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^ijV
IN MEMORIAM
FLORIAN CAJORI
'4.
I
SCHOOL ARITHMETIC
PRIMARY BOOK
BY
JOHN M. COLAW, A. M.
AS80CIATB EDITOB OF THE AMEBICAN MATHEMATICAL MONTHLY,
MONTEREY, VA.
J. K. ELLWOOD, A. M.
PBINOIPAL OP THE COLFAX PTJBUC SCHOOL, PITTSBUBG, PA., AUTHOB OP
TABLE BOOK AND TEST PBOBLBMS IN ELEMENTABY MATHEMATICS.
^
RICHMOND, VA.
B. F. JOHNSON PUBLISHING CO.
1900
XJHNSON SERIES
School Arithmetics
.. BY..
COU V AND HiVCOD
Primary Book^^^^^^J^^- _
± ^ ..number Vcarfc
2^1 Pages Price 55 Cents ■
Advanced Book ^^ j'^tenr^iiate and
Higher Grades
Wth an Introduction to Algebra
442 Pages Price, 6o Cents
J«
HANDBOOK FOR TEACHERS
Containing Suggestions as to the best methods of
teach J^ ^ithmetia»4 aw* ac^,viti6ns of diffi-
CAJORl
Oopy^ri^hU liMKi, by
J. M. COLAU' aii{J J. K. Ell WOOD.
\.
PREFACE.
TITO DEVELOP in the pupil's mind the idea of number and
I its uses, to give him facility in numerical operations, and
«-*^ to lead him to grasp firmly the principles involved requires
the serious effort of the most skilful teacher. The most any
author can do to aid him is to present, in more or less detail,
an outline of a practical scheme of instruction based upon the
latest and best thought in number teaching; and even this is
a task that none but the superficial would undertake without
" fear and trembling." Neither theory nor practice alone is
a suflBlcient endowment for the work. Every theory, every
method, every device must be weighed in the class-room balance.
That which is to be taught is the child — ^not arithmetic.
Holding these views, the writers of this book have spared
no effort in its preparation. With a wholesome respect for the
injunction, " Prove all things; hold fast that which is good,"
they have endeavored to steer carefully between the Scylla of
modern fad and the Charybdis of mechanical drudgery and
stupefying monotony. Their aim has been to furnish for the
teacher a sound and practical work presenting the matter in
an approved order and suggesting rational methods of obtaining
the most desirable results. As to how well they have succeeded
the teacher must decide.
Arrangement. — Before entering school the child learns a
little of a great many things, not a great deal about one thing.
There is no topical arrangement in nature. "And Nature, the
dear old nurse," permits the order of the child's mental develop-
ment to determine the arrangement of the material, which is
alv^ays a progressive one. The child learns a little about many
things to-day, a little more to-morrow, adds an increment to
his knowledge and widens his range of subjects day by day.
This arrangement keeps interest alive, without which there is
no substantial progress. This book aims to follow the natural
[v]
^11274
VI PBEFACE.
order as closely as may be, oonsldering the conditions under
which teachers are required to work.
" Fbom the Concbete to the Abstract." — The child's mind
must be approached through those ever open doors, the senses.
Primary number teaching must be begun by the pupil's observ-
ing and handling objects, yet the mere presence of concrete
things does not guarantee the presence of definite numerical
ideas in the mind of the pupil. They must be so presented as
to stimulate and aid the mental movement of discriminating
and relating which leads to definite ideas of number. The
mind must (a) recognize the like objects as distinct individuals,
and (6) group (put together) the objects into a whole. The
child's own activity must conceive a whole of parts, and relate
the parts in a definite whole. It is not enough that he knows
our country as 45 states; he must know the 45 states as one
country. He should recognize five, for example, not only as
five ones, but also as one five, considering the component ones
not chiefly for their own sake, but as giving definite value to
the whole, the group. By repeated acts of such measurement
or valuation the mind advances naturally and inevitably from
things to relations, from facts to principles, from the concrete
to the abstract. Believing that the concept of ratio — an abstract
idea — must be evolved in the young mind by its own activity,
and that therefore it should not be thrown nt the child in the
earlier stages of his progress, the authors have not explicitly
stated the ratio idea until it has had time to grow into a
recognizable and useful product of the pupil's mind.
Material. — The objects called for in this book, such as cubes,
splints, foot rules, quart measures, etc., can be provided by
the teacher with little trouble, and their use should precede
that of pictures and words. How long their use should be
continued with any given class must be determined by the
teach *^r. They should certainly not be laid aside until the child
i;fln brlnf^ their images into consciousness without the presen-
tation of the actual objects to his senses; but when these images
lire withio easy reach, their use should supersede that of objects.
The number pictures given in this book are an important aid
to the child's mental movement of abstracting and relating,
and must ^e used for economy of energy. Five dots analytically
arranged (J* J) are more easily grasped than .five dots placed
i^
PREFACE. Vii
promiscuously, or even in a row. Moreover, they are perceived
as one whole, rather than as separate, unrelated parts, and
they should symbolize any five units whatever — ^five $2 or five
10-ft. as well as five |1 or five 1-ft. In the perceptive form
• • • •
• • • • , twelve is seen as three fours and as four threes — ^as four
• • • •
three times and as three four times — and the child's idea of the
number is more definite than when the whole was measured
by but one unit, the individual. Besides, this use of pictures
suggests to the pupil a method by which he can discover for
himself the measuring units of quantity or determine the definite
value of a whole. In notation, fractions, measurement erf
surfaces, etc., the illustrations will be found highly beneficial;
their purpose is to aid, not to ornament.
Counting — Measuring. — Dr. Harris says, " The first lessons
in arithmetic should be based on the practice of measuring in
its varied applications." In its earlier stages measurement is
a vague estimate, a crude guess. Later an undefined unit of
measure is used to make a whole more definite, as when a
class is measured by the unit boy — an unmeasured unit. But
it is only when the unit itself is accurately defined that precise
numerical value is reached. The immediate purpose of measur-
ing 19 to make some whole more definite — to find how much
there is of it This can be done by learning how many units
are in it, and the ** how many " can be found only by counting;
hence measuring involves rational counting— the finding of the
sum of the units that compose a whole. It seems clear, there-
fore, that the child learning to count should be led to number
the parts that make up some whole, as the desks in a row — ^to
count with a definite end in vieio; that the starting point should
be a group of things — a whole to measure, parts to count and
relate. As soon as possible there should also be exact measure-
ments. The foot may be taken as the whole and measured by
4-inch units, 3-inch units, etc. Not only the idea of number
as the repetition of a unit of measure to equal a magnitude,
but also the law of commutation will be slowly, perhaps, but
surely developed through the use of the facts supplied by sense-
perception in the rational use of objects and number pictures.
