten

MULTIPLYING BY 8

Count by 8’

s to 24 ; to 64 ; to 96.

How many are 2 x 8 balls ? 3 x 8 books ? 4 x 8

boys ? 5 x 8 pens ? 6 x 8 apples ?

3 . Build the table of 8’s.

4 . Give quickly :6 x 8 8 x 6 7 x 8 5 x 8

8 x 4 8 x 1 0 8 x 2 8 x 1 1

8 x 1 2 4 x 8 6 x 8 8 x 5

Table of 3'

s5 . Memorize the table.6 . Give answers? x 8 = 32 7 x ?= 56

6 x ? = 48 ? x 5 = 40

? x 8 = 72 8 x

1 0 x ?= 80 ? x 3 = 27

1 2 x ?= 96 2 x ?= 1 8

Multiply by 8a c d

7 . 6230 51 78 8629 93 1 0

8 . 2937 8694 9083 8697

9 . 9048 6937 2865 4705


1 0 . 8 x 50 8 x 70

1 1 . 7 x 40 7 x 60

1 2 . 8 x 90 7 x 8l

Written] MULTIPLICATION 99

PRACTICAL PROBLEMS

1 . This schoolroom is 32feet long and 28 ‘ feet w ide .

W hat is the distance aroundit

2 . The glass in each w indow cost 3 How muchwas paid for all the glass ?

3 . Each desk costFind the cost of the desksin each long row .

4 . Find the value of the desks in the 6 rows .

5 . The attendance for the first 8 school days was as

follow s : 36, 43 , 42, 43 , 37, 41 , 43 , 43 , respectively .

What was the average attendance ?

N OTE . To find the average add the eight numbers and dividethe sumby 8.

6 . Eight tons of coal were used during the term.

How much was paid for the coal at 3 a ton

7 . What is the amount of the teacher’s salary for 8months, at 3 50 a month ?

8 . Find the entire cost of8 Advanced Geographies at 3 each .

8 Primary Geographies at 3 .45 each .

8 Grammars at 3 .50 each .

8 Language Lessons at each.

8 Readers at 3 .48 each .

THIRD YEAR [Oral and Written

1 . How many times is 7 contained in 1 4 ? m 2 1 ?

42 ? 63 ? 28 ? 35 ? 49 ? 70 ? 77 ? 56 ?

2 . Find -l, of 84 ; 63 ; 42 ; 35 ; 56 ; 70 ; 1 4 ; 2 1 .

Divide :

a b c d e f

3 . 7l42 7L49 7M

4 91 9 7199. 721 9

Divide by 75 . 84 56 68 45 36

6 . 2 1 7 364 637 273 696

Divide and testa b c d

7 .

e. 6 53079 722096

9 . 622867

1 0 . How many 7-pound boxes can be filled from259 pounds of barley ?

1 1 . How many w eeks are there in 49 days ?

1 2 . How many suits, each requiring 7 yards, can bemade from a piece of cloth containing 84 yards ?

1 3 . How many 7¢ packages of crackers can be boughtfor 3 1 , and how much money w ill be left ?

THIRD YEAR

MULTIPLICATION BY MIXED NUMBERS

A mixed number is composed of an integer and a.

fraction .

1 . Multiply 1 6 by1 6

21_ 2

12s of 1 6 = 8

2 x 1 6 = 32

SHORT Form

2% times 1 6means that

4 of 1 6 is to be added to2 times 1 6.

212~ x

Find products

d

a

m

-h

a

lo

oo

to

ll-4X 0

0at.

Find the cost of

20 . 87} gal . oil 1 2 51 .

2 1 . 6g; bu. potatoes 80

2 2 . 84yd . silk 3

2 3 . 7% gal . milk 1 6

24 . 6—41 doz . bananas 24

2 5 . 612doz. buttons 54

26 . 77} yd. ribbon

1 4 . 8} x 273

64x 258

1 6 . 84x 744

1 7 . 97} x 275

1 8 . 54x 392

1 9 . 92,x 41 3

1 5 .

2 7 . 73 doz. buttons 3 6 if.

2 8 . 93 hours’

work 1 8

2 9 . Si pounds butter 32 f.

30 . 6% pounds meat ! 1 6A

3 1 . 7} pk . peaches 40f.

3 2 . 34yd . muslin

3 3 . lb. candy 60f.

Oral and Written] MULTIPLICATION 1 03

MULTIPLYING BY 9

1 . Count by 9’s to 27 ; to 54 ; to 72 ; to 1 08.


s.

3 . Compare 6 x 9 and 9 x 6 ; 8 x 9 and 9 x 8 ; l0 x 9and 9 x 1 0.

4 . Multiply at sight by 940 60 80 20 50 1 0 30 70 90 3 1 51 71

Table of o'

s 5 . Memorize the table.

Give two numbers that formeach of these products

6 . 2 1, 36, 44, 48, 50, 40, 54, 45 , 33 , 1 8, 27, 99.

7 . 88,90

,60

, 77, 81 , 63 , 66, 72, 56, 1 08, 96, 80.

Multiply by 9a b d

8 . 4693 7286 8738

9 . 41 35 2874 1 869

1 0 . 8286 3697 2893

1 1 . 9387 2945 9387

1 2 . 6005 7894 6090

1 3 . 5020 4080 8005

1 04 THIRD YEAR Loral and Written

MULTIPLYING BY 9

Multiply by 9a b c d

1 . 4226 8393 3786 2468 8321

2 . 5483 6692 2294 8329 6245

3 . 6396 2594 4968 5692 9374

4 . 7278 7246 5328 7386 8928

Find the products5 . 9 x 38 gal . 9 x 24 da. 9 x 1 6min .

11 6 . 9 x 1 7 bu . 9 x 25 mo. 9 x 25 horses

7 . 9 x l2 ft . 9 x l8 ¢ 9 x 35 cows

8 . Find products by 7 by 8 ; by 6.

Table of Elementary Products

In multiplication, there are 45 different combinationsof figures taken two at a time

,and 36 difierent prod

nots. Use these combinations for drill frequently

1 06 THIRD YEAR [Written

DIVISION OF DOLLARS AND CENTS

Find the products test and read answersa b c

1 . 4 x 3 7 x 3 8 x 3

2 . 5 x 3 3 .86 8 x 3 46 .25 9 x 3 73 .86

3 . 6 x 3 9 x 3 7 x

4 . Divide 3 by 3 .

Divide by 3 , placing a decimal3 [3 point under the decimal point in the divi

dend . Write the dollar Sign before the

number of dollars in the quotient .

Find the quotients ; read and test answersa b c

5 . -z-2 -z-9

6 .

7 .

Find

8 . 13. of 3 1» of 3 11, of

9 .

12of 3 3 of 1 of 3

1 0 . 71 of of 5 of

Perform the operation indicated

1 1 .—z 6 -z—8 -z-6

1 2 . 3 x 5 3 x 9 3 7

1 3 . x 6 9

1 4 . 3 9 3 7 3 x 8

1 5 . 3 8 3 9 3 x 6

Written] MULTIPLICATION AND DIVISION 1 07

PRACTICAL PROBLEMS

1 . It requires 4 yd . ofmaterial to make eachof these girls an apron .

How much w ill be re

quired for the class of 7

girls

2 . At 8¢ a yd .

,how

much w ill 7 aprons cost ?

3 . Out of 94; yd . ofcambric, how many caps,requiring 4yd . each

, can

be made ?

4 . How many pupilscan be supplied w ithrolling pins and pie pansout of 3 9, if each pin costs 20 and each pan

5 . At 1 8¢ a yard, find the cost of lawn for sleeve

protectors for 7 girls, each sleeve requiring yd .

6 . Miss Blew,the teacher, purchases the following

7 flour cans 40 7 cake pans 25 7 sugar shakersFind the amount of her purchases .

7 . Entertaining the directors, this class uses 7 springchickens 2 pecks of potatoes 1 headcabbage 2 boxes tomatoes 1 0 3 lb . butter3 2 2 pt . cream and 4gallon ice cream 3

per gallon . How much does the dinner cost them?

THIRD YEAR [Written

MULTIPLICATION AND DIVISION

Multiply and divide by 8 ; b 9

a b c d e

1 . 2465 2469 281 6 6824 61 78

2 . 7381 8397 9375 4836 8293

Find3 . 3 of 4687 sheep 5 .

_15of 7353 bu. 7 .

«kof 3600

4 . 313of 9376 horses 6 . of 4347 gal . 8 . of 7479

How much change shall I receive from 3 1 0 for

the follow ing ? Name the coins in each purchase .

9 . 212. yd . Silk 60 1 1 . 24 lb . butter 3 3

Io. 73 doz . eggs 30¢ 1 2 . 33 bu . plums 3

MAR! E T REPORT

Grapes, per crate, 5 Peaches, per basket,Blackberries, per crate, Pears, per bbl. ,Raspberries, per crate, Apples, per bbl. ,

Elderberries, per crate, 3 5 Cantaloupes, per box,

Fromthe above report find the cost of :1 3 . 4 crates of blackberries . 20 . 9 baskets of peaches.

1 4 . 5 baskets of peaches . 2 1 . 6 crates of blackberries.

1 5 . 3 crates of grapes . 2 2 . 5 crates of elderberries.I6 . 3 crates of elderberries . 2 3 . 7 crates of raspberries .

1 7 . 4 bbl . of pears . 2 4 . 6 bbl . of pears .

1 8 . 2 boxes of cantaloupes . 2 5 . 8 boxes of cantaloupes.

1 9 . 6 bbl. of apples . 2 6 . 8 baskets of peaches .

Make other problems from this or another MarketReport .

1 .

THIRD YEAR

SUBTRACTION

From5000 take 3456 .

4 9 9 10

5 000

3 4 5 6

1 5 4 4

a

6734

4578

21 56

Subtract

4 .

a

9084

6097

9600

3097

5004

3904

8703

5008

7003

4906

6 from 1 0 leaves 45 from 9 leaves 44 from 9 leaves 53 from 4 leaves 1

d

6000

41 87

1 91 3

[W ritten

W ritten] REVIEW

TEST EXERCISES

1 1 1

Multiply,practicing until n ine products can be found

in 2 minutes.

1 . 4987 by 7

z . 6879 by 8

3 . 9836 by 9

1 0 . 8564 by 7

1 1 . 9873 by 9

1 2 . 8293 by 8

1 9 . 9365 by 8

20 . 8796 by 9

2 1 . 2493 by 7

Add rapidlya

as . 2401

6375

581 6

2487

1 789

29 . 7895

2398

201 5

1 920

6099

4 . 2475 by 8

5 . 8689 by 9

6 . 3978 by 7

1 3 .

1 4 .

1 5 .

2 2 .

2 3 .

8739 by 9

6927 by 8

8738 by 9

7693 by 78795 by 8

2 4 . 9283 by 9

c

81 45

2693

7856

9037

5009

7743

3838

9723

4587

8243

7 . 6894 by 98 . 9829 by 7

9 .

1 6 .

1 7 .

1 8 .

2 5 .

2 6 .

2 7 .

6375 by 8

8795 by 9

6938 by 7

9375 by 8

8756 by 9

7938 by 9

4695 by 7

e

8873

2345

5690

2295

7986

4498

7659

3376

5072

3490

1 1 2 THIRD YEAR [Written

PRACTICAL PROBLEMS

1 . The drafting room is 24 feet w ide and 28 feetlong. What is the distance around the room?

2 . There are 7 stands in the room. Each one cost

3 What was the cost of all

3 . Each stand requires a T square,angles

,scale,

erasers, thumb-tacks, etc . The instruments cost 3What was the average cost of each stand ?

4 . The first class worked 40 minutes on Mondayand Friday of each school week . How many minutes were spent by the class during 4 school w eeks ?

5 . Each of 7 boys required a drafting board costmgink

,paper

,pencils

,etc .

,costing 25 What was

the cost of these materials for the class ?

6 . The boys made two chairs valued at 3 each,

3 tabourettes at each,and 4 book racks at

3 each . What was the value of all the articles ?

THIRD Y EAR [W ritten

PRACTICAL PROBLEMS

1 . A huckster’s sales for the week w ere as follow s3 3 3 and 3 What was theamount of his sales ?

2 . A boy’s suit that was marked 3 was sold for3 less. What was the selling price of the su it ?

3 . James had he spent How muchhad he left ?

4 . What is the difference in the price of two hatsmarked 3 and 3

5 . The follow ing amounts w ere deposited in the

school savings bank : and

3 What was the total of these deposits ?

6 . Mrs. Jones paid 3 for a turkey, for

cranberries, for butter, and 3 .48 for cofiee. Whatwas the whole cost ?

7 . How many school badges 4 in. long can be madefrom2 yd. of ribbon ?

s. A clock that strikes the half hours strikes howmany times in a day ?

9 . How many square inches are there in an 8-inchsquare

1 0. There are 639 oranges in 9 baskets, w ith the samenumber in each. How many are there in each basket ?

1 1 . If you receive 3 and 3 and wantto change it into fiv e-dollar bills, how many should youget and how much money offer ?

W ritten] REVIEW 1 1 5

TEST EXERCISES

Multiply 6 examples in one minute

By 9 By 8 By 61 . 2467 6 . 6935 1 1 . 6238 1 6 . 6294

2 . 3258 7 . 91 86 1 2 . 1 459 1 7 . 7386

3 . 961 4 s . 2734 1 3 . 9345 1 8 . 9281

4 . 2836 9 . 8567 1 4 . 2764'

1 9 . 4936

5 . 92 1 4 1 0 . 2 1 37 1 5 . 3285 2 0 . 9275

Divide 8 examples in oneminute :

By 8 By 9 By 7 By 62 1 . 81 43 2 6 . 8769 3 1 . 8637 3 6 . 8425

2 2 . 2695 2 7 . 2893 3 2 . 2049 3 7 . 6439

2 3 . 7378 2 8 . 6241 3 3 . 9267 38 . 9375

2 4. 6291 2 9 . 7083 3 4 . 7328 3 9 . 81 62

2 5 . 9475 30 . 1 404 3 5 . 8264 40 . 3245

4 1 . A farmer’s w ife sold 72 eggs. How much did she

receive for themat 1 6 cents a dozen ?

42 . A girl went to the store w ith 96 cents. Shespent 24 cents for butter, and the remainder for sugarat 6 cents a pound. How much sugar did she buy ?

43 . Mr. Smith had 76 sheep . He kept 60 and soldthe remainder at 3 6 a head . How much did he receivefor them?

44 . There are 1 44 ounces in 9 pounds. How manyounces are there in 1 pound ?

45 . A man earned 3 1 00 a month, and spent $75 per

month . How much did he save in 6 mon ths ?


PRACTICAL PROBLEMS

1 , How many pints are there in 2679 gallons ?2 . Find the number of peeks in 7320 qt.3 . At 8 ¢ per quart, for how much does a milkman

retail 32 gallons ?

4 . Mr. Watson sold a wagon for 3 75. This was

3 more than it cost. Find the cost.

5 . A merchant paid 3 24 for dozen hats . At the

same rate, how much should he pay for 9 hats ?

6 . I sold a house for 3 7325, which was at a loss of3 890. How much did the house cost me ?

7 . If I pay 3 320 for 4 acres of land, how muchshould I pay for 8 acres of the same kind ?

8 . How many gallon cans can be filled from 2288

pints of cream?

9 . How much w ill 1 27 boxes of oranges cost at 3 6a box ?

1 0 . A man paid 3 for a hat, and 8 times as muchfor a suit. How much money did he spend ?

1 1 . At 8¢ a quarter-peck, for how much will a bushelof sweet potatoes retail ?

1 2 . I have 3 54, and pay out of it for fuel . Howmuch does the fuel cost ?

1 3 . If each of the followmg numbers is 2; of anothernumber, what is the number 111 each case ?

7 1 2 1 3 8 1 1 9 14 5


PRACTICAL PROBLEMS

1 . When going to the school picnic, the ch ildren

marched 4 abreast . How many row s were there if 81 6children attended the picnic ?

2 . At 3 pencils for 5 cents, how many pencils shouldbe received for 20 cents ?

3 . Ruth pays 82 if for butter and eggs . She pays32 for butter. How much does she pay for eggs ?

4 . Find the cost of 812bu . oats at 50 If a bushel .

5 . When peaches are selling at the rate of 3 for 5cents, how many peaches w ill 40 cents buy ?

6 . How much money would a lady have left froma

3 2 bill after buying some muslin for 24 lace forand ribbon for 27¢ 9

7 . There are 1 2 months in one year. How manymonths are there in 7% years ?

8 . A merchant has 6 clerks on his payroll, averaging per month . What is the amount of hispayroll for 2 months ?

9 . A train of cars runs 36 miles an hour . How farw ill it run from 1 1 A .M . to P .M . ?

1 0 . A trolley car moves at the rate of 352 ft. in a

minute . How far w ill it move in 7minutes ?

1 1 . At 3 240 a year, how much rent would a man

pay fromApril 1 , 1 907 to September of the same year ?1 2 . A dealer bought 8 gal . of ice cream at a

gallon and sold it at 20¢ a pint . What was his gain ?

W ritten] FUNDAMENTAL OPERATIONS 1 1 9

REVIEW OF ADDITION AND SUBTRACTION

In review drills like the following the teacher shouldset a time limit

, and make tests of accuracy .

IAdd

a b1 . 2404 429

6020 8500

798 639

3787 1 0851

6252 3487

2 . 6028 3875

1 6090 40290

39099 53961

1 0906 8756

49067 6207

Subtract3 . 893 26

4967

4 . 1 0050

6765

5 . 87441

29902

Mul tiply6 . 6 x 735 s . 6 x 54307 1 0 . 7 x 1 5064

7 . 9 x 1 97205 9 . 5 x 49306 1 1 . 8 x 55034

1 20 THIRD YEAR

REVIEW OF

Divide and test :a b

1 22 4

2 .

3 . 4296

4 . 5 385 521 25

5 . 63 84

6 .

7 .

Give quotients at sight

8 . 1 52 8 1 77 3

9 . 264 6 1 32 2

1 0 . 371 7 78 2

1 1 . 468 9 96 4

1 2 . 1 56 6 1 02 3

1 3 . 1 25 5 1 1 6 4

Divide and te st :

1 4 . 1 3935 5

1 5 . 1 6092 2

1 6 . 1 7841 3

1 7 . 20404 4

[Oral

c d

211 8 21 1 6

3 1193.

4m 421 24

52970

61564

T 6963

821 9656 8 242408

1 72 4 1 84 8

1 96 6 1 92 6

1 72 4 1 48 4

235 5 273 -i 3

324 6 256 4

1 61 7 1 75 7

1 8 . 25676 6

1 9 . 307027 7

20 . 729074 8

2 1 . 630072 9

1 22 THIRD YEAR [Oral

REVIEW OF FUNDAMENTAL OPERATIONS

Answer quickly :a b c d e

1 . 6 x 3 5 x 4 1 0 — 2 4 x 5 § of 24

2 . 7 x 1 0'

6 x 6 1 8 — 6 4 x 3 64 4 8

3 . 9 x 2 8 x 1 0 40 — 1 0 7 x 6 % of 48

4 . 7 x 3 6 x 5 é} of 42 9 x 2 7 x 8

5 . 4 x 7 l0 x 9 5 x 5 7 x 4

6 . 20— 4 i x 28 8 x 3 1 6 — 1 0

7 . 22 — 7 -0f 20 7 x 6 é- of 24 333-of 36

8 . 6 x 4 3 1 — 6 % 0f 27 8 x 7 5 x 5

9 . 4 x 9 3 x 1 0 54 — 6 9 x 6

1 0 . 5 x 2 % Of 25 8 x 3 % of 30

1 1 . 8 x 6 7 x 9 é of 35 6 x 1 0

1 2 . 8 x 5 4 x 7 4x 1 8 3 x 3

1 3 . 3 x 6 % x 72 8 x 8 9 x 7

1 4 . 54 — 6 i of 48 5 x 9 8 x 3

1 5 . 39 — 7 9 x 8 47— 8 i of 44 g~ of 66

1 6 . % of 63 72 — 9 % Of 40 gof 421 7 . 35 x 36 1 0— 2 7 x 7 4x 1 8 i of 36

1 8 . 7 x 8 9 x 9 8 x 7

1 9 . 6 x 7 9 x 9 % of 30 6 x 1 1 8 x 1 2

20 . 9 x l2 7 x l2 3 x 6 44 4-1 1


COMPARISON

1 . Compare 1 0 with 5 ; thus, 1 0 is two times 5.

2 . Compare 5 w ith 1 0; thus, 5 is 35 of 1 0.

N OTE — W e might also compare 5 with 1 0 by saying 1 0 is 5more than 5 ; but, unless otherwise stated, compare

” in this

book means “ find the quotient of the first number div ided by thesecond .

”

3 . Compare 30 w ith 1 0; 20 w ith 5 ; 24 w ith 6 .

4 . Compare 5 w ith 1 5 ; 8 w ith 24 ; 1 2 with 48.

5 . Compare 40 w ith 1 0; w ith 8 ; w ith 5 ; w ith 4.

6 . Compare 25 w ith 5 ; 5 w ith 25 .

7 . When 2 pencils cost 1 0 how much w ill 8 cost ?

8 . When 6 hats cost 3 1 2, how much w ill 1 2 cost ?

9 . When 4 kn ives cost 3 6, how much w ill 8 cost ?

1 0 . At 6 pens for 1 0 how much w ill 1 8 cost ?

1 1 . When 6 horses cost 3 900, how much w ill 24 cost ?24 horses are 4 times 6 horses. Hence, they will cost 4 x 3 900,

or 3 3600.

1 2 . When 5 cows cost 3 1 60, how much w ill 30 cost?

1 3 . When 3 barrels of apples cost how muchw ill 1 2 cost ?

1 4 . If 5 tons of hard coal cost how much w ill30 tons cost ?

1 5 . At 3 45 for 60 bu . Of wheat,how much w ill 1 2

bu . cost ?

1 6 . If 1 2 men earn 3 51 in one day, how much w ill60 men earn in one day at the same rate ?

1 24 THIRD YEAR [Oral

MEASURES OF TIME

1 . Name the letters on the faceof the clock . Tell the time .

2 . Observe the small spaces on

the outer edge of the face . Theseare called minute spaces .

3 . Over how many of these spacesdoes the minute hand move in pass

ing around the face fromXII to XII again ?

4 . How long is the minute hand in passing fromXII to I ? fromV to VI ? fromX to XI ?

5 . There are the same number of minute spaces between any two hours .

6 . While the minute hand passes fromXII to XIIagain, how far does the hour hand move ?

7 . How many minutes are there in an hour ? (seep . 44) in 2 hr. ? in 4 hr. ? in 4 1m?

8 . When the hour hand is at XII, what is the timeif the minute hand points to V ? to III? to I ?

9 . Count the hours on the clock face from 9 O’clock ,

the Opening of school,until 9 O’clock, the next morn

ing. How many are there ? These 24 hours includeboth day time and night time .

1 26 THIRD YEAR [Oral and W ritten

MEASURES OF SURFACE

1 . Draw a square 1 inch long and 1 inch W ide.

What shall we call it ?

2 . Draw on the blackboard a square 1 foot long and1 foot w ide . Call it a square foot .

3 . Draw On the blackboard a square 1 yard longand 1 yard wide . Call it a square yard .

4 . Separate by points , eachside of the square yard into 3equal parts. Connect thesepoints by straight lines . Whatis the size of each square ? Howmany square feet are there ina square yard ?

5 . This picture shows a

square yard,smaller than it really is . How many

square feet does it Show ?

rows there

6 . This picture Show s an

Oblong 6 inches by 4 inches.Divide it into square inches.

How many square inches arethere in one row ? in 2 rows ?in 3 row s ? in 4 rows ?

In 1 now there are 6 sq . in.

4 x 6 sq . in . 24 sq . in.

W ritten] SURFACES 1 27

SURFACES

Draw figures and find the number Of square inches in1 . An oblong 1 in . w ide and 4 in . long.

2 . An Oblong 2 in . w ide and 6 in . long .

3 . An envelope 2 in . w ide and 6 in . long.

4 . A blotter 3 in . w ide and 6 in . long .

5 . A page 4 in . wide and 6 in . long .

6 . A square 3 in . on a side .

7 . A square 4 in . on a Side .

8 . The top Of a box 5 in . on a side.

9 . A picture 4 in . by 6 in .

With one inch representing a foot, draw figures andfind the number of square feet in :

1 0 . A rug 3 ft . w ide and 8 ft . long .

1 1 . A hallway 4 ft . w ide and 1 0 ft . long.

1 2 . A table cover 7 ft. by 4 ft.

1 3 . A w indow glass 4 ft. by 9 ft .

1 4 . The glass for a picture 2 ft . by 3 ft .

W ith one inch representing a yard, draw figures and

find the number Of square yards in :

1 5 . A room 4 yards by 6 yards.

1 6 . A porch floor 2 yards w ide and 8 yards long.

1 7 . A hallway 3 yards w ide and 1 2 yards long.

1 8 . A rug 3 yards w ide and 5 yards long.

1 9 . A porch rug 2 yards w ide and 4 yards long.

20 . A wall 3 yards in height and 6 yards long.

2 1 . A blackboard 1 yard in height and 8 yards long.


PRACTICAL PROBLEMSMAR! ET REPORT

Apples. Best,

Fair grades, 8 per bbl.

Peaches. Good ,

Fancy, per bu.

Pears. Best, 8 per bu.

Grapes.

basket .

Concords, 28 it per 10-lb . basket.

Niagara, 25 7 per 1 0-lb.

Eggs. 1 8 f per doz.

Butter. Creamery, 28 f per 1h.

Dairy, 25 is per lb.

Cheese . Full cream, 1 2 } per lb.

American, 1 5 f per lb .

Potatoes. 50 per bu.

Sweet potatoes. V irginia, 80}Jersey, 3 per bu.

From this market report find the cost Of the following

5& bu. of potatoes.

a

s

se

r

t: 8 bu . of fancy peaches .

442lb . Of butter, creamery.

8 1 0-1b. baskets of Concord grapes.

7 bbl . of apples, best quality.

6 . 9 cases Of eggs, 30 dozen each .

7 . 8 1 0-lb . baskets of Niagara grapes.8 . 8% bu . of sweet potatoes

,Virginia.

9 . 7 bu. Of peaches, good.

1 0 . 9 full cream cheese , 1 5 lb . each .

1 1 . 7 1 0-lb. baskets of Concord grapes.

1 2 . 94 bu. of pears, best quality .

1 3 . 8 bbl . of apples, fair grades .

1 4 . 7 lb . of creamery butter and 32 lb . of dairy butter1 5 . 8 bu. Of fancy peaches, and 42 bu .

,good quality.

1 6 . 8 1 0-lb. baskets of Concord grapes, and 6

IO-lb. baskets Of Niagara grapes .

THIRD YEAR [Written

PRACTICAL PROBLEMS

1 . How many pounds of sugar are there in 7 packages Of 25 lb . each ?

2 . There are 248 pages in a book . When 89 pagesare read

,how many pages remain unread ?

3 . A barrel of flour weighs 1 96 pounds. HOW muchis left after 68 pounds have been sold ?

4 . There are 32 quarts in a bushel. How manyquarts equal 7 bushels ?

5 . If there are 9 school months in a year, how manyschool months are there in 1 2 years ?

6 . In a purse there are 3 3 , 3 quarters, 6 dimes, 4nickels, and 4 cents. HOW muchmoney is in the purse ?

7 . A horse traveled 36 miles in 6 hours ; a bicyclethe same distance in 4 hours. Find the speed of each .

8 . There are 1 81 pupils on the second floor of a

school building and 1 57 on the third floor. How manyare there on both floors ? How many more are on the

second floor than on the third ?

9 . A bushel of shelled corn weighs 56 pounds. Howmany pounds are there in a box holding 8 bushels ?

1 0 . There are 1 44 pens in a gross. How many are

there in 9 gross ?

1 1 . There are 24 sheets of paper in a quire. Howmany are there in 8 quires ?

1 2 . How much w ill 1 8 pounds of figs cost at 95 cents

per pound ?

Oral and Written]

Subtract1 . 989 2 . 686 3 . 9988 4 . 9659

877 540 8965 6806

5 . Add the remainders in examples 1 , 2 , 3, and 4 .

Add the products ; show a short way of testing each

problem:

6 . 4 x 40 7 . 7 x 36 8 . 6 x 65 9 . 3 x 78

+ 5 x 40 + 2 x 36 + 2 x 65 + 6 x 78

Div ide and test

1 0 . 342 by 3 1 4 . 868 by 8

1 1 . 964 by 8 1 5 . 594 by 6

1 2 . 982 by 7 1 6 . 805 by 8

1 3 . 878 by 8 1 7 . 959 by 7


22 . 220 2 2 6 . 330 3

2 3 . 840 4 2 7 . 960 9

24 . 720+ 9 28 .

25 . 860 4-4 2 9 . 980 4— 4


3 4 . 4 x 40 3 8 . 6 x 1 1 0

3 5 . 6 x 50 3 9 . 3 x 202

3 6 . 8 x 20 40 . 5 x 1 05

3 7 . 9 x 50 41 . 4 x 222


REVIEW OF THIRD YEAR

1 . There are 8 pints in one gallon . HOW manypints are there in 36 gallons ?

2 . A train runs 26 miles in 1 hour. HOW far can

it run in 9 hours ?

3 . How much W ill 81 yards Of cloth cost at 32 cents

per yard ?

4 . At the rate Of 9 pages an hour, how long w illit take to finish a story of 27 pages ?

5 . Nine girls spent at a picnic. What wasthe average amount spent by ea ch ?

6 . At 6 cents a pound, how many pounds of sugarcan be bought for 1 38 cents ?

7 . There are 1 68 cabbage plants in 8 rows. Howmany are there in each row ?

8 . James saves 3 7 a week from his wages. Howlong w ill it take him to pay for a lot valued at

3 238 ?

9 . A drover paid 3 2040 for sheep at 3 6 a head.

How many did he buy ?

1 0 . Eight lamps cost Find the cost of one .

1 1 . How many bushels equal 396 peeks ?

1 2 . How many gallons equal 792 pints ?

1 3 . How many tons of coal,at 3 6 a ton, can be

bought for 3 786 ?

1 4 . How much milk at 8 cents a quart can be boughtfor

1 34 THIRD YEAR [W ritten

3 7. Seven O’clock AM . is how many hours after midn ight

3 8 . 1 44 square inches make one square foot. Howmany square inches equal 8 square feet ?

3 9 . At 3 each, how much w ill 7 suits of clothingcost

40 . How much w ill 84 pounds of pork cost at 1 2 ¢ apound ?