Figure Processes only the Means to an End. — The child
must learn figure processes, not for their own sake, but as an aid
in discerning relation. Figures are not at all necessary to
VIU PREFACE.
numerical perception, but when this is to be supplanted by
numerical facility they should be employed as a convenient
tool. The real subjects of thought are magnitudes (of value, of
space, of weight, etc.) and their relations; figures are mere
symbols of these. The essential thing is the discernment of
relation by comparing magnitudes; figure processes may or
may not be an aid in securing this end — ^they can never be
anything more. It is evident, therefore, that the mere manipu-
lation of figures — the mechanical work — is of small value in
comparison with the thought processes — ^the mental work;
yet as the means to an end it is of great importance, and to
secure absolute accuracy therein should be the constant aim
of every teacher.
Suggestive Questions and Directions. — The exercises of
this book are more abundant and varied than is usual in books
of this kind, and much additional work will be called forth
by the suggestive nature of many of the questions and directions.
There is an especial need of an abundance of constructive
exercises. The pupil must be active, must do as well as see.
Knotcing and doing are correlative. Things are grasped most
readily when there is a necessity, real or apparent, for knowing
them. Boys who sell papers or fruit on the streets, being under
the necessity of computing and making change, enter school
with a surprising stock of number facts. Excellent number
woik may be had in connection with the occupations of the
school-room — passing pencils, making boxes, modeling, playing
number games, measuring things used in nature study and
manual training, etc. The questions and directions given
indicate the kind of^work that should be done, but the quantity
of it needed must be determined by the teacher, and by him
supplied when necessary. Figures and signs are not used until
the child has acquired some familiarity with the names of
numbers to twelve and with a few of the simpler processes and
facts. This should at least suggest that the figure symbol
should not be given until the child can understand that it is a
mere mechanical tool by which he can obtain rapid and at the
same time equally true results.
It is neither necessary nor desirable to keep this book out
of the hands of young pupils until they are able to read it
with ease. They should at least get the benefit of the number
pictures and the picture exercises. Anything too difficult for the
_ I
PBEFAOE. IX
children sihould be read by the teacher, and answers onli/ required
of the pupile. Formal analysis should be deferred; when
insisted upon at too early a stage, it interferes with progress
and deadens the pupil's interest
It is believed that in plan, matter, and method this book is in
substantial accord with the views of progressive teachers in
the best schools, and that It will prove a suitable foundation
for and introduction to the more formal and rigorous treatment
presented in the Advanced book of the series. Its contents are
such, however, that pupils who can complete only this book
will find themselves .fitted to cope with the ordinary problems
of every-day life.
The Authors.
July 2, 1900,
CONTENTS.
First Steps:
Indefinite Comparison, Form, Counting, Measuring —
Use of Ruler, Concrete Exercises .... 1-43
Primary Number Work :
Numbers to 10— Combinations (Emphasis on Adding
and Subtracting), Pint, Quart, Gallon, Half, Fourth,
Third, Peck, Bushel 44-74
Tens 74-83
Review and Drill 84-91
Writing and Reading Numbers from 1 to 100 . . 92-95
The Signs X and ^ ^^ . .7^^ 96-99
Numbers to 20— Tens and Ones, Combinations, Month,
Year, Roman Notation, Fifth, Ounce, Pound, Sixth, 100-134
Review and Drill 135-136
Twenty— Two Tens, Tenth 137-142
Numbers to 100— Development of Tens and Ones . 143-147
Addition and Subtraction 148-154
Numbers to 30— Table of 3's, Square Foot, Easy Areas, 155-160
Numbers to 40— Table of 4's ..... 161-168
Numbers to 50— Table of 5's, Square Yard . . . 169-173
Addition and Subtraction 174-188
Numbers to 60— Table of 6's, Hour, Minute, Second . 189-195
Numbersto70— Tableof 7's 196-202
Numbers to 80— Table of 8's, Perimeter . . . 203-208
Numbers to 100-Table of 9's, Cubic Inch . . . 209-216
Review and Drill Work 217-227
Hundreds— Cent, Dollar 228-232
Hundreds and Tens -. . 233-235
(xi)
pOHOOL ABITHMETIO.
Show me the shortest.
Show me the next shortest.
How many of these splints are longer than B?
How many of these splints are longer than A?
How many of these splints are shorter than B?
How many of these splints are shorter than C?
^=1
Oi
A B
3. Blocks of this shape are called cubes.
Which is the largest cube?
Which is the next largest cube?
Which is the smallest cube?
Which is the next smallest cube?
How many cubes are larger than C?
How many cubes are smaller than A?
What can you tell me about B?
4 Which is longer, the length of your desk or its width?
Which is wider, the sidewalk or the street?
Which is longer, your arithmetic or your slate?
Which is thicker, your book or your slate?
Which is larger, a boy or a man?
Which is higher, your house or the school-house?
COMPARISON. 3
5. Here are two groups of cubes. |^
Which is the larger group? Jp JP IP JP •
How many more cubes in the larger group than in the
smaller one?
© ©
Which of these rings has the most dots in it?
The ring on the left has how many more dots than the
one on the right?
Are there more girls than boys in the class? How many
more ?
Note. — Children should be given sufficient exercise in making
comparison to familiarize them with the use of the terms longer,
shorter, larger, smaller, higher, wider, etc. They may compare
solids, surfaces, lines, sounds, or any objects within reach or sight.
6, Here are pictures of a square, a circle, a triangle,
and a sphere.
Show me the square. Show me the circle.
Now show me the triangle. Show me the sphere.
Take four sticks of the same length and make a square.
Cut a square out of paper. Name something that
resembles a square in shape.
4 SCHOOL ABTTHMETIC.
From pasteboard cut out six equal squares. Make a
box of them. What have you? Name some object shaped
like a cube.
Lay a penny on paper and draw a line around it.
Cut out the circle. Name something that is a circle
in shape.
Draw a square on the blackboard. Now draw a circle.
Did you draw straight lines in making the square?
What kind of line around the circle?
Here is a marble. What is it shaped like? Is your ball
a sphere? What part of the body is almost a sphere?
Note. — Have pupils observe and handle solids until they know
the familiar cube, sphere, square, triangle, circle. Have them
model simple forms, and cut squares, circles, etc., from paper.
Oounting to Twelve.
7. How many boys are in the class? How many girls?
How many seats are in this row?
How many sides has this square?
Count the faces of this cube.
How many pairs of shoes in the class?
How many groups of three blocks?
m m
e e e e e e e
Here are twelve spools. Arrange them in pairs, and
count the number of pairs.
Arrange them in groups of three, and count the groups.
MEASURING USE OP RULER. O
Here are some dots.
How many twos? ••••••••••••
How many threes? \^ S« S^ S^ S^ S« S« S«
How many fours? XX •• •• •• •• ••
Measuring — Use of Ruler.
8. This line is an inch long.
Draw a line as long as the one above.
Cut four sticks each as long as the line. How long is
each stick?
How many sticks are as long as the line below?
Then how long is this line?
Find how many inches wide this book is.
How long is your pencil?
Draw a line four inches long.
An inch lower, draw another line four inches long.
Rule a page of this paper with lines an inch apart.
9. How long is this square? How wide
is it?
Are all four sides of the same length?
A sqnsLre that is an inch on a side is
called a square inch.
Draw a square inch on paper. Cut it
out.
6
SCHOOL ARITHMETIC.
Cut out a piece of paper two inches long and one inch
wide.
How many square inches can you make of it?
Draw a square two inches on a side.
Into how many square inches can you cut it?
4 5
8 9
10
12
10. This is a picture of a ruler reduced in size.
Here is a real ioot-rule. It is a foot long.
Use the rule to find how long this table is.
How many feet wide is the table?
Measure this line on the blackboard. How long is it?
What is the length of this blackboard?
Cut a strip of paper an inch long.
Find how many strips are as long as the foot-rule.
There are twelve inches in a foot
The Numbers One and Two.
• • •
11. How many dots are on the first card?
Hold up one finger. Hold up one more finger.
How many fingers are you holding up?
How many fingers are one finger and one finger?
Show me two hands. Show me two buttons.
Two boys are how many more than one boy?
THE NUMBER THREE. 1
Here is a square. □ Make pictures of two squares.
How many stars are ^ and ^ ?
How many books are one book and one book?
How many are one and one?
Here are two squares. □ □ Push away the one on
the right. How many are left?
Make two marks on the board. Kub out one mark.
How many are left?
One marble from two marbles leaves how many marbles ?
How many more cents are ^ ^ than ^ ?
How many cents must be put with one cent to have
two cents?
A\ and /\ are how many triangles?
O and O ^^^ ^^^ many circles?
• from S leaves how many dots?
□ and are n n ?
How many ones in two?
The Number Three.
:.
12. How many dots are two dots and one dot?
Make the three dots on the board.
Show me three books. Three fingers.
Say school three times.
How many sides has this triangle? ^
8 HOlUHiU ABITHMKnO.
Wlmt inuuber coineH before three? Before two?
Wluit luunber in l)otvvoen one and three?
Iliuv umny rings uro O O aii^l O ?
IIqw mmxy ntarn uro ^ and ^ ^ ?
Jltjw many oowh are two eows and one cow?
1 June ono (*nbe, (Jive \\\v enongh to make three.
Here aiv thiHH> dots, • • • Cover one dot. How many
aiv not eoveit^d?
(\ner two dots. How many ean yon see?
|l| |l| fn^n^ |l| |l| |l| 1ea\ i^ liow many tl^igs f
ci^ J^ J^ *^^"^ J^ «^^ '^^^^^* "^^"^^ ^^^^^^-
Meas\uv this yaixlstiok with ymir t\H^t-ruU\ How long
is hi
19L How many t>/^^^' in J* I
How many ^»vn in JJ 1
How uiany ; (/ ".-s ^♦f t\vv>s- in 22 •• ^
Saow n'o two ''i-'^^s^ u^ri^ ^p*:y"s.
Make T>iv*ritivs «>r "^rt-*. ^r»u::'?- <«r ^rars*
Make *>icPirv< *►:' ''i-te ^'.r^ "i :liks^
a
.V. ^^
*.A^ *,A> *.jik> -^-^ -^^-^' ^^^*^AkS'
THE NUMBER FOUB. 9
15. Two dogs and one dog are how many dogs?
One foot and two feet are feet.
There were three birds on the fence, but one flew away.
How many were left?
Mary had three pennies, but now she has only two. How
many did she spend?
My hat cost three dollars. I have paid one dollar; how
much do I owe?
Tom ate one apple and had two left. How many had
he at first?
Charles has three rabbits, and Paul has one less. How
many has Paul?
The Number Pour.
• • • •
• • •
16. Make a triangle with these three splints.
Now try to make a square with them.
How many more splints do you need?
How many dots are on the card to the right?
How many sides has a square?
How many seasons in the year?
Tell me the names of four boys.
How many letters in the word four?
Take two cubes in each hand. How many cubes have
you?
10 SCHOOL ARITHMETIC.
How many triangles can you make with these twelve
splints ?
I have one cube. Give me enough to make four.
If I give you one, how many will I have left?
Cover two of the dots on the right-hand card. How
many can you see?
Show me the number of splints these words stand for:
three, two, four.
Copy these pictures, and write under each group the
word for the number (how many) in each group:
^ DDDn OO AAA
17. How many tops are ^ ^ ^ and ^ ?
How many marbles are ^^ and ^0 ^0 ^0 ?
How many cents are ^p ^p and ^ @ ?
(^ from (^ (^ (^ (^ leaves how many apples?
O O O O less O O a^e liow many circles?
There are four splints. Give me half of them.
How many have I? How many have you?
This line ' is one inch long.
In one inch there are half inches.
This line '— : 1 ' is two inches
long.
In two inches there are half inches.
In (^ there are H M (haK-circles).
In two circles there are half-circles.