4 1 . At 3 each, how much w ill 8 hats cost ?

42 . Mrs. White paid a yard for v elvet . Howmuch would she pay for 7 yards at the same rate ?

43 . Joseph Black employs 8 clerks at a salary ofa week each. How much must he pay his

c lerks at the end Of the week ?

44 . At 3 palings to the foot,how many palings are

required for a fence 1 2 yards and 2 feet in length ?

45 . How much w ill an 84 pound roast of v eal cost at1 6 15 a pound ?

46 . 8 gallons of ice cream were sold at 1 53 a pint.How much was received for it ?

47 . At 25¢ a peek, for how much w ill 2 bu. of tomatoes retail ?

48 . A man sold a horse for 3 230 and lost 3 56.

How much did the horse cost him?

49 . Mr. Frank rented a house at 3 360 a year. Howmuch rent will he pay in 74years ?

Written] REVIEW OF THIRD YEAR 1 35

50 . Aman hires a horse for 3545an hour. How muchmust he pay if he uses the horse from 1 0 A.H. until5 P.M . ?

-5 1 . A man bought a lot for 3 1 275 . He built a storeroomon it for 3 2450. He sold the property for 3 5000.

F ind his gain .

5 2 . What is the weight of 6 sacks Of wheat,each

w eighing 1 68 pounds ?

5 3 . HOW much w ill 84 tons of coal cost at 3 aton

54 . 9 tons Of coal for a school cost 3 HOWmuch was that a ton‘ ?

5 5 . A school has 2 floors,w ith 4 rooms on each floor.

HOW many pupils are there in the school,if there are

3 6 pupils in each room?

56 . A teacher in this school earns 3 65 per month,and spends 3 35. How much does he save in 9

months ?

5 7 . Find the cost of 84 yards Of dress goods at 48cents per yard .

58 . A pair of shoes costs 3 24. How much w ill 7

pairs cost ?

5 9 . If I pay 96 cents for 3 yards of ribbon, how muchshould I pay for 1 yard ? for 14yards .

9

60 . The distance fromNew York to Pittsburg is 444

miles . What is the fare for a round trip,at 2 ¢ per

mile ?

1 36 THIRD YEAR [W ritten

61 . The fare at 2 f per mile, from Pittsburg to

Harrisburg is 3 Find the distance.

62 . Trains leave Pittsburg for Wheeling, 7 A .M.

and A.M .

,returning RM . and P.M.

Find the difference in time Of leaving ; in time Ofreturning .

63 . HOW much w ill 74 yd . of cloth cost at 3 a

yard ?64 . A spool Of thread contains 200 yards . Howmany feet of thread are there on 4 dozen spools ?

65 . Tell the meaning of each figure in these numbers4069 ; 27304 ; 501 00 ; 7361 4 ; 80001 .

66 . Express in words : 84244 ; 9371 2 ; 651 1 1 ; 523 1 6 ;CCXV ; CCCXL ; LXXXIX.

6 7 . If you sold a person goods to the amount Of 94

cents, and received 3 2 in payment, what coins might

you give in change

es . Nine persons were served w ith meals ateach , 5 persons were served at 3 each , and 3 persons at 90 If each. Find the total amount Of moneyreceived .

69 . A train reached the city at A .M . and leftat P.M . How long did it remain in the city ?

70 . A man earns 3 1 25 a month and spends 3 96 a

month . How much can he save in 4 a year ?

71 . By selling a house for 3 4785,Mr. Thompson lost3 895 . How much did the house cost him?

1 38 FOURTH YEAR [Oral and Written

READING AND WRITING NUMBERS

Express in figures

I . Forty-two thousand .

2 . Sixty-six thousand four.

Seventy-five thousand fifty.

Thirty-n ine thousand one hundred twenty-two.

Two hundred ten thousand three hundred fifty .

One million one hundred twenty-five thousand .

3

4

5

6 . Five hundred sixty-fi ve thousand one hundred .

7

8 . Three million six hundred thousand thirty-five .

9 Twenty-five million nine thousand twenty-six.

1 0 . Eighty million twenty-Six thousand Sixty-four.

1 1 . Nine hundred thousand nine .

1 2 . Forty-six million four thousand Sixteen .

1 3 . One hundred ten million five hundred .

1 4 . Three hundred thirty-sixmillion one hundred four.

1 5 . Five hundred seven million five thousand six.

1 6 . Seventeen million three thousand seventy-fiv e .

1 7 . One million two thousand seven hundred four.

1 8 . 1 million, 1 04 thousand, 1 85.

1 9 . 2 1 million, 1 1 0 thousand , 1 09.

20. 604 million ,622 thousand

,468.

2 1 . 1 01 million, 1 0 thousand, 1 0.

Oral and Written] ADDITION AND SUBTRACTION 1 39

ADDITION AND SUBTRACTION

1 . Count by 4’s from 2 to 1 00 ; from 3 to 99.

2 . Count by 6’

s from 3 to 99 ; from 5 to 1 01 .

3 . Count by 8’s from 3 to 99 ; from 4 to 1 00.

Add the follow ing by columns and in lines, allowingfive minutes for each

a b c d

4 . 3 32 1 65

3

s.

3

Subtract,allow ing one half minute for each

ba C

6 .

7 .

1 40 FOURTH YEAR [Written

PRACTICAL PROBLEMS

1 . A man paid for a hat and for asuit . How much did he pay for both ?

3 cost of hat .

cost of suit.

3 cost of both .

2 . A merchant sold 425 bu . of potatoes, 232 bu . of

apples, and 1 89 bu . of onions . Find the total number

of bushels sold .

3 . A lady paid 3 25 for a carpet, 3 71 for a rug, and

3 7 for curtains. What was the amount of her bill ?

4 . How many days are there in the last six monthsof the year ?

5 . Aman left his estate to his w ife, son, and daughter.

His w ife received 39845, his son and his daughter 3 3500. What was the value of the whole estate ?

6 . I sold my house for 3 5675, thereby losing 3 897.

How much did the house cost

7 . A lawn is 30 ft . long and 24 ft . w ide . How manyfeet is it around the lawn ?

8 . New York is 327 miles east of Altoona by railroad and Pittsburg is 1 1 7 miles west. How far is itfromNew York to Pittsburg ?

9 . The pupils of a school deposited money in a savings bank as follow s : January, 3 February,3 March, 3 and April, 3 Find thetotal deposits .

1 42 FOURTH YEAR [om

MULTIPLYING BY 1 0

1 . Count by l0’s to 1 00. Build the table of 1 0’s .

2 . How many are 9 x 1 0 ? 90+ How

many 1 0’

s are there in 1 00 ?

3 . Place a naught to the right of 4. What numberhave you 40 is how many times four ? Place a naughtto the right of 6 ; 3 ; 7 ; 9 ; 1 1 ; 1 2 . See whe thereach product has become ten times the minuend .

Annexing a naught to the right of a number multip liesit by 1 0.

4 . Annex 0 to each number. Notice the efi ect4 20 36 75 42 87 275

93 87 692 387 509 938 765

Table of 1 0’s 5 . Memorize the table .

6 . Compare1 0 x 5 w ith 5 x 1 0

8 x 1 0 w ith l0 x 8

1 1 x 1 0 w ith 1 0 x 1 140 and 80 1 00 and 1 0

1 20 and 1 2 1 1 0 and 1 1

Find the cost of

7 . 1 0 newspapers 9% lb . lard8 . 8 ladies’ hats 3 5 . 1 2 doz . buttons 1 0p.

9 . 1 0 oranges 2 for 1 0 qt . milk

1 0 . 1 05 yd . muslin 1 2 bu . tomatoes

Oral] MULTIPLICATION 1 43

MULTIPLYING BY 1 1

1 . Count by 1 l ’s to 33 ; to 66 ; to 99. Build thetable of 1 1 ’s.

2 . 9 x 1 1 = ? How many 1 1 ’s= 1 1 0 ?

3 . 1 0 x 1 1 : 1 0 times 1 1 , plus 1 1 = How manyare 1 1 x 1 1 ?

4 . To find 1 2 x 1 1 how many mustbe added to l 1 x 1 1 ? 1 2 x 1 1 = ?

5 . Give at sight1 0 x 1 1 1 2 x 1 1 5 x 1 1

3 x 1 1 4 x l 1 8 x 1 1

6 x 1 1 l 1 x 9 l 1 x 7

Table of 1 1’s 6 . Memorize the table .

1 x 1 1 = 1 1 7 x 1 1 7 . Compare :

2 x 1 1 = 22 8 x 1 1 1 1 x 7 w ith 7 x 1 1

3 x 1 1 = 33 9 x 1 1 9 x 1 1 w ith l 1 x 9

4 x 1 1 = 44 1 0 x 1 1 = 1 1 0 4 W ith 4 x 1 1

5 x 1 1 = 55 1 1 x 1 1 = 1 2 1 w ith 1 1 x 1 2

6 x 1 1 = 66 1 2 x 1 1 = 1 32 6 X 1 1 with l 1 x 6

8 . Find the products

1 1 x 60 1 1 x 80 1 1 x 40 1 1 x 1 00 1 1 x 30

1 1 x 90 1 1 x 50 l1 x 20 1 1 x 80 1 1 x 25

1 1 x1 3 1 1 x 30 l 1 x 70 l 1 x 1 5 1 1 x 1 8

Find9 . ft of 1 32 ; of 88 ; of 1 2 1 ; of 1 1 0.


MULTIPLYING BY 1 2

1 . Count by 1 2 ’

s to 36 ; to 72 to 1 44. How manyare 1 2 times 1 2 ? Build the table of 1 2 ’s.

Table of 1 z ’

s 2 . Memorize the table .

3 . Multiply by 1 2 ; by 1 1465 236 789

546 783 928

784 937 693

785 51 4 938

978 694 296

4 . What two numbers make the following products ?

25 27 28 30 32 35 36 40 42 45 48

49 56 60 63 64 66 72 80 84 88 96

MULTIPLICATION BY A MIXED NUMBER

1 . Multiply 34 by 45» 4135 times 34 means that 3 of34 34 is to be added to 4 x 34.

1 7 of 34 Find the products

1 36 4 times 34 2 . 835x 48 4 . 83 x 1 20

1 53 422L times 34 3 . 9% x 72 5 . x 1 80

e. 73 x 84 7 . 53 x 242 a. x 224


DIVIDING BY 1 1 AND 1 2

1 . Subtract by 1 1 ’s from 1 32 to 0.

2 . State quotients at sight :3 3 + 1 1 66 1 1 88 + 1 1

44 1 1 77 1 1 99 1 1 1 2 1 1 1

3 . Find of : 88 ; 99 ; 22 ; 78 ; 33 ; 48 ; 44 ; 55 ;69 ; 1 1 ; 66 ; 81 ; 77 ; 92 ; 88 ; 99 ; 1 1 0 ; 1 21 ; 83 .

Div ide by 1 1 : Test answ ers.

4 . 2738 7 . 6954 1 0. 8923

5 . 8294 8 . 3986 1 1 . 2 1 58

6 . 2036 9 . 3007 1 2 . 8057

1 6 . Subtract by 1 2 ’s from 1 44 to 0.

1 7 . State quotients at sight

36 1 2 60+ 1 2 1 32 + 1 2

24 1 2 96 1 2 1 08 1 2 1 44 1 2

1 8 . Find11?

of : 96 ; 84 ; 72 ; 36 ; 1 08 ; 24 ; 1 20 ;

1 32 ; 60 ; 48 ; 1 44.

Divide by 1 2 : Test answ ers.1 9 . 3678 2 4 . 781 7 29 . 42 1 92

20. 41 35 25 . 2936 3 0 . 69378

2 1 . 6973 26 . 9238 3 1 . 73945

2 2 . 71 28 2 7 . 4697 3 2 . 82659

2 3 . 4693 28 . 9384 3 3 . 37296

Oral] MULTIPLICATION AND DIVISION 1 47

REVIEW

Find the cost of1 . 9 rings 3 3

2 . 1 2 cows 3 35

3 . 1 0 hats

4 . 1 0 rugs

5 . 3 wagons 3 85

6 . 9 plates

7 . 1 0 knives

Find the cost of 1,W hen

1 5 . 1 2 lamps cost 3 51

1 6 . 4 cases cost

1 7 . 1 0 sleds cost

1 8 . 1 0 sheep cost

1 9 . 1 1 desks cost

20 . 8 trunks cost

2 1 . 1 0 clocks cost

2 2 . 5 hats cost 3 1 5

1 2 hats cost 3 27

8 lb. rice cost 96¢

3 clocks cost

9 books cost

2 7 . 5 chairs cost

2 8 . 9 lb . nuts cost

2 9 . 8 bu . coal cost

2 3 .

2 4 .

2 5 .

2 6 .

8 . 1 0 vases

9 . 1 0 horses 3 95

1 0. 1 1 books

1 1 . 1 1 sheep

1 2 . 1 0 chairs

1 3 . 6 chickens 75¢

1 4 . 1 2 pictures

3 0 . 1 0 satchels cost

3 1 . 1 2 yd . lace cost 48

3 2 . 1 1 lb . steak cost

3 3 . 6 gal. vinegar cost 72 ¢

3 4 . 1 2 bu . potatoes cost 3 9

3 5 . 1 2 pk . tomatoes cost 3 3

3 6 . 1 0 toy engines cost 3 35

3 7 . 5 lb . steak cost

as . 8 qt . cream cost

3 9 . 4 bu . cherries cost 3 1 5

40 . 1 0 yd . silk cost

4 1 . 1 0 pt . creamcost

42 . 1 1 lb . butter cost

43 . 3 pairs shoes cost

44 . 1 2 collars cost


REVIEW

1 . A train runs 378 miles in 7 hours. HOWmany miles is that in 1 hour ?

2 . A ticket agent has 3 in his drawer. Afterselling 2 tickets at 90¢ each , 8 tickets at 70¢ each , and1 mileage book for 3 20, how much money should hisdrawer contain ?

3 . While the hour hand is going 8 times aroundthe dial how often does the minute hand go around ?

4 . The treasury of a school district contains 3 2642 .

After paying the salaries of six teachers for 8 monthsat 3 45 per month, how much remains ?

5 . A farmer sold 4 jars of butter containing re

spectively, 24 pounds, 27 pounds, 26 pounds, and 33

pounds; How many pounds did he sell ?

6 . A newsboy earns 30 cents a day. How muchw ill he earn in 4 weeks of 6 days each ?

7 . What is left froma 3 1 0 bill after paying for 1 05lb . of tea at 60 cents a pound ?

8 . The expenses for a family for a year are as follows 3food

, 3 485 ; fuel and light, 3 86 car fare , 3 35 ; clothing, 3 285 ; church, 3 68 books and papers

, 3 25 ser

vant , 3 1 65 ; other expenses, 3 278 . Find the entireexpenses .

9 . In a school of 897 pupils, there are 487 girls.How many boys are there ?

1 50

Subtract and test 5 problems in 1 minute.

a

1 .

2 .

3

4 .

5 .

6 .

7 .

8 .

FOURTH YEAR

DRILL WOR!

6 6

[Written

OralJ

Give products at sight :

1 .

a

1 2

5

b

8

4

DRILL WOR!

SIGHT -DRILLS

C

8

1 2

00

00

d

9

7

N1

0!

1 2

1 2

1 0

1 0

9

8

1 1

1 1 CO

CQ

e . i of 1 2 ; of 24 ; 36 ; 60 ; 72 ; 1 00.