THE NUMBER EOtlB. 11
18. How many ones in JJ ? How manj twos?
Show me four twos with splints.
Make pictures of four pairs of tents.
Here are four tops. ^ ^ ^ ^ How many boys
can have one top each?
Here are four pears. ^ ^ , ^ ^ How many girls
can have two pears each?
Cut a strip of paper three inches long.
Find how many strips are as long as your foot-rule.
Cut a strip of paper four inches long and one inch wide.
Find how many square inches will cover it.
Ask your papa how many quarters make a dollar.
Ask your mamma how many quarts in a gallon.
19, Copy and complete, then read:
m D cuvuJL n cxAAy .
O cuvbcL O O O ou^Ji. .
A A A A t(L>€i>c^ A ciA.^ .
]^ ]^ ]^ ]^ ^^^^ ]^ ]^ ]^ aA>o .
20. Three boys and one boy are how many boys?
One tree and three trees are how many trees?
Two sheep and two sheep are sheep.
12 SCHOOL ARTTHMETIO.
Harry had four apples, but gave one to May. How
many had he left?
You have four fingers on one hand. If two were cut
off, how many would you have left on?
Alice had four kittens, but three of them died. How
many has she left?
How many ears have two rabbits?
How many boys have four heads?
How many bicycles have as many wheels as a wagon?
The Number Five.
• • • * •
21. How many dots on the left-hand card?
How many more are on the other card?
How many fingers on your left hand?
How many, counting the thumb?
Tell me the names of five boys.
How many cents is a nickel worth?
What number follows four?
What number is between three and five?
I have four beans. Give me enough to make five.
Take three blocks. Now take enough more to make five.
Take five beans. Separate them into two piles, thus:
Two beans and three beans are how many beans?
THE NUMBER FIVE. 13
Take one bean from the smaller pile and put it into
the larger.
Now what two numbers make five?
Here are five rings. O O O O O Cover one of
them. How many are not covered?
Cover two of them. How many can you see?
Ask your papa how many nickels make a quarter.
22. How many ones in J*J ?
Show me two fives with beans.
Show me five twos with beans.
I
ABC D
By how many squares is D larger than C? Than B?
Than A?
A and B together are as large as .
How can we make C as large as D?
Take one square from D and put it with B.
B is now as large as or .
Draw a line five inches long on paper.
Draw a line five feet long on the blackboard.
14 SCHOOL ABITHMETIO.
23. Copy and complete, then read:
O O O O cvvbcL O oJxjo .
AAA cuvixL A A oJxJu .
f^ ]^ ^ ^ ^ ItJiA^ ^ 1^ ^ aA<^
24, Four dolls and one doll are how many dolls?
One finger and four fingers are fingers.
How many splints will make a triangle and a tent, if
the tent is made like this /\ ?
Sam had five cents. He spent one cent for candy. How
many has he left?
Fred had five marbles and lost four. How many has
he left? .
We have school five days each week. If you stay at
home two days, how many days do you come to school?
Xed had five chickens. The cat killed three of them.
How many has he left?
If your papa gives you a cent every day, in how many
days will you have a nickel.
Jennie bought a tablet for four cents. She gave the
clerk a nickel. How many cents should she receive back?
THB NUMBER SIX.
16
The Number Six.
• • •
• • •
25. Here are five splints. Make a triangle and then
make a tent like this /\.
Can you make two triangles with the same splints?
How many more splints do you need?
How many dots are on the card to the left?
How many more dots are on the other card?
Five dots and one dot are how many dots?
Hold up six fingers.
Here are twelve splints. Make as many tents like that
above as you can with them. Now count them.
What number follows five? What number comes
before six? Before five?
I have five cubes. Give me enough to make six cubes.
Take six blocks. Put four in one pile, two in another.
Are six blocks as many as four blocks and two blocks?
Now arrange the six blocks in two equal rows.
How many are in each row?
Three blocks and three blocks are how many blocks?
How many dots are here? •••!••• Cover one of
them. How many do you see?
16
SCHOOL AMTHMETIO.
One dot from six dots leaves how many dots?
Cover two of them. Tell me what you see.
Two dots from six dots leaves how many dots?
Cover three dots. How many can you see?
Three dots from six dots leaves how many dots?
How many dots can you see* if you cover four of them?
Cover five of them. Tell me what you see.
Copy the cards below, and put in the dots needed to
make six dots on each card.
• • • • • •
• • • • •
26. How many twos in J J J ? How many threes?
Show me two sixes with cubes.
How many cubes have you used? _
Cut a strip of paper two inches long.
How many strips are as long as your foot-rule?
Cut a strip of paper six inches long and one inch wide.
Into how many square inches can you cut it?
Draw a line six feet long on the blackboard.
Measure the line with this yardstick. How many yards
long is it?
A line six feet long is yards long.
Ask your mamma bow many eggs there are in a half-
dozen.
THE NUMBER SIX. 17
27. Copy and complete, then read:
^ ^ ^ i^ ^ a/yuL -^ oAju .
/// ouruL /// oAAy -^ .
• • • • CUTUL OAA. J J J.
O O O O O O teA^ O O aA>e. .
A A AAA A ^^^^(^ oA^ A A.
€uyuJuJ^ c4 AAA AAA '^ -
28. How many days in a week, not counting Sunday?
George gave me five roses and Ed gave me one. How
many did I then have?
One pig and five pigs are — » — pigs.
Robert is four years old. How old will he be in two
years ?
Two bears and four bears are how many bears?
There are three cows on each side of a fence. How
many cows are there?
Name two numbers that make six. Two other numbers.
From six blocks take away two blocks. How many are
left?
How many more are six cents than one cent?
Then what two pieces of money make six cents?
This morning I had six apples* Now I have only three*
How many have I eaten?
18
BOHOOL ARITHMETIC.
What part of them have I eaten? What part have I
left?
Make six dots on your slate. Put a ring around one-
half of them.
One-half of six dots is dots.
Ask your papa how many cents will pay for three two-
cent stamps.
The Number Seven.
• • •
• • •
• • • •
• • •
29. Make two ^'s with these six splints.
Can you make a triangle and a square with the same
six splints? Why not?
How many more splints do you need?
Six dots and one dot are how many dots?
Show me seven dots. Seven cubes.