9 . l0 x 35 ; 1 0 x 52 ; 20 x 30 ; 20 x 40.

1 0 . Give two factors that form: 1 8 ; 27 ; 42 ;

72 96 .

q

mfi

0°

C!)

1 5 1

1 52 FOURTH YEAR

DRILLS

32 + 8

72 + 6

1 8 + 2

24 + 4

20 + 4

20+ 2

56 + 8

42 + 7

24+ 2

40+ 8

1 08 + 9

70+ 7

63 + 9

33 + 3

72 + 8

80+ 8

1 54 FOURTH YEAR [om

MULTIPLIERS ENDING IN NAUGHT

1 . Annex a naught to the right of 3 ; then multiply3 by 1 0. Is there any difference in the result ?

Annexing a naught to the right of a number multip liesit by 1 0.

2 . Multiply by 1 0: 40 ; 20 ; 60; 800 ; 300; 700 ; 900.

3 . Multiply 3 by 1 00 ; 8 by 1 00 ; 9 by 1 00 ; 20 by 1 00.

How many times greater has each of the numbersbecome ? How many naughts were added to each ?

Annexing two naughts to the right of a number multi

plies it by 1 00.

4 . Find

1 00 x 4 1 00 x 1 5 1 00 x 50 1 00 x 75

1 00 x 7 1 00 x 95 1 00 x 85 1 00 x 1 2

1 00 x 5 1 00 x 37 1 00 x 91 1 00 x 36

5 . What is the difference between 1 000 x 3 and 3 x

1 000? between 1 000 x 6 and 6 x 1 000 ? How manynaughts were annexed to 3 ? to 6 ? HOW many timesgreater has each become ?

Annexing three naughts to the right of a number multi

plies it by 1 000.

6 . From what you have learned make a rule formultiplying any number by 1 0 ; 1 00 1 000 ; 1 0000.

7 . Multiply :

8 by 1 000; 7 by 1 000; 9 by 1 000; 4 by 1 000; 1 3 by1 000; 1 2 by 1 0000; 1 4 by 1 000 ; 1 9 by 1 000 ; 25 by1 00; 36 by 1 0; 95 by 1 00; 72 by 1 0; 72 by 1 0000.


1 . HOW many cents are there in 1 00 dimes?

2 . HOW many cents are there in 3 6 ?

Find the weight of

3 . 1 000 two-pound packages of rolled oats.

4 . 1 000 fi ve-pound boxes of starch.

5 . 25 one hundred-pound kegs of nails.

6 . 1 00 lambs at an average of 45 lb . each.

7 . Find the cost of 1 000 one-cent postal cards and1 00 two-cent stamps.

8. Multiply 63 by 2000.

Write the 2 of themultiplierunder the figure63 in ones’ place of the multiplicand. 2 x 63 is2000 1 26 . Annex three naughts to the right of 1 26,

1 26000 making 1 26000. 1 000x 63 63000 2000x

63 1 26000.

Multiply,and read the product

9 . 71 1 0. 85 1 1 . 245 1 2 . 71 5

200 3000 4000 700

1 3 . 347 by 20 1 8 . 293 by 500 2 3 . 481 by 2000

1 4 . 409 by 30 1 9 . 780 by 700 2 4 . 894 by 4000

1 5 . 71 5 by 60 20. 1 84 by 400 2 5 . 906 by 7000

1 6 . 329 by 80 2 1 . 796 by 600 2 6 . 728 by 9000

1 7 . 475 by 90 2 2 . 832 by 200 2 7 . 365 by 1 200

1 56 FOURTH YEAR [Oral

DIVISORS ENDING IN NAUGHT

1 . Divide 60 by 1 0. Remove 0 from60. 60 is how

many times 6 ?2 . Compare 40 and 4 ; 30 and 3 ; 2 x 1 0 and 20 1 0.

What efiect has the removing of naught from the rightof a number upon the value of the number?

3 . Div ide by 1 0: 20; 900; 350; 470; 530; 260; 740.

4 . How many are 1 00 x 6 ? 1 00 x 9 ? 600+

How many naughts are removed fromthe right of 900 when it is divided by 1 00 ? from the

right of 600? What effect has the removing of two

naughts fromthe right of a number upon the value ofthe number

5 . Find 1 000x 9 ; 1 000 x 3 ; 9000 1 000 3000

1 000. How many naughts are removed from the rightof 9000 when it is divided by 1 000 ? from the right of3000 What effect has the removing of three naughtsfrom the right of a number upon the number ?

Removing one naught from the right of a numberdivides the number by 1 0; removing two naughts, dividesit by 1 00 removing three naughts, divides it by 1 000, etc.

Find quotients6 . 30 1 0

7 . 90 1 0

8 . 70 1 0

9 . 200+ 1 0

1 0. 300 1 00 1 4 . 4000 1 00

1 1 . 600 1 00 1 5 . 5000 1 000

1 2 . 700 1 00 1 6 . 9000 1 000

1 3 . 900 1 00 1 7 . 7000 1 000

1 58 FOURTH YEAR [W ritten

MULTIPLICATION BY TWO—FIGURE NUMBERS

1 . Multiply 64 by 23 .

Multiplicand 64 64

Multiplier 23

lst partial product 1 92 3 X 64 1 92

2d partial product 1 280 20 X 64 1 28

Entire product 1 472 23 X 64 1 472

In practice the 0 in the second partial product isomitted, and 1 280 is written as 1 28 tens by placingthe right-hand figure of that product in tens ’ place .

2 . 3 .

327 203

35 42

1 635 406

981 81 2

1 1 445 8526

Written] MULTIPLICATION 1 59

1 . 426 by 23 1 1 . 634 by 37 2 1 . 9006 by 48z . 372 by 41 1 2 . 298 by 73 2 2 . 2694 by 75

3 . 256 by 33 1 3 . 604 by 48 2 3 . 8002 by 38

4 . 307 by 32 1 4 . 729 by 40 24 . 4293 by 67

5 . 269 by 43 1 5 . 903 by 86 2 5 . 91 28 by 39

6 . 307 by 27 1 6 . 694 by 79 2 6 . 2807 by 74

7 . 538 by 36 1 7 . 928 by 89 2 7 . 6293 by 56

a. 736 by 63 1 8 . 726 by 75 28 . 4060 by 1 39 . 487 by 52 1 9 . 349 by 28 29 . 2734 by 27

1 0 . 994 by 35 20 . 723 by 1 4 30 . 41 69 by 323 1 . Announce products at sight

50 x 90 9ox 7o 20 x 80 70 x 60 70 x 40

80 x 70 60 x 50 40 x 30 30 x 30 90 x 90

3 x 9 is the square of 3 . 6 x 36 is thesquare of 6 .

Tofind the square of a number, wemultip ly it by itself .

3 2 . Find the s quares and memorize2,3 , 4, 5, 6, 7, 8, 9, 1 0, 1 1 , 1 4, 1 5, 1 8,

Multiply3 3 . 463 by 73 3 7 . 9869 by 84 41 . 8693 by 28

3 4 . 938 by 84 3 8 . 3278 by 93 42 . 9281 by 39

3 5 . 697 by 95 3 9 . 9009 by 49 43 . 7375 by 47

3 6 . 893 by 96 40 . 6075 by 74 44 . 4069 by 56

1 60 FOURTH YEAR [W ritten

MULTIPLICATION OF CONCRETE NUMBERSWhich of the follow ing numbers are abstract ? Which

are concrete Why ?

1 . 8 ; 6 days ; $4 ; 25 ; 4 feet ; 8 horses.

2 . Name the multiplier and the multip licand in eachproblem

3 8 64 days 81 horses 72 orangesx 5 x 4 x 7 x 3

3 . Observe in each of the above problems that theproduct must have the same name as the multiplicand.

Themultip lier is always an abstract number.

4 . When two numbers are multiplied,the number in

the product remains the same in whatever order the

numbers are taken ; thus : 7 x 1 2 1 2 x 7.

5 . How much do I earn in 1 25 days at 353 per day ?In problems like this where the multiplier-has more

figures than the multiplicand, the product of the numbers may be found thus : 1 25, but the analysis of the

3

375

problem should be given in this wayI earn in one day, $3 .

I earn in 1 25 days, 1 25 x $3 , or $375.

Find the cost of How many6 . 3 1 9 days

’

work 8 3 1 0. Pints in 327 qt .

7 . 81 7 tons coal 5 1 1 . Inches in 845 ft . ?

3 . 1 98 lb. meal 9¢ 1 2 . Peeks in 1 64 bu . ?

9 . 345 doz. buttons 8¢ 1 3 . Ounces in 375 lb. ?


STATEMENTS

Make problems from the following statements andbring solutions to the class :

1 . Mr. Hall bought 26 acres of land at 3 26 an acre.

2 . A man took 1 6 lb. of butter to the store and soldit at 25 ii a pound . He took in payment shoes at

3 . A milkman has 25 customers . Each receives2 quarts of milk daily .

4 . A boy bought 6 doz . bananas at 3 for 5 it and soldthemat 3 for a dime .

5 . A new sboy sells 46 penny papers, on which he

gains 4 each .

6 . A farmer bought 1 2 sheep at each .

7 . A dealer sold a suite of furniture forlosing

a. 30 boys have an average of

9 . A fruit dealer bought 2 crates of berries,each

containing 32 quarts, at 7 a quart.

1 0 . William sold of a bushel of plums at 8 it a quart.

1 1 . A man had and spent

1 2 . A milliner sold 6 hats at 5 each .

1 3 . John attended 1 63 days of the 200 school days.1 4 . 1 5 yards were sold from a piece of cloth contain

ing 68 yards .

1 5 . The Limited left New York at PM .

and ran at the rate of 45 miles an hour.

Oral and Written] MULTIPLICATION AND DIVISION 1 63

COMPARISON

In the follow ing comparisons the first number is tobe divided by the second :

1 . Compare 1 2 and 4 ; 1 2 and 3 ; 1 6 and 4.

2 . Compare 5 and 1 5.

3 . Compare :1 8 and 6 1 6 and 4 6 and 1 2.

20 and 5 45 and,

9 6 and 30.

4 . When 3 oranges cost 1 0 cents, how much w ill 1 2oranges cost ?

N orm— 1 2 oranges equal 4 x 3 oranges ; hence they will cost4 x 1 0 cents, or 40 cents.

5 . At 6 melons for 25 cents, how much w ill 24 cost ?

6 . At 1 2 lemons for 1 5 cents, how much w ill 72 cost ?

7 . If 8 tons of coal cost 3 54, how much w ill 40 tonscost

3 . If 3 collars cost 35 cents, how much w ill 24 collarscost

9 . When 1 2 cords of wood cost 348, how much w ill3 cords cost ?

1 0 . How much w ill 4 qt . of milk cost when 1 6 qt .

cost

1 1 . When 7 tons of hay sell for 391 , how much w illa farmer receive for 35 tons ?

1 2 . If 96 acres of land are worth 3 2592 , how muchare 1 2 acres w orth ?

FOURTH YEAR

REVIEW OF SHORT DIVISION

Answer at sight

1 . 2232 5L3_5_ 5215

2 . 621 2 711 41 82872 923699 824056

Give answers quickly

12‘ of 1 6 ; 1 8 ; 26 ; 28 ° 32 ° 36 ; 40.

t} of 24 ; 27 ; 36 ; 1 8 60 90 ; 1 20.

1» of 48 ; 24 ; 60 ; 72 ; 36 ; 44 ;

of 60 ; 55 ; 1 00 ; 1 50 ; 75 ; 45 ; 65.

{34 of 72 ; 96 ; 84 ; 24 ; 48 ; 240 ; 36.

2 oi 84 ; 91 ; 49 ; 63 ; 1 05 ; 350 ; 2 1 00.

of 96 ; 72 ; 640 ; 960 ; 560 ; 1 20 ; 880.

1 0 . 31,of 1 08 ; 1 35 ; 360 ; 720 ; 54 ; 7209 ; 1 080.

1 1 .

116of 1 00 ; 1 20 ; 1 30 ; 1 90 ; 1 250 ; 1 950 ; 1 780.

1 2 .

Ila-of 1 32 ; 88 ; 99 ; 77 ; 1 1 00 ; 1 320 ; 1 21 0.

1 3 .

119 of 1 44 ; 288 ; 96 ; 84 ; 960 ; 840 ; 1 080.

Divide and test

1 4 . 1 1 22244 1 1 22882

3 .

4 .

5 .

6 .

7 .

8 .

9 .

1 5 . 1 2289640 1 226072 1 2 29060

Give quotients at sight :

1 6 .


FINDING THE QUOTIENT FIGURE IN DIVISION

Think how many times the first figure of the divisoris contained in the first figure of the dividend . The

number w ill be the first figure of the quotient .

1 . 252 4-2 1 4 . 71 4 —9 2 1 7 . 504 4-21

2 . 525 —9 2 1 5 . 651 3 .

3 . 6 . 9 .

Think how many times the first figure of the divisoris contained in the first figure

,or in

'

the first two figures,of the dividend . The number w ill be the first figureof the quotient

1 0 . 71 3 3 1 1 4 . 7061 23 1 3 . 683 1 33

1 1 . 899 3 1 1 5 . 9269 23 1 9 . 1 984 32

1 2 . 6727 3 1 1 6 . 5028 42 2 0 . 2272 32

1 3 . 8323 41 1 7 . 1 344 42 2 1 . 1 683 51

2 2 . Divide 8 1 9 by 2 1 .

Since the product of the divisor39

4and quotient is greater than 81 , the

63

84quotient figure is too large. Try a

1 89smaller quo tient figure .

1 89

23 . Divide 651 by 2 1 .

3 1

Since the remainder is greater than 21 )651the divisor, the quotient figure is too 63

small. Try a larger quotient figure . 21

21

Written] DIVISION 1 67

Divide and test

1 . 2 1 2882 1 3 . 23 2 575 2 5 . 332462 3 7 . 4321 333

2 1 2903 1 4 . 232736 26 . 332858 3 3 . 4326880

2 1 2504 1 5 . 232966 2 7 . 332561 3 9 . 43 9460

2 1 281 9 1 6 . 2321 38 2 3 . 332627 40 . 4321 376

2 1 23 1 5 1 7 . 3 1 2775 29 . 41 . 51 21 683

2 1 2567 1 3 . 3 1 2744 3 0 . 41 22296 42 . 51 23672

1 9 . 3 1 2899 3 1 . 41 21 1 07 43 . 51 23264

2 1 2441 20 . 3 1 22 1 7 3 2 . 41 21 435 44 . 51 21 428

22281 4 21 . 322672 3 3 . 4221 008 45 . 5221 508

1 0 . 222638 2 2 . 322928 3 4 . 4221 596 46 . 5222288

1 1 . 222352 2 3 . 3221 60 3 5 . 4221 680 47 . 5322385

1 2 . 222660 24 . 3221 92 3 6 . 4221 722 43 . 5321 908

49 . A butcher paid 3 1 476 for 41 head of cattle .

How much was that per head ?

5 0 . If a railroad trackman walks 1 6 miles each day,how long w ill he be in walking 832miles ?

5 1 . If there are 496 ounces m 3 1 pounds, how many

Ounces are there in 1 pound ?

5 2 . If 24 barrels of oil cost 3 what is the priceof 1 barrel ?

5 3 . If a bushel of oats weighs 32 lh .,how many

bushels w ill weigh 28640 lb. ?

54 . How long w ill it take a train that travels 35miles an hour to go a distance of 3 1 5 miles ?

5 5 . At 38 15 a word, how many words can I cable fromNew York to Sweden for


LONG DIVISION

1 . Divide 741 6 by 25.

Q uotient Write the remainder

252741 6 over the divisor, and

50 annex it to the right

241 Of the quotient .

225 Test . 296 x 25

1 66 7400;1 50

1 6 remainder -i z5= éDivide and test

2 . 2397 by 51 1 3 . 1 281 by 21 24 . 6938 by 943 . 3888 by 86 1 4 . 1 703 by 27 2 5 . 71 59 by 394 . 1 302 by 2 1 1 5 . 3034 by 46 2 6 . 8697 by 28

5 . 2945 by 38 1 6 . 4697 by 61 27 . 491 0 by 45

6 . 321 3 by 51 1 7 . 4368 by 98 2 3 . 3682 by 73

7 . 1 827 by 27 1 3 . 4544 by 76 2 9 . 491 8 by 943 . 3007 by 36 1 9 . 2867 by 61 3 0 . 81 68 by 869 . 6256 by 81 20 . 2058 by 27 3 1 . 7369 by 69

1 0 . 5096 by 95 2 1 . 2668 by 3 1 3 2 . 8925 by 281 1 . 2542 by 41 2 2 . 3592 by 43 3 3 . 801 0 by 651 2 . 3567 by 87 23 . 2047 by 83 3 4 . 91 02 by 983 5 . How many suits, at 3 32 each, can be bought for

3 1 095, and what amount w ill be left ?

3 6 . Find the number of barrels of Oil , 51 gallons each,that can be filled from a vessel containing 408 gallons.


DIVISION AND PARTITION

Division is the process of finding how many times onenumber contains another, or of separating a number intoequal parts.

1 . How many times is 3 3 contained in 3 1 5 ?

This problem gives the size of the equal parts ( 3 3)into which the dividend ( 3 1 5) is to be divided , andasks for the number of equal parts . 3 1 5 + 3 3 = 5, the

number of equal parts .

2 . What is the quotient of 3 1 5 divided by 3This problem gives the number of equal parts (3) into

which the dividend ( 3 1 5) is to be divided, and asks forthe size of each part . 4of 3 1 5= 3 5, the size of eachpart . This kind of division is called partition.

First state whether each problem calls for the numberof equal parts or the size of each part

,and then give

answers

3 . 1 44 in . + 1 2 in . 7 . 1 92 bu . + 1 6 bu.

1 25 yd. + 5 8 . 1 08 ln . + 9

5 . 9 .

110-Of 3 250

6 . 1 50 ft . + 1 0 1 0 . 5 Oi 1 28 da .

1 1 . At 45 ¢ a bushel, how many bushels of corn w illsell for 3

1 2 . If 28 Stanhope buggies are sold for 3 291 2, whatis the average price ?

1 3 . If a train runs 1 036 miles in 37 hours, how far

w ill it run in one hour ?

Written] DIVISION 1 71

LONG DIVISION

1 . Div ide 1 3892 by 23 .

What is the product of 6 x2 3 ?

Is there any remainder ? What is the

1 38next operation ? Does 9 contain 23 ?

92Since 9 does not contain 23, w rite 0

92in the quotient, and bring down 2

,

making the number to be divided 92 .

Find quotients and test2 . 26322 46 9 . 23229 29 1 6 . 56079 73

3 . 3 1 356 39 1 0 . 73784 92 1 7 . 45825 65

4 . 23641 47 1 1 . 1 563 1 77 1 3 . 1 9844 49

33522 37 1 2 . 36792 73 1 9 . 1 9266 38

3 1 590 45 1 3 . 58056 82 20 . 83396 98

49248 81 1 4 . 67596 74 2 1 . 41 1 57 51

201 30 66 1 5 . 1 6685 54 2 2 . 1 51 00 25


9

s

s»

a

2 3 . 64 32 so. 200 20 3 7 . 90 45

2 4 . 96 —x 48 3 1 . 70 35 3 3 . 60 -i 20

2 5 . 40 20 3 2 . 45 1 5 3 9 . 48 24

2 6 . 50 25 3 3 . 46 23 4o. 56 28

2 7 . 60 30 3 4 . 556 28 4 1 . 63 2 1

2 3 . 90 45 3 5 . 99 33 42 . 84 2 1

2 9 . 1 00 50 3 6 . 64 32 4 3 . 62 3 1


SIGHT WOR! IN MULTIPLICATION AND DIVISION

These problems should be worked by writing the an

swers directly, w ithout placing the multiplier under themultiplicand.

Find the cost of Give products at sight

1 . 3 houses 3 2500. 1 5 . 4 x 30

2 . 750 bu . coal 1 6 . 1 0 x 1 0

3 . 60 hats 1 7 . 2 x 25

4 . 1 doz . chairs 1 3 . 5 x 50

5 . 25 suits 3 1 0. 1 9. 6 x 60

6 . 6 gal . Oil 20 . 8 x 90

7. 8 gal . varnish 2 1 . 1 2 x 50

3 . 1 50 yd . cloth 2 2 . 1 1 x 30

9 . 1 2 lb. butter 25 2 3 . 9 x 25

1 0 . 25 doz. eggs 25 2 4 . 1 0 x 35

1 1 doz. lemons 30it. 2 5 . 1 2 x 1 2

1 2 . 1 5 pails of lard 40 2 6 . 1 2 x 40

1 3 . 3 gal. maple sirup 2 7 . 1 2 x 1 5

1 4 . 3 hams 23 . 1 2 x 45

Find the cost of 1 when Give quotien ts at sight

29. 9 bbl . flour cost 3 54. 3 4 . 360 9

3 0 . 1 2 doz . oranges cost 3 3 . 3 5 . 328'

8

3 1 . 8 coats cost 348 . 3 6 . 455 7

3 2 . 4 sheep cost 3 22 . 3 7 . 1 56 1 2

3 3 . 1 5 lb . butter cost 3 3 . 3 3 . 1 2 1 1 1 =


PRACTICAL WOR!

MAR! ET REPORT

Potatoes, 7593 per bu. Corn, 457 per bu.

Beans, per bu. Baked beans, per doz. cans.

Butter, Print,33 y per lb . Celery, 25 7 per doz.

Dairy,25 per 1b. Eggplant, 75 per doz.

Sugar, 100 lb . bag, W atercress,407 per doz .

Flour, per bbl. , Blackberries, per crate ,

From the market report find the cost of each of thefollow ing :

1 . 7 bu. potatoes . 7 . 8 bu. corn .

2 . 1 5 lb . print butter. 3 . 1 0 bags sugar.

3 . 1 2 doz . celery. 9 . 25 bbl. flour.

4 . 25 doz . watercress. 1 0 . 2 doz . cans baked beans.

5 . 5 bu. beans. 1 1 . 7 doz . eggplant.

6 . 1 2 lb. dairy butter. 1 2 . 3 crates blackberries.At 1 22 if each find the cost of

1 3 . 72 lb. of meat. 1 3 . 1 76 cards of buttons .

1 4 . 1 44 books. 1 9 . 272 peeks Of potatoes.

1 5 . 64 vases. 20 . 1 28 baskets of tomatoes.

1 6 . 1 68 cups. 96 watermelons.

1 7 . 256 yd . of lawn. 2 2 . 1 52 yd. of ribbon .

2 3 . If it is 8 miles fromA to B,and 42 times as far

fromB to 0, how far is it fromA to C ?

24 . James bought 1 0 lb. Of sugar at 532cents a pound ;

43 lh. of butter at 20 cents a pound ; 6 lemons at 3 for5 cents ; and two 8-cent loaves of bread. He gave the grocer a two-dollar bill . How much change did he receive ?

Written] REVIEW 1 75

PRACTICAL WOR!

1 . The ledger of a supply house shows the followingfor the sales of 5 different articles for a week . Whatwas the amount of sales for each clay ? the amount re

ceived for each article ? the amount of sales for thew eek

MON . TUEs. W ED . THURS. FRI

Pipe 3 3 3 3 3 3W ire rope

O il cans

Nails

Files

2 . I can buy a box of 40 cakes of soap for 3 or

the same soap at 2 cakes for 1 5 cents. Which is thecheaper, and how much per cake ?

3 . In buying 2 doz. cans ofi

cherries, how much isgained by purchasing at 3 a dozen instead of buying 3 cans for 75 cents ?

4 . How much is gained by buyingoa barrel (1 96 lb.)of flour for 3 instead of buying the same amountat 5¢ a pound

5 . Aman paid 3 275 for a lot. He built a house onit at 4 times the price of the lot , and spent 3 26 forshade trees

, 3 3 1 for a fence, and 3 for a cementwalk. He sold the property for 3 2000. How muchdid he gain ?

6 . How much w ill be received for 3 bu. of chestnutsat a quart ?


PRACTICAL PROBLEMS

1 . A farmer has 28 cow s in three fields . If thereare 1 2 in the first, and 9 in the second, how many cowsare there in the third field ?

2 . The farmer values his cow s at an average Of 3 35each . What is the value of all ?

3 . The fields over which they graze contain 24 acres,1 8 acres

,and 1 4 acres . How much grazing land is there

,

and what is the value of this land at 3 353 an acre ?

4 . If the farmer receives 2 1 560 gallons of milk ayear

,how much is it worth at 1 2 cents a gallon ?

5 . His Jersey cow yields 350 lb . of butter a year,which he sells at 28 cents a pound. How much does hereceive for it ?

6 . He sold 5 of the cow s at an average price of

3 How much did he receive for them?

7 . He keeps 2 men at 3 2212 a month, to work on

the farm. How much does the labor for the year cost ?3 . He sold 1 4 calves for 3 98. How much did he

receive, on an average, for each ?

9 . His grocery bill averaged 3 permonth . Findhis bill for the year.

1 0 . He purchased 2 horses, one at 3 1 25, and one at

3 1 50 ; and 2 wagons at 3 85 each. Repairs on the

farm cost 3 Find the amount paid .

1 1 . He bought 14 doz . milk cans at each.

How much did they cost ?


MEASURES

4 . A dealer buys 1 50 bales of hay, averaging 90pounds to the bale . How many tons and pounds overdoes he buy ?

5 . At 3 cents an Ounce, how much w ill 1 pound ofmustard cost ?

6 . Find the cost of six kegs of nails, each keg w eighing 1 00 lb .

, at cents a pound .

7 . 2 tons of rolled oats were packed in pound packages. How many packages were there ?

3 . How many ounces are there in a ton ?

9 . A load of hay weighed 3000 pounds . How manytons did it w eigh ? What was its value at 3 1 4 a ton ?

WEIGHT

1 . Name some articles bought by the ounce

by the pound .

2 . How many ouncesare there in 1 pound ? in1 0 pounds ?

Coal, hay, sand, plaster, etc .

,in largequanti

ties, are sold by the tonOf 2000 pounds.

3 . Memorize the table

Oral and Written] MEASURES 1 79


1 . Name the measures that you have already learned .

2 . A foot inches .

3 . A yard feet .

4 . What measure should you use to measure thelength of your book ? of your desk ? the w idth of yourschoolroom? the length of the blackboard ?

5 . Measure 54 yards or 1 62 feet along the street oron the school ground . Call it one rod .

6 . Secure a tape measure 53; yards long, and withit measure the length and the w idth of your schoolgrounds in yards and feet .

7 . With a pole or a tape , a rod in length,measure thedistance in rods and feet around a square or a field .

3 . 20 city blocks, each 1 6 rods in length,are 320

rods long . This is called onemile . 1 mile 320 rods .

9 . 320 x 1 64 ft . feet . (Why do w e multiply ft . by 320 ?2

1 0 . 5280 ft .-3 yards . (Why do we divide

5280 ft . by

1 1 . Memorize this table



Change

1 . 60 ft . to yd. 7 . 5 ft . to in .

2 . 27 rd . to ft. 3 . 1 20 in . to ft .

3 . 1 6 ft . to in . 9 . 72 ft . to yd .

4 . 42 in . to ft . 1 0 . 420 in . to ft .

5 . 320 rd . to ft . 1 1 . 1 250 yd . to ft .

6 . 1 760 yd . to ft . 1 2 . 1 20 rd . to ft .

1 3 . How many feet of fence are required for a gardenin the form of an oblong 26 yards long and 1 2 yardsw ide

1 4 . James lives 1 80 rods fromthe schoolhouse . Howmany feet does he travel in going to and coming fromschool each day ?

1 5 . A boy travels 1 35 yards each day in carrying themail . How many yards does he travel in 6 days ?How much less than a mile does he travel ?

MEASURES OF SURFACE

1 . Draw a square inch . What two things Showthat it is a square inch ?

2 . Draw on the blackboard one square foot . Whattwo things show that it is a square foot ?

3 . Separate each side of a square foot into 1 2 equalparts . Connect these points by straight lines . Whatis the size of each square ? the name of each square ?How many square inches equal one square foot ?


MEASURES OF SURFACE

Find the area in square inches of :1 . An oblong 6 in . by 4 in . 5 . An 8-in . square.

2 . A square 7 in . on each side . 6 . A 1 2-in . square.

3 . A page 8 in . by 5 in . 7 . A 9-ln . square .

4 . A slate 1 0 in . by 1 2 in . 3 . A 1 0-ln . square.

9 . Draw a figure to represent an oblong 5O

in . longand 3 in . w ide . Find its area. Find the distancearound the oblong .

The distance around a figure is called the perimeter.

1 0 . Find the perimeter, in inches, of each figure described ln problems 1 to 9.

Represent the follow ing figures by a scale of 1 inch tothe foot

, and find the area and the perimeter :

1 1 . A 6-ft . square . 1 3 . A wall 9 ft . by 6 ft .

1 2 . A rug 9 ft. by 4 ft . 1 4 . A table 6 ft . by 5 ft.

Find the area and the perimeter. Represent on a

scale of 1 inch to a yard :

1 5 . A schoolroom 1 0 yd . long and 8 yd . w ide .

1 6 . A hall 1 5 yd . long and 3 yd . wide .

1 7 . A sidewalk 1 2 yd . long and 2 yd . wide .

1 3 . Matting for a room5 yd . long and 4 yd . w ide.

1 9 . Measure,in even yards, the length and W idth of

your schoolroom floor, and draw the figure on a scaleof 1 in . to the yard ; 1 in . to the foot.

Oral, Written] READING AND WRITING NUMBERS 1 83

READING AND WRITING NUMBERS

1 . How are large numbers pointed off before beingread

2 . Name the periods of numbers up to millions.3 . Read Notice that in reading a num

ber the units’ period is not named . Thus this numberis read 2 million, 28 thousand , 375 ; not 375 units.The next period aftermillions is called billions’ period .

Copy, point off, and reada b c d

4 . 2405 30670 6800907 8645742689

5 . 3065 49007 400745 750680009

6 . 7005 40074 8790007 406009807

7 . 8900 87090 4057042 6804704924

3 . 6666 90703 301 2890 9000000250

9 . 3050 65002 7000002 8057000000

1 0 . 9580 73200 9050601 5700809563

Write :

1 1 . Six thousand six hundred six.

1 2 . Two billion ten million four .

1 3 . Seventy-five thousand nine hundred six.

1 4 . One billion eight million seventy-five.

1 5 . Eighty-four million six hundred five thousand.

1 6 . Twenty-five thousand thirty-eight .