Copy these cards:
• • •
• • •
• •
• •
• •
•
• •
• •
•
•
•
I want you to make each card have seven dots.
Xame two numbers that together make seven. Two
other numbers.
Here are four blocks. Add enough to make seven.
Ifow take two away. How many remain?
THE NUMBER SEVEN. 19
Here are one-cent, two-cent, three-cent, four-cent, and
five-cent postage stamps. Pick out any two that you can
buy with seven cents.
90. Make pictures of seven tents.
Draw a line around three of them. How many are
outside?
Show me two sevens with dots.
Cut out a strip of paper seven inches long and one inch
wide.
Into how many square inches can you cut it?
Draw a line one inch long. Close to the right end draw
a line six inches long.
Ifow draw a line below them as long as both.
How many inches long is this line?
This line ' is two inches
long. How much longer is a seven-inch line?
31. Copy and complete:
O O O O O a/vuL O O oJvu .
A A A A A A A f^>^^ ojvu A A.
20
SCHOOI. ARITHMETIC.
32. How many days in a week?
Name the days of the week, beginning with Sunday.
The middle of the week is W .
On Wednesday morning how many days of the week
are gone? How many are left?
How many sides have a ^ and a | | ?
Five girls and two boys went out. How many are out?
When one comes in, how many will be out?
Each week we come to school five days and stay at
home days.
Joe had seven cakes. The cat took three of them. How
many had he left?
Here are seven apples. OOOOOOO Name
each number of apples that you can take away, and tell
how many will remain.
The Number Eight.
• ••• ••••
• • • • • • •
33, Make a triangle and a square with splints. How
many splints have you used?
Try to make two squares with the splints.
How many more splints must you have ?
Seven splints and one splint are how many splints?
Show me eight dots. Show me eight buttons. Point
to eight corners in this room.
THE NUMBER EIGHT.
21
Make a pile of eight blocks.
Now make two piles of them, putting the same number
in each. How many in each pile?
. Four blocks and four blocks are how many blocks?
Take a block from one pile and place it on the other.
Now how many in each pile?
Five blocks and three blocks are how many blocks?
Take another block from the smaller pile and place it
on the larger. How many in each pile?
Six blocks and two blocks are how many blocks?
Name two numbers that make eight. Two other
numbers. Who can name still two other numbers?
What number comes before eight? Before seven?
Before six? Before five?
What number is between five and seven? Between six
and eight?
A nickel and how many cents make eight cents?
Copy these blank cards, and put in each the number of
dots indicated by the word written under it:
eight
six
seven
five
four
three
34. Make four dots, thus: ZX' Draw a line around
one-half of them.
Into how many eqwal parts have you divided them?
One-half of four dots is dots.
22 SCHOOL ARITHMETIC.
Make eight dots, thus: S • • • •
Draw a square around one-half of them. Draw a line
around the other half.
One-half of eight dots is dots.
Show me one-half of six dots.
H9W many squares are there here?
What part of them is black?
Four squares are one-half of squares.
How much of this circle is black? ^^p
A dollar is worth how many half-dollars?
Find by trial to-night how many quarts in a half-gallon.
35. How many fours in J J J J ^ How many twosi
Show me eight shoes. How many pairs are there?
Draw four rings above a line, and four below it. How
many times did you draw four rings?
Draw a line around one-half of the rings. How many
rings are inside of the line?
Make pictures of eight tents, four in a row. Cross
out one-half of them. How many are left ?
Make pictures of eight stars, two in a row. How many
rows have you?
Make pictures of one-half of eight squares. 1 ■ 1
Tell all you can about these figures. I I I IM
Two horses need pairs of shoes. In four pairs-
there are shoes.
The spider has legs. How many pairs of legs
does the spider have? ,^1^
THE NUMBER EIGHT. 23
36. Copy and complete:
A A A A A o/vixL A A A aA>e. .
• ••••• CUTUL oJVh S S S S.
X X X X a/vuL X X X X oJxJO .
/////// o^^xAj / oJvo .
A>/k>.A:.d^ t.^ J^ aA>^ .
37. Seven bugs and one bug are how many bugs?
One bean and seven beans are beans.
A man has six white sheep and two black sheep. How
many sheep has he?
There are five eggs in a dish. We need eight for dinner.
How many more must we find?
Mr. Jones has eight horses in two fields. There are
four in one field. How many are in the other field?
Eight birds were sitting on a fence. A bad boy shot
one. How many were left?
A boy had two fingers cut off. How many were left on?
We have two gallons of milk. How many quarts have
we? Find by trial.
Draw a figure four squares long and two squares wide.
This figure contains squares.
M
SCHOOL ARITHMETIO.
The Number Nine.
• • • •
• • • •
• • • •
38. Make two squares with splints. How many splints
have you used?
Try to make three triangles with the splints. How
many more splints doeyou need?
How many more than eight dots are on the card to the
right?
Eight dots and one dot are how many dots?
Take nine blocks and lay them in a row.
Push one away. How many are left?
One block and eight blocks are how many blocks?
One block from nine blocks leaves how many blocks?
If you push three blocks away, how many will be left?
Take away all but two. How many have you taken?
/Lay the nine blocks in three rows, three in a row.
I Now tell me how many threes make nine.
(^opy these cards:
• ••
•
• ••
• ••
• ••
• •
•
• •
• •
• •
•
Add enough dots to make each card have nine.
Name two numbers that together make nine. Two other
numbers.
THE NUMBER NINE.
25
How many splints will make three triangles?
Draw a square like this:
How many of the nine small
squares are white?
Make another black. Two black squares and
white squares are nine squares.
Cut out a paper triangle three inches on a side. How
long are all the sides?
Copy these squares, and put in each square the number
of dots indicated by the word written under it :
none
four
SIX
eight
nine
39. There are eight pigs in the pen and one on the
road. How many pigs?
The white hen has seven chicks, the black hen has two.
How many chicks?
There are six eggs in one nest and three in another.
How many eggs in both nests?
Five boys and four girls are how many children?
Dan has three pennies, Nell has three, and Kate has
three. How many have they all?
Xine sheep were in a field, but one jumped out. How
many were left in?
26 SCHOOL ABITHMETIO.
Here are nine tents,
If the wind blows two down, how many will remain
standing?