1 7 . Nine hundred million nine hundred ninety-n ine.1 3 . Two million six thousand thirty.

1 9 . One billion one million one thousand.


REVIEW

1 . Begin w ith 9 and count by 9’

s to 1 26.2 3 2

2 . Begin w ith 1 and count by 9’

s to 1 1 8 .3

Add by columns and by lines : 4

a b c d e f 5 .

3 3 . 6’

4 . 9 . 7

5 . Io. 9 .

6 . 1 1 . 1 0.

7 . 1 2 . 1 1 .

1 3.

a b c d1 3 '

1 3 . s423 5+ 3 9 + 9 829 51 4

1 4 . 1 3 6 9+ 327 8 + 6 27+1 6

1 5 . 24 1 + 41 6 5+ 96 +1 7 :

1 6. 36 74+

1 8 °

1 7 . 838 9+ 43 62 + 93 7+1 9 °

if:

1 8, 3 3 3 3 93 .

1 9 . 3756 5 34.

20 . 95 .

2 1 . 76 45+ 2 6 .

2 2 . 83 6 4+ 226 8+ 856 87 2 7 .

as.

3 0 .

2 3 . From the numbers at the right repre3 1

senting the daily circulation of a paper, findits circulation for July .

186 FOURTH YEAR

REVIEW OF ADDITION

[Written

Add (when written) 4 problems in 1 % minutesa

1 . 3

b3

3

0

3

3

Written] SUBTRACTION

REVIEW OF SUBTRACTION

1 87

Write, subtract, and test 4 problems in 25minutesa

1 . 3

2 3

3 . 3

8 .

9

3

3

3

3

3

3

b

3

3

3

3

3

3

3

3

3

C

3 48892 00

1 5079 63

3

3 45269 79

273 1 9 27

3 37461 2 7

1 9842 07

3

3

3

3

3

d

3

3

3

3

3 27004 49

1 901 76 3

3 75009 75

691 359 2

3 973829 9

398537 5

3 321 489 1

1 4269 90

3 33 1 978 4

1 90575 5

FOURTH YEAR

DRILL IN MULTIPLICATION

1 . Give products at sight

8 x 4 7 x 8 6 x 6

3 x 9 9 x 6 7 x 6

4 x 7 7 x 9 l 1 x 5

6 x 5 8 x 8 8 x 6

a b c d e

z. 1 2 9 8 1 2 1 1

6 1 0 1 1 5 3

3 . 1 1 8 7 1 1 1 0

6 7 8 7 5

1 1 1 2 9 1 2

8 1 1 1 1 1 2 1 0

5 Give at sight two factors that form

84 81 72

99 33 96

36 54 84

25 30 56

28 35 60

6 . Give products

40 x 40 70 x 60

80 x 40 90 x 80

90 x 30 1 00 x 40

60 x 50 200 x 25

50 x 70 300 x 1 5


AND SUBTRACTION OF HALVESAND FOURTHS

Fourths

3 equal one W hole umt ;

1 equal one W hole unit ;

1}1 3

— 3First add, then subtract3 . 53 4 . 92 5 . 91} 8334 23 32

Add :

8 . 345 9 . 671 1 0 . 654,

1 1 . 255} 1 2 . 56}43 73 84 73

99, 81

1 53In example 8, or 1 ; Write the

fraction 12and add the 1 to the whole number.

Written] FRACTIONS 1 91

HALVES, FOURTHS, AND EIGHTHS

2

4

1 -t i t. e. t — t=é2 . Compare and gof the same circle .3 . Compare 1

2» and of the same circle.

4 . 1» is What part of 12=?

s-e + 1 t6 . Into how many eighths can the Whole circle be

divided ? into how many fourths ?Add

7 . 3% a. 7g 9 . 6g 1 0. 9-3 1 1 . 5§3§ 84} 71» 1 1 1 25;

Ht 9% 9%_

25

1 2 . or 2 Whole units ;many whole units

Subtract, then add

1 3 . 1 0% 1 4 . 1 2%

i t i t.

1 8 . 62% 1 9 . 63geat. eat


THIRDS, SIXTHS, AND NINTHS

Thirds Ninths

z

2 t+ t+ t t or— unit ; 4; i s é + t=

First add and then subtract

4 . 2911; 5 . 815 6 . 42—3m_ i li t. an 131

7 . 62g 8 . 1 55 9 . 1 637; 1 0 . 1 9%

l_

z_i 1 2g 1 01 1 2%

1 1 . Mrs. Clark bought 1 —2 dozen lemons and used 13;dozen . How many remained ?

1 2 . Henry studies 4% hours a day, and James fighours. How much longer does James study each daythan Henry ?

1 3 . A flower bed is 4gft . long and 2gft . W ide . Findthe distance around it .

1 4 . If it takes Henry 35» hours to walk a certain d istance

, or L}, hours to ride it on his bicycle, how muchtime does he save by riding ?

1 94 FOURTH YEAR lWritten

MULTIPLICATION

1 . Multiply 273 by 304.

273273

304304

1 0921 092

000

81 981 9

8299282992

Do not multiply by 0 as in the first illustration.

When multiplying by 3 hundreds, write the partialproduct as 8 1 9 hundreds by placing the right handfigure of that product in hundreds’ place.

3

x 2040

1 22400

61 20

624240 0

6 . 275

x 306

1 0 . 709

x 504

x 603

Written] MULTIPLICATION 1 95

How many are

1 . 704 x 3096 e. 309 x 4039

809 x 9409 7 . 907 x 7008

609 x 7320 a. 408 x 6007

507 x 8060 9 . 502 x 91 03

608 x 3724 1 0 . 903 x 7030

Multiply

1 6 . 8945 by 643 2 6 . 6785 by 904 3 6 . 5078 by 2061 7 . 3089 by 1 36 2 7 . 7856 by 685 3 7 . 9067 by 508

1 8 . 4506 by 275 2 8 . 9786 by 607 3 8 . 8906 by 379

1 9 . 3875 by 609 29 . 7869 by 783 3 9 . 6709 by 806

2 0 . 5783 by 382 3 0 . 6778 by 579 40 . 6076 by 927

2 1 . 3296 by 907 3 1 . 9868 by 632 4 1 . 8405 by 403

2 2 . 7395 by 834 3 2 . 5846 by 597 42 . 6035 by 876

2 3 . 3837 by 958 3 3 . 6484 by 460 43 . 8708 by 804

2 4 . 6574 by 687 3 4 . 9676 by 329 7083 by 705

2 5 . 8936 by 706 3 5 . 6798 by 376 45 . 5067 by 770

46 . Mr. Watson had 2475 boxes of soap . Each con

tained 1 75 cakes . Find the entire number of cakes .

47 . A factory averages 2485 articles for 3 1 0 days ofthe year. What is the entire numbermade ?

48 . Mrs. Thompson raised 246 turkeys and sold themat each . How much did she receive for them?

49 . A suit factorymanufactured 3685 suits during theseason . At each, hoW much was received forthem?

1 96 FOURTH YEAR [Oral and written

PARTS OF NUMBERS

1 . Find of 24.

A} of 24 is 8 How do we find 3} of a num

2of 24 _ 2 x 8, or 1 6 .

ber ? i of a number ? % Oi a

number, etc . g of a number2 x % of the number. of a number= 3 x l} of the

number,etc.

Give rapidly .

of each number : 1 6,24

, 36, 44, 48, 50.

l 2 .3 .

3and

3of each number

4 . i and of each number : 1 6, 20, 28, 32 , 48 .

5 .

13, g, and gof each number : 20, 35, 45, 40, 80.

Find

6 .

31; of 1 8 1 2 . gof 1 8 1 8 . of 2 1 24 . gof 75

21,Of 24 1 3 .

£2 of 28 1 9 . 7gof 20 2 5 . g of 75

6 -% of 1 6 1 4 . % of 56 zo. § of 40 - Of 96

9 of 42 1 5 . of 64 2 1 . of 24 of 1 44

1 0 of 24 1 6 . of 63 2 2 . g of 65 28 . g. of 1 60

1 1 goi 25 1 7 .

32; of 63 2 3 . gof 48 29 . gof 255

Find

of $24 5} of 1 2 lb .

got $1 6 - of 9 ft.

of $50 71; of 1 2 yd .

g of $1 8 {2 Of 1 6 gal .

gof $20 fi of 8 bu.

1 98 FOURTH YEAR

FRACTIONAL PARTS OF A DOLLAR

Give at sight the cost of

1 . 6 bushels of apples at .50 a bushel .Hu n — 6 x se= sg= sa

z . 8 gallons of vinegar at .25 a gallon.

3 . 8 yards of silk at .50 a yard .

4 . 8 pounds of meat at .1 2 51, a pound.

5 . 1 0 dozen eggs at .20 a dozen .

6 . 9 yards ofmuslin at .1 0 a yard.

7 . 6 pecks of pears at $ 25 a peck.

8 . 1 2 pictures at .75 each .

9 . 1 0 yards of lawn at . 1 0 a yard.

1 o. 6 gallons of vinegar at .50 a gallon.

1 1 . 8 gallons of oil at S.25 a gallon .

1 2 . 1 2 dozen oranges at .25 a dozen .

1 3 . 6 bushels of apples at .50 a bushel.1 4 . 1 6 pounds of rice at . 1 2} a pound.

1 5 . 1 0 pecks of peaches at .20 a peck .

1 6 . 8 gallons of milk at 1 25 a gallon.

[Oral

Oral and Written] DIVISION 1 99


a b c d

1 00 1 0 280 1 40 993 33 1 3 1 5 1 05

500 50 930 3 1 0 645 1 29 972 324

300-1; 30 860+ 1 72 725 —z 1 45

250 50 396 1 32 284 1 42 932 466

400 80 960 320 788 1 97 260 1 30

844 21 1 330 882 1 26 775 1 55

Divide 1 75608 by 324. 8 . Divide 793320 by 264 .

542 3005

1 620 792

1 360 1 320

1 296 1 320

648Since 264 is larger than 1 3

,what

do we write in the quotient ?648

Divide

a b c

9 . 63596 by 1 26 46785 by 1 35 1 3940 by 340

1 0 . 78563 by 341 78568 by 244 81 282 by 408

1 1 . 48842 by 1 44 65375 by 255 23674 by 726

1 2 . 26786 by 354 78634 by 1 84 83765 by 41 5

1 3 . 46785 by 1 65 79673 by 263 27854 by 1 29

1 4 . 83761 by 2 1 9 86572 by 1 96 76348 by 366

200 FOURTH YEAR [Written

DIVISION

1 . Divide 7284by 600.

6509122941 2696

2 . 9754 by 800.

1 24g%.

3 . Divide 48525 by 2300.

2 143 5

46

25

23

225 Rem.

Divide

4 . 76856 by 2200

5 . 86040 by 3 1 00

6 . 86075 by 2500

7 . 40673 by 3200

8 . 87604 by 2300

Find quotients

1 4 . 869325 463

1 5 . 7391 86 956

1 6 . 293869 409

1 7 . 891 382 786

1 8 . 632007 81 7

Cutting ofi the naughts in thedivisor and 2 figures in the dividend divides both by 1 00, w itha remainder of 25 in the dividend . 485 hundreds divided by23 equals 2 1

, with a remainderof 2 hundreds . Bring down thefirst remainder of 25 to formthe

complete remainder, 225 .

9 . 68025 by 4200

1 0 . 56078 by 2400

1 1 . 70642 by 41 00

1 2 . 47630 by 51 00

1 3 . 85763 by 1 300

283756 268

873700 945

5861 38 71 5

938004 807

1 39287 800


5 . A man’s salary is $950 per year. He pays $260for board, $1 36 for clothing, and for otherexpenses . How much has he left ?

6 . A grocer deposited in bank during the w eek thefollow ing sums :

and After making the last deposit,

he found there was a balance to his credit ofHow much had he w ithdrawn ?

7 . If a freight car costs $475, and a locomotive$1 4625 , what is the value of a train containing 27 carsand a locomotive ?

8 . A woman sold at a store 1 6 doz . eggs at 1 8 ¢ a

dozen, 1 31 lb . of butter at 28 ¢ a pound, and 27 lb . ofdressed chicken at 1 6 ¢ a pound . How much did she

receive for all ?

9 . A lady bought at a store8 lb . of coffee94 lb . of rice24 lb . of sugar8 cans tomatoes 1 3

20 cans beans 1 9

Find the amount of her purchases .

1 0 . Find the cost of :

27% lb . of cheese 1 89!

1 42 lb . of lard1 7 lb . of butter 27

25 bottles ammonia 8

1 2 cans peas 1 8

Written] PROBLEMS OF Two OPERATIONS 203

1 1 . A man earned each day in one week as follow s

Find hisaverage daily earnings.

Study of Problem3 1 . W hat is given in this

problem5 2 . What is required ?

3 . What is the first stepin the solution ? the second ?

4. W hy do you divide by6 to find the average

5 . Show that the answeraverage each day.

IS correct.

1 2 . Twomen contribute equal amounts to buy a lot for875 to build a storeroom for $4860 for furniture,$520; and for goods to begin business

, $5785 . Howmuch does each pay ?

1 3 . A creamery received milk for six days as follows7640 gallons, 8675 gallons, 9634 gallons , 8432 gallons,8763 gallons, and 8604 gallons . What were the

average daily receipts ?

1 4 . If Helen received 85 in arithmetic, 79 in grammar

,89 in history, 92 in geography

,86 in physi

ology,and in writing

,what was her average in these

studies ?

1 5 . The attendance at a school was 604 on Monday

607 on Tuesday, 598 on Wednesday, 603 on Thursday

598 on Friday . What was the average daily attend

ance for the week ?

204 FOURTH YEAR [written

1 6 . 39 ladies’ suits, each requiring 1 2 yards,weremadefrom a lot of cloth containing 576 yards. How manyyards were left ?

Study of Problem

1 . State this problem in

another way.

1 2 yd . in 1 suit .

39 number of suits.

1 08 2 . What operation is em36 ployed in the first step in the468 yd . in 39 suits. 801 11 1310 1 1 in the second

3 . Prove that the answer

576 yd 468 yd : 1 08 yd° is correct.

1 7 .A boy sold 1 6 books at 20 cents each, and 36 toys

at 26 cents each . How much more did he receive forthe toys than for the books ?

1 8 . Mr. Boyd ’s mail route is 23 12~ miles, and Mr. Bur

ton ’s is 1 71» miles . How much farther does Mr. Boydtravel in 84 days than Mr. Burton ?

1 9 . A school term is 1 80 days . If James attends gof the term,

how many days is he absent from school?

20 . A bookkeeper receives $1 50 a month , and saves

$68 a month . How much does he spend in a year ?

2 1 . Harry works 4845 hours after school each month,at 1 2 cents per hour, and Henry 52% hours at 1 6 cents

per hour . Find the difference in their wages .2 2 . What is the difference between the cost of 1 7

horses at $1 56 each, and 69 cows at $37 each ?

2 3 . A merchant buys 28 bbl . of sugar at $23 a barrel.and 36 bbl . at $24 a barrel . If he sells all for $1 856,how much does he gain ?


3 1 . A laborer worked 1 6 days at a day, and

w ith his earnings bought potatoes at 64 if a bushel.How many bushels did he receive ?

Study of Problem

1 . State this problemin another way .

daily wages.

1 6 number of days worked.

9 60 2 . How can w e find

1 6 0 the totalamoun t earned?

total wages.3 . What Operation is

involved in the fi rst step

of the solution in the

Price of 40 times, or bushels. second step

1 bu. .64) total Wages. 4. Prove that the ahswer is correct.

3 2 . If 1 24 bags of coffee, each w eighing 48 lh.

, werebought for what was the price per pound ?

3 3 . At 209“

per hour how long w ill it take a laborerto earn $80, working 8 hours per day ?

34 . If 96 bu . of corn sell for what is thevalue of 250 bushels at the same price ?3 5 . A trackman averages 2 miles per hour for 8

hours each day . His record book Show s 960 mileswalked . Find the number of days .

3 6 . If a dozen lemons cost $ 36, how much w ill 840lemons cost ?

3 7 . If 25 bbl . of flour weigh 4900 1b .

,how much will

56 bbl . w eigh ?

3 8 . If 23 carriages cost $4025, how much are 84

such carriages worth ?

Written] PROBLEMS OF TWO OPERATIONS 207

3 9 . If 600 bu . of shelled corn weigh lh., how

much w ill 468 bu . w eigh ?

40 . When 9 bales of cotton, weighing 325 lb . each,

sell for what is the price per pound ?

4 1 . If a peach basket holds 2 peeks, how manybushels are there in 1 2 carloads

,each contain ing 456

baskets ?

42 . How many books each 2 inches thick can beplaced in a bookcase containing 4 shelves

,each shelf

of which is 3 ft . in length ?

43 . If 1 23 tons of coal cost how much w ill1 6 tons cost ?

44 . 24 cords of wood cost $90 ; how much w ill 1 8cords cost at the same rate ?

45 . If a newsboy earns in 1 8 days, how muchw ill he earn at the same rate in 360 days ?

46 . When 525 gallons of milk sell for $84, for howmuch w ill 71 5 sell ?

47 . Mary bought 1 6 pounds of coffee at 1 414 a pound,8 lb . of butter at 28¢ a pound, and 1 2 cans of corn at

1 5¢ a can . She gave the merchant in payment a $1 0bill. How much change should she receive ?

48 . A drover sold 56 Sheep at $4 each, 8 cow s at$3 6 each, and 48 hogs at $1 2 each . If he received

$275 on the day of the sale, how much is still due him

49 . A lady had $1 00. If she bought 4 chairs at $6each

,a couch for $28, and a rocking chair for $1 6,

how much had she left ?


50 . I bought 57 yards of cloth at 25¢ a yard, and 1 6yards of matting at 28¢ a yard. Find the cost of both.

5 1 . A lady sold 6 doz . eggs at 1 8 cents a dozen, and

8 lb. of butter at 27 cents a pound. How much did she

receive for both ?

52 . A merchant bought 546 bbl. of pork at a

barrel, and sold it so as to gain $1 638. At what price

per barrel did he sell the pork ?

53 . James earned per day and saved 85 cents.

If his savings were how many days did he work ?

54 . A farmer bought 4 horses at 1 37 each, 7 cowsat $27 each, and 38 sheep at each . Find thecost of all .

5 5 . What w ill be the cost of 1 08 lb . of ham at 1 64cents a pound

,and 48 lb . of breakfast bacon at 1 8 cents

a pound ?

5 6 . Two automobile parties travel in opposite directions

,one at an average of 1 27 miles, the other at 78

miles a day. How far apart w ill they be in 1 6 days ?5 7 . A factory employs 56 men at a day, and

1 2 men at a day. Other expenses are 1 25 a day.

How much does it cost to run the factory 26 days ?5 8 . A man paid 1 65 for a carriage, and 3§ times as

much for a span of horses. How much did he pay forboth

59 . Mr. Hall deposited in the bank 3524 a monthfor 8 -1nonths, and $27 a month for 4 months. HOWmuch did he deposit in the year ?


COMBINING PROCESSES

1 .

z. 7 + 6 — 5

The parenthesis indicates that all numbers inclosed by it are to be considered as one number ; thus,

(7 9) (4 5) means that the sumOf 4 and 5 is to betaken fromthe sumof 7 and 9.

The vinculum is sometimes used instead of

the parenthesis ; thus, 7 9 4 5 7.

Solve3 .

4 .

— 7

5 .

6 . 87

7. (97 — 35)

8 . 86 — 28

COUNTING BY MIXED NUMBERS

1 . Count by 24 to 40 ; by to 40 ; by 61» to 50.

2 . Announce at sight

14x 4 14x 6 l§ x 6 li x

2 l§x 4 21

2-x 6 2§ x 6 2i x 4

34x 4 34x 6 3§ x 6 3i x

4gx 4 4-2l x 6 4

4x 6 44 x 4

3 . Build Similar tables w ith and 1g.

ANALYSIS

ANALYSIS

1 . Find the cost of 3 doz . oranges at 20 per dozen .

1 doz. oranges cost 20 3 doz . cost 3 times 20 60

2 . At 1 2 cents a quart for berries, how much w ill8 quarts cost ?

3 . At 30 a peck,how much w ill a bushel of beans

cost

4 . When peaches are 50 cents a basket, how muchw ill 7 baskets cost ?

5 . A ton of coal costs $5 . How much w ill 9 tonscost ?

6 . A boy rides his wheel 6 miles in one hour. Howfar w ill he ride in 7 hours ?

7 . When 5 boxes of matches cost 502, how muchw ill 1 box cost ?

Cost of 5 boxes 50

Cost of 1 box 4 of 50 or 1 0

8 . A boy bought 4 balls for 80 cents. How muchwas that apiece ?

9 . When 8 yards of velvet cost $24, how much w ill1 yard cost ?

1 0 . A box of Shoes containing 1 2 pairs costs $36 .

Find the cost per pair.

1 1 . Six cow s were sold for $246. What was theaverage selling price ?

1 2 . When a telegram of 1 0 words costs 40 cents,what is the average cost of each word ?


ANALYSIS

1 . When 1 pencil costs 1 0 how many can you buyfor 60 f

W hen 1 pencil costs 1 0 f, for 60¢ you can buy as many pencils as 1 0 if is contained in 60

2 . At 1 2 per yard, how many yards of ribbon can

be bought for 963 . Cherries are 8 If a quart . How many quarts can

be bought for 72

4 . When 3 tons of coal cost $1 8, how much w ill 7tons cost ? Cost of 3 tons 1 8 ;

Cost of 1 ton 1} of $ 1 8, or $6 ;Cost of 7 tons= 7 x $6, or $42 .

5 . How much w ill 9 dozen lemons cost when 3dozen sell for 45 cents

6 . Three men earn $30 in a certam time . Howmuch w ill 8 men earn in the same time

7 . W hen 4, a bushel of potatoes sells for 25 cents,how much w ill 3 bushels cost ?

Cost of bu.

Cost of 1 bu . 2 x or 50f ;Cost of 3 bu . 3 x 50 or

8 . At 20 cents a peck, how much w ill 2 bushels ofapples cost ?

9 . When milk is selling at 5 a quart,how much will

3 gallons cost ?

1 0 . If 7} of a yard of velvet costs 60 how much will2 yards cost ?


1 6 . A boy picked 1 8 quarts of chestnuts and soldthem at the rate of 2 quarts for 25 cents . How muchdid he receive for them?

1 7 . If 3 pounds of steak cost 48 cents, how muchw ill 1 0 pounds cost ?

1 8 . A farmer raised 40 bushels of Shelled corn per

acre on 74 acres. At the same rate, how many bushelswould he raise from 224acres ?

Find the cost of

1 9 . 288 chairs, when 9 chairs cost 5.

20 . 350 rings, when 7 rings cost

2 1 . 285 fans, when 5 fans cost

2 2 . 1 44 knives,when 6 knives cost

2 3 . 78 vases,when 6 vases cost

24 . 248 hats, when 8 hats cost

2 5 . 24 pictures,when 4 pictures cost

2 6 . 48 lamps,when 1 6 lamps cost

2 7 . 54 clocks, when 27 clocks cost

2 8 . 28 desks, when 1 4 desks cost

29 . 78 rockers,when 26 rockers cost

3 0 . 36 watches,when 1 8 watches cost 702 .

3 1 . 36 cords of wood,when 6 cords cost

3 2 . 1 28 tons of coal, when 8 tons cost

3 3 . 1 80 quarts of milk,when 1 8 quarts cost

3 4 . 56 crates of melons,when 8 crates cost

3 5 . 328 books,when 8 books cost

Written] BILLS 21 5

BILLS

PITTSBURG, PA ., 435 4 . I, 1 907.

Bought of C. H. MORRISON CC .,

1 854 PENN AVENUE .

2 644 . afififee ,8 eta/

1) . 6994 , 2 5

2 665. flou t ,

Observe that this bill shows : (1 ) the p lace and the

date ; (2) who bought the goods ; (3) who sold the

goods ; (4) the name of the goods sold and thep rice and

the amount of each sale .

The abbreviation for at should always be usedin making out a bill .To foot 8 bill means to add the cost of all the separ

ate articles .The word totalmeans the amount of the sales.Make bills of the follow ing sales, using a schoolmate

’

sname as purchaser, and your grocer as the one who sellsthe goods.

1 . 2 lb . butter, 25 ¢

6 lb . meat,

3 bars soap, 1 0


Make out bills as suggested on previous page .

2 . 3 skeins yarn ,

4 papers needles, 05

5 yd . ribbon, 50

3 . 5 bu . potatoes, 5

3 boxes peaches,

1 2 doz . lemons, 40

4 . 4 spools thread,

6 papers pins, 1 0

5 cards hooks and eyes, 02

5 . 5 lb . roast beef,3 lb . pork chops; 1 5

4 lb . lamb chops, 1 8

6 . 7 Silver forks,3 sterling spoons,4 napkin rings ,

7 . 4 nickel sponge racks,

5 hairbrushes,6 nickel towel rods

, 75

8 . 4 doz. linen writing paper,4 doz . linen envelopes, 1 5

1 2 stamps, 02

9 . 1 2 pkgs . flax seed,

3 oz . cologne, 1 0

5 lb. paint, 20

1 o. 2 music cabinets,5 rocking chairs,3 medicine cabinets

,


MEASURESChange1 . 1 6 pt . to gallons . 8 . 74 pk . to bushels.

2 . 24 bu . to peeks . 9 . 3750 yd . to feet .

3 . 3 sq . ft . to sq . inches. 1 0 . 3 in . to feet .

4 . 1 7 yd . to feet . 1 1 . 6 mi. to rods .

5 . 1 20 ft . to inches . 1 2 . 360 ft . to yards.

6 . 50 lb . to ounces . 1 3 . 4860 in . to feet .

7 . 6 T . to pounds . 1 4 . 6966 sq . ft . to sq . yd.

1 5 . How many dozen oranges,and how many over

are there in a box containing 1 43 oranges ? 1 65 oranges?1 95 oranges ?

1 6 . Find the number of square inches in a flow er bed4 feet long and 3 feet w ide .

1 7 . The slate blackboard is 3 feet w ide and 26 feetlong . Find its surface in square feet .

1 8 . A fruit dealer buys chestnuts at $3 per bushel,and sells themat $ 1 0 per quart . Find his profit .

1 9 . The schoolroom floor is 36 feet long and 28 feetw ide . Find the number of square feet in the floor ; inthe ceiling .

20 . James walks to school every morning, 600 yards .How many feet does he walk each day

,in going to and

coming from school ?

2 1 . A huckster sells 1 0 bushel-crates of peaches at 20cents per quarter peck . Find the amount fromthe saleof the peaches .

Written] PRACTICAL WOR! 21 9

PRACTICAL WOR!

2 4 0 f f.

MAIN STREET

1 . Mr. Stokes, a real estate agent, purchased this

plan of lots at $70 per front foot on Main Street . Findthe cost of the plan of lots .

2 . Mr. R . M . Holland purchased lot A at $1 1 0 per

front foot, and built on it a house for $6450. Find thecost of Mr. Holland’s property .

3 . Mr. Remington purchased lots B and C for $8000.

He put an iron fence around his lots at per foot .

Find the cost of the fence .

4 . The concrete sidewalk on Main St . is 1 0 ft . in

w idth . Find the cost of Mr. Remington’s walk at 1 9¢

per Square foot.

5 . Mr. Stokes sells lots D,E

, and F to L . F . Holtzman for $9500. Find his profits on these lots .


TEST PROBLEMS

Find the cost of 1 , when8 yards of cloth cost

4 barrels of flour cost $30.

1 2 kegs of nails cost

1 0 pounds of sugar cost $5 0.

8 pounds of butter cost $3 20.

9 gallons of milk cost

1 .

2

3

4

5 . 5 weeks’

wages are

6

7

8 2 bushels of peanuts cost

9 6 yards of cloth cost

1 0 . 8 pounds of dates cost

1 1 . 3 tons of hay cost $42 .

1 2 . 6 pairs of Shoes cost

1 3 . 3 crates of berries cost

1 4 . 1 2 dozen eggs cost

1 5 . What is the amount of a five-dollar bill, two

dollar bill,a half-dollar

,3 quarters, 2 dimes, a nickel, and

2 cents ?

1 6 . How much change w ill be given in takingfrom a ten-dollar bill ?

1 7 . Find the sum of 5 five-dollar bills, a two-dollarbill , 5 quarters, 4 dimes, and 3 nickels .

1 8 . How many minutes are there in 24 hours ?

1 9 . Write in Roman numerals the numbers from 1 00to 1 50.

222 FOURTH YEAR [Oral and Written

Add these examples in two minutes

Write and subtract in three minute

3 7 . 42 .

38 . 4 3 .

3 9 . 44 .

40 . 45 .

41 . 46 .

47 . Tell what you understand by each of the following : Sum, Q uotient, Plus, Minuend, Product , Addition ,

x Divisor,Multiplier, Remainder, Addends,

Units, pt .

,Roman numerals

,Dividend

,Subtrahend,

Multiplicand, Hundreds, Tens, bu ., qt., Diflerence,

ft., gal . , yd . , yr., mo .

,Subtraction

,

48 . Miss Pratt bought a ! odak for $20, a tripod fora roller for 75 cents , films for and a

carrying case for How much did she spend forthe outfit ?

49 . A street-car conductor collected 50 five-cent fareson the down trip and 63 five-cent fares on the returntrip. What was the amount collected

Written] TEST PROBLEMS 223

50 . Make change : Name the pieces in each instance .

Purchase Payment 1 0.

7.

5 .

.67 2.

.32 4.

$20.

$1 0.

$40.

5 1 . There are 1 489 children of school age in a borough ;the number enrolled in school is 896 . How many arenot enrolled

How many days are there in May,June

,July.

and August ? how many hours ?

53 . The Federal Constitution was adopted in 1 787.

How long ago was that ?

54 . Massachusetts was settled in 1 620. How old

was the colony in 1 776 ?

5 5 . How much must be added to to make$650 ?

56 . Mr. Tate earns $1 850 a year. He spends

$454 for food, $1 27 for clothing, $240 for rent,and

$376 for other expenses . How much does he save ?

5 7 . A man buys a lot for $675 . If he pays in threepayments $1 38, $225, and $1 75, how much does hestill owe ?

5 3 . An automobile cost $1 800. After paying $42for repairs it was sold for $1 520. Find the loss.


59 . In one yearmy coal cost me in addition tofor wheeling it into my cellar. The next year it

cost and for wheeling . Find the difference in cost for the two years .

6o. I paid $2875 for my house, and 1 267 less formy barn . Find the cost of both .