If I take three of them away, how many will be left?
How many times can you take three tents away?
If a book costs nine cents, it will take a nickel and
pennies to pay for it.
This line on the blackboard is nine feet long. Find
how many yards long it is.
The Number Ten.
• • • • • • •
• • • • •
• • • • • • •
40. How many fingers and thumbs have you? How
many more than nine?
Make a pile of ten blocks.
How many cents is this dime worth? ^a
Copy, and add dots enough to make ten dots on each
card:
• ••
• ••
• ••
• •••
• •••
• ••
•
• ••
• ••
• ••
• •
•
• •
Make eight tents and two tents. How many have you
made?
Make seven stars and three stars. How many?
THE NUMBER TEN. 27
Draw six rings and four rings. How many rings?
Five fingers and five fingers are how many fingers?
How many dots on the right-hand card?
How many fives do you see on it?
How many nickels make a dime?
How many tents can you make with ten splints, if the
tents are made like this /\ ?
Xame two numbers that make ten. Two other numbers.
Lay ten blocks in a row. Push one away. How many
are left?
If you take two away, how many will be left?
Two blocks from ten blocks leaves how many blocks?
Draw a square. Make ten dots. Now put one half of
the dots inside the square.
One-half of ten dots is how many dots?
Make two piles of ten blocks each. How many tens?
Two tens and three tens are how many tens?
Xine fives and one five are how many fives?
Use dots to show me three twos.
Four twos and one two are how many twos?
Show me five twos with dots. How many ones?
How many fingers have two boys?
How many clocks have ten hands?
Find whether this room is ten yards long.
How many feet less or more?
41. Willie had nine cents and his uncle gave him one
more. He then had cents, or one .
How many children are eig'ht boys and two girls?
J
2o SCHOOL ARITHMETIC.
A week and three days are how many days?
This line on the blackboard is ten inches long, and this
one is nine inches long. How much longer is one than
the other?
Dan had ten cents. He spent two cents for a pencil.
How many cents had he left?
A man had three of his toes cut off. How many were
left on?
Bessie started to the store with ten cents (two nickels),
but lost one-half of her money. How much had she left?
How many two-cent stamps are worth a dime?
If you have ten cents, how often can you spend five
cents?
If one orange costs five cents, how much money will be
needed to buy two oranges?
The Numbers Eleven and Twelve.
• • • •
• • •
• • • •
• •
42. How many dots are on the left-hand card? How
many more than ten?
Ten dots and one dot are how many dots?
A dime and a penny are how many cents?
THE NUMBERS ELEVEN AND TWELVE. z9
Here is one block. Put enough more here to make
eleven.
Name two numbers that make eleven. Two other
numbers.
Make two squares and a triangle with splints. How
many splints have you used?
Try to make three squares with the same splints. How
many more do you need?
Eleven splints and one splint are how many splints?
Make a pile of twelve blocks.
Now take two blocks away. How many are left?
Twelve blocks are how many more than ten blocks?
How many dots do you see here? !•••••
How many sixes in twelve? How many twos? How
many fours?
Cut a strip of paper six inches long. How many strips
are as long as your foot-rule?
How many six-inches in twelve inches?
Find how many strips each four inches long are as long
as your ruler.
How many four-inches make twelve inches? How many
two-inches ?
Make twelve tents with splints. Let the wind blow
down one-half of them. How many are left?
43. Twelve boys are how many more than eleven boys?
There are ten eggs in a nest. When the hen lays two
more there will be eggs in the nest.
80 SCHOOL ARnHMETTC.
My two horses ate twelve ears of com. The gray horse
ate six ears. How many ears did the bay horse eat?
Mamma bought a dozen oranges at the store. We ate
six for breakfast, llow many were left?
I found a nest with twelve eggs in it. I took out all
but one. How many did I take?
Twelve of Mr. Smith's sheep were sick. Two of them
died. How many got well?
Six boys were playing soldiers on one side and five on
the other. How many boys were there altogether?
Henry's father gave him a dozen pencils. How many
had he left after using four?
Marvin has a five-cent piece and three pennies. How
many more cents must he have to pay for a top worth
eleven cents?
Harry's knife has two blades. How many blades do six
such knives have?
We learned five new words yesterday. If we learn one
more to-day than we did yesterday, how many have we
learned in both days?
PRIMARY NUMBER WORK,
• • •
12 3
44. How many ones on the middle card? How many
twos?
Two dots are how many more than one dot?
Three dots are how many more than two dots?
How many dots on the first two cards?
Cover two of the dots on the last card. How many do
you see?
One dot and one dot are dots.
Two tents and one tent are tents.
One square and two squares are squares.
Two stars less one star are star.
Three tents less one tent are tents.
Make pictures of:
Two stars and one star are three stars.
One tent and two tents are three tents.
Three dots less one dot are two dots.
Three rings less two rings are one ring.
How many ones in two? In three? What two numbers
make three?
[31]
32 SCHOOL ABITHMETIC.
Make the figure that stands for the number one — y.
Make the figure that stands for the number two — ^.
Make the figure that stands for the number three — J,
Use figures instead of these pictures :
^ lir and ^ are ^ ^ ^.
^3P XJf^ XJ}^ less XJP are X2f^ ^3P.
nnn less nn ar^ d
2 dots and 1 dot are dots.
1 star and 1 star are stars.
2 tents less 1 tent are tent.
3 cents less 1 cent are cents.
3 squares less two squares are square.
46. Here are some squares:
D 1
DP 2
nnn 3
Write the figure for the number of squares in the
upper row.
Under this write the figure for the number of squares
in the second row.
One square and two squares are squares.
Write 3 under the 2 with a line between. Is 3 the
number of squares in both upper rows?
Three squares is the sum of one square and two squares.
Finding the sum of two or more numbers is c^ed
adding.
NUUBEBS 1 TO 3. 33
Add these numbers:
1
1
2
1
1
2
DD 3
■ 1
DD ^
Take one square from 3 squares. How many are left?
Taking one number from another is called subtracting.
Subtract the following:
2 3 3
112
46. Add:
1 foot
2 feet
Subtract:
2 feet
1 foot
Complete:
1 and 1 are ( ).
2 and 1 are ( ).
1 and 2 are ( ).
2 cents
1 cent
3 yards
1 yard
3 cents
2 cents
1 yard
1 yard
2 tops
2 tops
2 less 1 are ( ). 3 less 2 are ( ).
2 and ( ) are 3. 3 less ( ) are 2.
3 less 1 are ( ). 3 less ( ) are 1.
J
34 SCHOOL ARITHMETIC.
47. Make a picture for 2 and 1 are 3. (J and • are J^).
Tell a story about 1 and 1 are 2.
Ans.— My dolly had 1 dress, and I made her 1 more. She then
had 2 dresses.
Tell a story about 1 and 2 are 3.
Emma has two pairs of shoes, and Lillie has one pair.
How many pairs have they both?
Mary had three dimes, but lost one. How many had
she left?
Tell another story about 3 less 1 are 2.
My hat cost two dollars. I have paid one dollar. How
much do I owe?
We have three quarts of milk for sale. How many
times can we sell one quart?
Then how many quarts are 3 times 1 quart?
How many fives are one five and two fives?
Clara ate one peach, and has two left. How many had
she at first?
John had three marbles and gave one to Sam. Ask a
question and answer it.
Here are 3 pears. ^ C^ ^ How many boys can
each have 1 pear?
How many ones in 3?
Count forwards to three, then backwards to one.
Tell me some things you have learned about the number
ihr$e.
Pour
FOUR — 4. 35
48. How many ones are pictured on this card? How
many twos?
Four dots are how many more than three dots? How
many more than two dots?
Name two numbers whose sum is four. Two other
numbers.
Show with splints that your answers are correct.
Here are four tents. Cover one. How many are not
covered?
If two tents were taken away, how many would be left?
How many times can one tent be taken away?
Then four times one tent are tents.
Here are four blocks. Eva may take two blocks. Now
she may take two more.
How many times has she taken two blocks? -How
many blocks has she?
Then two times two blocks are blocks.
Show with pegs that two twos are as many as four ones.
Here are four cents, i^ ^p @ @ How many
girls can have one cent each? How many ones in four?
How many boys can have two cents each? How many
twos in four?
36 SCHOOL ABITHMETIC.
49. Separate four blocks
into two equal parts y thus: ^^ ^
What is one part called?
What must you do with an apple to get one-half of it?
(Divide it into two equal parts.)
What must you do with four blocks to find one-half of
them?
If anything is divided into two equal parts, what is
one of the parts called?
In an apple there are half -apples.
How many halves make a whole pie?
One half from two halves leaves half.
Draw two squares and divide them into halves.
In two squares there are half-squares.
We write one-half thus: i.
Two blocks are i of blocks.
Write the figure that stands for the number four — ^.
50. The sign + stands for and. Copy the following,
using + instead of and:
1 and 1 are 2. 8 and 1 are 4.
2 and 1 are 3. 2 and 2 are' 4.
Bead these:
1 + 2 are 3. 1 + 3 are 4.
1 + 1 are 2. 2 + 2 are 4.
FOUR 4.
37
The sign — stands for less. Copy the following, using
— instead of less:
2 less 1 are 1.
3 less 1 are 2.
3 less 2 are 1.
4 less 1 are 3.
Kead these:
3 — 1 are 2. 4 — 2 are 2.
3 — 2 are 1. 4 — 3 are 1.
We may use the sign = for are.
Eead these:
2 + 1 = 3. 2 + 2 = 4. 4 — 2 = 2.
3 + 1 = 4. 4 — 1 = 3. 3 — 2 = 1.
Copy and complete:
3+l=()
l+3=()
2+2=()
4==3 + ()
4=l+()
3 + () = 4.
1 + () = 4.
2 + () = 4.
4-() = 3.
4-() = l.
4-2=()
4-l=(>
4-3=()
4-()-2
4=--=2 + ()
Note. — To secure facility on the part of the pupils the teacher
should, as often as may be found necessary, require them to an-
nounce results at sight He should also train them to give answers
immediately upon hearing the numbers and operations named.
This applies to all exercises involving the " combinations."
38 SCHOOL ABITHMEriO.
51. Make a picture for 2 + 2 = 4.
How many boys together have as many legs as a horse?
George earned one quarter on Monday and three
quarters on Tuesday. How much did he earn in both days?
Ask your papa how many quarters there are in a dollar.
Tell a story about 8 + 1 = 4.
I bought four pounds of meat. Two pounds of it was
pork and the rest beef. Ask a question and answer it.
Charlie has four rabbits and Paul has one less. How
many has Paul?
How many more fingers than thumbs has your hand?
Count from one to four; then count from four back
to one.
If one-half of a lemon is worth two cents, how much is
the lemon worth?
If a cake is worth four cents, how much is one-half of
it worth?
One half-dollar and one half-dollar are .
PIKT QUART OALLON
52. Which of these measures is the largest? Which
is the smallest?
Fill each measure with water, then tell me which is
the heaviest.
FOUR — 4. 39
The gallon measure is full of water. Find how many
times it will fill the quart measure.
Find how many times you can fill the quart measure
and empty it into the gallon measure.
One gallon is as much as quarts.
4 quarts make 1 gallon.
Mabel had a gallon of milk, but fell and spilled a quart.
She had quarts left.
Papa brought home a gallon of oil in a can. There is
only one quart in it now. How much has been used?
Fill the pint measure and empty it into the quart
measure. How many times must you do this to fill the
quart measure?
One quart is as much as pints.
2 pints make 1 quart.
A pint is what part of a quart?
Two quarts are what part of a gallon?
When milk is two cents a pint, how much does a quart
cost?
Jennie paid four cents for a quart of vinegar. How
much did a pint cost?
Mamma gave four quarters for a gallon of molasses.
How much did a quart cost?
Tell a story about a quart and a gallon.
Tell me some things you have learned about the
number four.
40 SCHOOL AEITHMETIO.
Five
63. How many dots on this card? Of what number
are they a picture?
Without the one in the center, how many are there?
Cover the two at the right. How many can you see?
Are three dots and two dots as many as four dots and
one dot?
Name two numbers whose sum is five. Two other
numbers.
What number is one less than five? Two less?
Are five ones as many as one five?
Which would you rather have — ^five pennies or a
nickel? Why?
Count these squares, beginning at the left. O Bj CH CH C]
Which square did you call one? Which did you call
two?