6 1 . A merchant had in cash He receivedfromsales during the day and paid outWhat was his cash balance at the close of the day ?

6 2 . A lady spent for gloves, for calico,. 1 9 for needles, and .56 for lace . How much changedid she get froma 1 0 bill ?

6 3 . A ship sails 4825 miles in 25 days . What isher average daily rate of speed

64 . The President ’s salary is a year. Howmuch is that a month ? a day ?

65 . How many days are there in 1 632 hours ?

66 . There are 36 inches in a yard. How manyyards are there in 241 2 inches ?

67 . During one month I paid for groceries,for meat, for milk

,for gas

,and

for light . How much did I pay for all ?

68 . Mr. Wilt pays 5 a month for fuel, it for

light, and for water. How much do the threecost him in a year ?

69 . A merchant deposits in the bank on six successive days , $475, $688, $ 1 365, $2475, $866, and

$3684. Find the amount of his deposits .

226 FOURTH YEAR {Written

80 . Make out a bill for the follow ing sales

1 0 lb . cheese 1 1 ¢ 1 2 1b . meat20 lb. sugar 54 2 sacks flour

81 . The Irving Public School had 360 pupils present on Monday, 365 on Tuesday, 350 Wednesday, 380Thursday, and 375 Friday . What was the average dailyattendance for the week ?

82 . Find the perimeter of your schoolroom.

83 . Find the number of square yards in a playground50 yards long and 30 yards w ide .

84 . Make a diagram 4 inch to 1 foot to show a rec

tangle 1 2 ft . long and 8 ft . wide . Find its area in squareyards.

85 . Explain how we find the number of square inches,square feet, or square yards in any rectangular surface.

86 . Amilk dealer pays $ 1 5 a gallon for hismilk, andretails it at 8¢ a quart . How much does he gain on

1 gallon ? How much does he gain on 25 gallons ?

87 . A load of hay w eighs 3700 lb . The wagon weighs1 200 lb . What is the value of the hay at $1 6 a ton ?

88 . Mr. Winter’s tax is $3 1 0. He pays $90 on

one property, on another, and the balance on

his home . Find the tax on his home .

89 . A man has $500 left after spending $300 of his

salary for rent, $225 for food and clothing, $75 forother expenses. Find his yearly salary.

Written] TEST PROBLEMS 227

90 . A fruit dealer bought 3 baskets of plums forHow much would 6 baskets cost at the same rate ? 2 1baskets

9 1 . The daily expenses of a salesman for one weekwere as follows : Mon .

, Tues ,Wed.,

Thurs , Fri. , Sat .

,If he

earned how much had he left ?

92 . How many working days are there fromMondaymorning, Sept. 4, to Sunday, Nov . 1 9?

93 . A clerk earns $24 a w eek, and spends $8 . In

how many weeks can he save enough to buy a suit at

$45 and a hat at $3 ?

94 . Each side of a box is 6 inches . How many squareinches of paper w ill be needed to cover it ?

95 . How many 5¢ pads can I buy for

96 . I bought a hamweighing 1 3 lb. at 1 3 55 a pound,and a 5-lb . pail of lard at 1 543 a pound, and gave $5 inpayment . How much change should I receive ?

97 . When a 20-lb. cheese is worth how muchwill a 1 0-lb. cheese cost at the same rate ?

98 . Amerchant sold in one day 3 dozen hats at $34each . Find the receipts from the sale of the hats.

99 . How much does a huckster receive for 3 bbl. ofapples 24bu. each, which he retails at 1 2 it a half peck ?

1 00 . Mr. Lykens employs in his store 24men at

a day, and 48 women at a day . His other ex

penses are $90 a day. How much does it cost himtoOperate his store for 1 day ?


1 01 . St. Clair School uses 379 pads of paper in one

school month . How many pads w ill it use in two

terms of 9 months each ?

1 02 . In 2 months James saves and his brothersaves How much can they both save in 4months

1 03 . Find the cost of 247 pk . of berries at 6¢ perquart .

1 04 . A box of soap costs A druggist buys 2boxes a month . How much does he pay for soap in3 months ?1 05 . Mr. Brown sets aside 1 00 for his vacation . He

Spends for traveling, $28 for board, and

for sundries . How much has he left ?1 06 . Mary bought sugar for soap for pota

toes for 24 coffee for 35$4, berries for 25 and meatfor 1 8 How much change should she receive froma

two-dollar bill ?

1 07 . At 8 15 a qt ., find the cost of 74gal . of milk .

1 08 . If a man earns 1 00 each month, and pays 22

for rent, and 36 for living expenses

,how much money

does he save each month ?

1 09 . How much does a merchant receive for 4 kegsof nails

,each keg contain ing 1 00 lb.

,sold at 44¢ per

lb. ?

1 1 0 . A wholesale dealer bought 67 bbl . of apples for1 75, 85 bbl . of flour for 1 69, 34 bbl . of potatoes for

$1 25 . How many barrels did he get, and howmuch didhe pay for them

230

Divide and test

N

N

H

H

H

H

H

H

H

H

H

I—l

w

p

o

go

q

gi

m

tb

w

n

p

p

2 2 .

2 3 .

9

9

71

9

9

6

00

8

“

a

1 6434 by 64

34643 by 28

1 9603 by 83

94432 by 62

26341 by 74

36236 by 37

42624 by 41

76342 by 36

64283 by 24

55022 by 82

44302 by 74

1 6792 by 81

28644 by 73

74305 by 37

83265 by 87

78325 by 75

85679 by 41

3941 0 by 52

80624 by 63

73 1 02 by 74

81 1 03 by 85

77777 by 96

88888 by 72

FOURTH YEAR

REVIEW

b

28792 by 270

75639 by 770

66041 by 602

77006 by 784

60424 by 603

90328 by 735

76028 by 344

84605 by 766

1 6248 by 860

74637 by 450

68026 by 360

841 32 by 770

70066 by 880

50468 by 480

66399 by 790

241 66 by 670

1 2345 by 1 54

67890 by 221

89765 by 336

432 1 0 by 742

34786 by 8 1 9

57602 by 745

80703 by 61 3

[Written

6

33467 by 890

77304 by 860

44384 by 280

35690 by 76188762 by 892

56044 by 883

76428 by 444

23688 by 985

55624 by 666

34632 by 555

99240 by 461

36002 by 880

45676 by 390

76324 by 302

2532 1 by 440

65436 by 784

70504 by 621

62 1 3 1 by 905

88776 by 860

54340 by 40882 1 07 by 32962434 by 75293785 by 607

Written] REVIEW 23 1

24 . A real estate agent bought a field of 20 acres for$2000. He sold 8 acres at $1 25 an acre, and the restat $90 an acre . How much did he gain ?

2 5 . My gas bill averages $3% per month, and my telephone bill 83—12 permonth. Find the yearly cost of both .

2 6 . At 9 palings to the yard how many palings arerequired to fence an oblong garden 20 yards long and1 5 yards w ide ?

2 7 . A man living in Chester does business in Philadelphia

, which is 1 395 miles distant . How many milesdoes he travel in going and returning every week of

6 days ?

2 8 . In the morning he takes a train leaving atand arriving at in the even ing a train leaving at

and arriving at How many hours andminutes does he travel on the train during the week ?

29 . A lady buys 2 pieces of ribbon for paying5 cents per yard . There are 8 yards in one piece .

How many yards are there in the other ?3 0. I bought a horse for $250, and sold it at a gain

of of the cost. At what price did I sell it ?

3 1 . How much is received for a barrel of potatoes containing 2§ bushels, if it is retailed at 1 0¢ a half peck ?

3 2 . A workman,who earns $295 a day, is injured by

an accident and loses 8 days’ work . How much moneydoes he lose ?

3 3 . Find the cost of 6 dozen oranges at the rate of 4

oranges for 1 2 cents.

232 FOURTH YEAR

3 4 . There are 30 passengers seated and 1 3 standingin a car, in which the conductor has collected in

5 ¢ fares . How many people have left the car ?

3 5 . An oblong field is 80 rods long and 25 rods wide.Howmany rods of fence w ill it take to inclose it ?

3 6 . How many square yards are there in a room1 8 feet long and 1 5 feet w ide ?

3 7 . Find the perimeter of the roomin Ex . 36 in yards ;in feet ; in inches .

38 . A newsboy buys L eaders at the rate of 5 for 3 f,and N ews at the rate of 7 for 1 0 How much does hegain on the sale of 65 L eaders at 1 ¢ each, and 35 N ews

at 2 15 each ?

3 9 . Find the perimeter in feet, and the area in squareinches of an oblong 26 inches long and 1 8 incheswide .

40 . By selling a horse for $260, I lost $35. Howmuch should I have gained by selling it for $3 1 0 ?

41 . A lady bought 4 pairs of kid gloves at a

pair, 1 8 yd . of cambric at 1 5 15 a yard, 8 yd . of muslinat a yard

,and 1

,dozen ' linen napkins at $4 a

dozen . Find the cost of all .

42 . The population of the United States increasedfrom in 1 820

,to in 1 906. Find

the increase in this time .

43 . A boy earns each working day,and his ex

penses are a week . Find his profits in 4 weeks.

234 FOURTH YEAR [Oral

6T 2

1 r 2 .

1 : 7 I ? ) 19? 7 , 5‘ ‘

33 5 “

P 5454 " ? — 0nes.

2 . g oi a circle equals { 7 of the same circle .

Draw circles or oblongs to show these relations.

3 . Which is larger, 137 of an apple or g. of the same

apple ? 33: of a dollar or gof a dollar.

7 .

4 ° t — 1‘

z r s r e fi t if? — 0n93

In the fraction the four show s into how manyparts some single thing has been divided, and the threeshow s how many parts are taken.

The number in a fraction that tells the number ofparts taken is called the numerator.

The number in a fraction that show s the number ofparts into wh ich some single thing has been di’vided iscalled the denominator.

5 . Name the numerators,then the denominators, in

the following fractions

t ; «37 ; vi ; i} ; 171

To change a fraction into ones and parts of ones, di

vide the numerator by the denominator.

— ones ; l63 = fir ; 1

Written] FRACTIONS 235

1 . Add % and 3.

it

‘h ‘ l' s {i

2 . Add ; and g.1

T4,

31

3 . From 1 23 take 1 2 1 2%9 9g

1 2g dlfference

First add,then subtract

6 . 1 2% 8 . l6ig» 1 0 . 1 5gr 1 2 . 1 2g6% 6g 5; log 1 0g

5 . 1 11-90

7 . 6-3 9 . 41 -3 1 1 . 1 6% 1 3 . 1 5177

4g 5% 1 63} 1 2g 54,

Add

1 4 . + g. 1 6 . 1 8 . ao.

112

1 5 .1 1 1 7 . 1 9 . {7 1

2a 2 1 . 1 35 3i» .

2 2 . James worked 3% hr. on Saturday and 1ghr. on

Monday . How many more hours did he work on Sat

urday than on Monday

2 3 . Frank ’s marks for the month average 915, andJohn ’s average Find the difference in theiraverages .

236 FOURTH YEAR [Oral and Written

Sixteenths

1 . Draw circles as here shown, divided as indicated.

2 . Compare in size the first fraction w ith the second

i-and2

8 ;l and l and

fi ; 3and g; a; and I

-92

3 . Draw circles and show that156= iii" :

41

5 . Change to fractions, having the smallest possiblenumber in both numerator and denominator :

. o . .

5 : 155 : I 5 : i s , I s :

195 : 355 » t ut

6 . Draw circles or oblongs and show that 12 1

93

.

7 . Change to ones and parts of ones :-; i ; 15

9s24

1 —5

First add, then subtract

8 . 1 055T 1 0 . 1 553 1 2 . 1 6155 1 4 .

435 4}

9 . 1 9g“ 1 1 . 8fl 1 3 . 1 5§43:

5: 1 0:

238 FOURTH YEAR [W ritten

1 . The floor of a room is 1 3 13 ft. long and 1 2} ft.w ide . Find the distance around the room. How muchlonger is the room than

‘

it is w ide ?

2 . Mary’s hair ribbon is 1 5§ in . long and 12 in . w ide.Find the difierence between the length and the W idthof the ribbon .

3 . James worked after school 1 § hr. Monday, 1 1> hr .

Tuesday, 1 % hr. Wednesday, 2 hr. Thursday, and 1ghr. Friday. On Saturday he worked hr. Howmany hours did he work during the week ?

4 . Morgan lives 1 %mi. fromschool, and Frank mi.in the same direction . In going to school, Morganwalks how much farther than Frank ? Find the distance both walk in going to, and coming fromschool ina day .

Find fractional parts

5 . g of 48. 9 .

136of 1 260 yd . 1 3 .

152 of 360 da.

6 . f} of $92 . 1 0 . of $9600. 1 4 . of

7 . of $80. 1 1 . g of $1 89. 1 5 . {v} of

9 . g— of 550 rd . 1 2 . of 984. 1 6 . gof 3

1 7 . There are 21 36 pupils on the school roll. If H»

were there Monday,how many were absent ?

1 8 . A gardener sold 2032 qt. of berries in one summer.

He received 8¢ per quart for gof the berries, and 5 f

per quart for the balance . For how much did he sellthe berries ?

Oral] SOLIDS 239

This block or solid is 1 in .

long,1 in . W ide

, and 1 in .

high .

It has six equal sides lin.

called faces, and each facecontains 1 square inch .

A block or solid w ith 6

equal square faces is called a lin.

cube.

A cube whose faces are each a square inch contains acubic inch , written cu. in .

To THE TEACHER. Secure 50 1 -in . cubicalblocks. Have pupilsbuild solids

,and count the number of cubic inches in each solid ;

the number of square inches on each face.

1 . Build figure 1 with inch cubes .How many cubes does it take ?

2 . Build figure 2 w ith inch cubes.How many layers of blocks are there.?

E m' 1 ° How many in each layer ?

In 1 layer there are 6 cu . in .

In 2 layers there are 2 x 6 cu. in .

1 2 cu. in .

The number of cubic inches or cubicfeet in a solid is called the volume or

FIG . 2 .

contents of the solid .

3 . Build 1 2 blocks into a solid thathas 4 blocks in each layer. How many layers are there ?


4 . Build figure 3 w ith inch cubes . How many doesit take ? How many layers ? Howmany are there in each layer ? 3 x 6

cu. in . 1 8 cu . in. in the solid .

5 . Build 1 0 other solids w ithblocks

,and ascertain the number of

blocks in each .

6 . A brick is 8 in . long,4 in . w ide,

and 2 in . thick . Find its volume incubic inches.

7 . A piece of wood is 3 in . w ide, 3 in . thick, and 4 in .

long . How many cubic inches does it contain

8 . A boy’s book is 4 in . w ide, 1 in . thick, and 6 in .

long. Find the number of cubic inches in the book .

9 . Mrs. Adams has a flower box that is 24 in . long,

8 in . w ide,and 6 in . deep, inside measurement . How

many cubic inches of soil w ill it take to fill it ?

1 0 . A square stick is 3 in . w ide, 3 in . thick, and 1 2 in .

long . How many cubic inches are there in the stick ?

The inside of a box is 5 in . long,4 in . w ide, and

3 in . high. How many inch cubes can be built into it ?

1 2 . A box is 1 0 in . long, 6 in . w ide, and 5 in . high ,

inside measurement. How many cubic inches of sandw ill it contain ?

Primary Arithmetic for Graded Schools - Forgotten Books

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