Is the black square really two squares, or merely
another one square?
The first square and the second square are how many
squares ?
Make the figure that stands for the number five — S,
54. Here are five balls. © © © © ©
If Owen takes 1 ball at a time for 5 times, how many
balls will he have?
Then 5 times 1 baU are how many balls?
FIVE 5. 41
5 times 1 are how many?
Here are five cents. @
How many boys can have 1 cent apiece?
How many ones in 5 ?
How many boys can have 2 cents apiece?
How many will be left for another boy?
Two 2's and 1 are .
^B
A
C
-E
-D
The line D and the line A equal which line?
The line B and the line C equal which line?
The line B is how many times as long as the line A?
The line D is how many times as long as the line B?
If from the line E we take a line equal to the line A,
which line will the remainder equal?
Show me the number of blocks these figures represent:
3, 5, 1, 4, 2.
Now make the figures that represent the number of
blocks I show you. (Show blocks.)
56. Copy, complete, and read:
4 + l-=(). 5-l=(). 4 + () = 5. 5-() = 3.
1 + 4 = (). 5-4=(). 3 + ()==5. 5-() = 2.
3 + 2 = (). 5-2 --=(). 5-()=4. 5 = 4-f-().
2 + 3 = (). 5 — 3=(). 6-() = l. 6=--2 + ().
42 SCHOOL AMTHMETIO.
56. Make a picture for 3 + 2 == 5.
Four little toes and one great toe are toes.
My hat cost three dollars and my shoes two dollars.
How much did both cost?
A lady bought two pounds of coffee at one store and
three pounds at another. Ask a question and answer it.
2 pounds + 3 pounds = pounds.
We have school five days each week. If you stay at
home two days, how many days do you come to school?
Tell a story about 5 — 4 ^= 1.
It is five miles to Salem. When we have traveled
three miles, how far have we yet to go?
This line on the blackboard is one foot long, and this
one is five feet long. Tell me all you can about the two
lines.
In O O and D5 how many half -circles are there?
For a nickel I can buy 2-cent stamps and
1-cent stamp.
Tell some other things you can buy with a nickel.
Helen, please tell all you know about four.
Ans. — 3 and 1 are four, 2 and 2 are four, 1 and 3 are four ; two twos
are four ; 4 less 1 are three, 2 from 4 leaves two, etc., etc.
James, be kind enough to state what you know about
five.
8IX — 6. 48
Six
• • •
6
67. How many cents can you get for a nickel?
If I should give you one more penny, how many cents
would you have?
Would you have a cent for every dot on this card?
Show me five fingers and one finger. How many?
Draw a line four inches long. At one end of it draw
a line two inches long. Both together make a line
inches long.
Here are six tops. ^ ^ ^ T T T
If Ben takes two tops at a time for three times, how
many tops will he have?
Then how many tops are 3 times 2 tops?
Here are six balls. © © © © © ©
Jack may take 3 balls; then 3 more.
How many times has Jack taken 3 balls?
Here are 6 marbles. Q Q Q Q Q Q
How many boys can have 1 marble each?
How many ones in 6?
How many boys can have 2 marbles each?
How many twos in six?
How many boys can have 3 marbles each?
How many threes in six?
44 SCHOOL ARITHMETIO.
How many threes do you see on the card? Two threes
are .
How many twos are on the card? Three twos are .
Show me with blocks that two threes are as many as
three twos.
Here are four squares. 11110 How many
more must we draw to have six?
The sum of five and one is six. Name two other num-
bers whose sum is six. Two others.
Draw a line six inches long on your slate. Rub out
one inch of it. How long is the remainder?
If two dots are taken from six dots, how many dots will
remain?
Make the figure that stands for the number six — ^.
58. Divide 6 dots into three equal parts thus:
How many dots are there in each part?
When a number of things is divided into three equal
partSy each part is one-third of the whole number.
What is one-third of 6 dots? One-third is written — h
i of 6 cents is cents.
Into how many equal parts is the first
circle divided? The second?
What part of the first circle is dark?
What part is light?
How much of the second circle is dark?
03
SIX — 6. 45
Which is greater — one-half or one-third of anything?
Two thirds of a pie and one third of a pie are how much
of the pie?
Cut this apple, giving one-third to John, one-third to
Charley, and keeping one-third yourself. In one apple
how many thirds of an apple?
Tn 2 apples there are thirds of an apple?
69. Copy, complete and read:
5-f 1 = ()
1+5 =
4+2 = ()
2 + 4=()
3+()=6
3 + 3 = ( ). 6-4 = ( ). 2-f ( ) = 6
6-l = ( ). 6-3 = (). 6-( ) = 4
6-5 = ( ). 4 + ( ) = 6. l + ( ) = 6
6 — 2 = (). 6 — () = 2. iof6 = ()
6 — () = 3. iof6 = (). iof3 = ()
60. Make a picture for 3 + 3 = 6.
Harry made five rings and Stella made one. How
many did both make?
Maud, you may draw two circles. Annie may draw
four. How many have both drawn?
The black cow gives a gallon of milk, the red cow two
quarts. How much do both give?
There are three horses on each side of a fence. How
many horses are there? Draw the picture.
Draw a line two yards long. How many feet long is it?
A lady who had six dollars gave one dollar for gloves.
Ask a question and answer it.
A man had six ten-dollar bills, but spent two of them.
How many had he left?
46 SCHOOL ARITHMETIO.
Henry gets two dollars a day. How much does he earn
in three days?
Our hens lay three eggs a day. How many do they lay
in two days?
A man gets six dollars for working a day. How much
does he get for working half a day?
Tell a story about 6 — 3 = 3.
If one orange costs 3 cents, what does one-third of the
orange cost?
If one-third of a melon is worth 2 cents, what is the
whole melon worth?
Alice has one-half of 6 cents and Frances has one-third
of 6 cents. Which has the more money?
Who wants to tell me all about six? James may tell.
Now you may all go to the board and write what he has
told us.
Seven
• • • •
• • •
61. Make two triangles with splints. How many have
you used?
Can you make a triangle and a square with the same
splints? How many more do you need?
Six dots and one dot are dots.
How many days in a week? Name them.
Draw a line six inches long, and another one inch long.
What is the l?n^h of both lines?
SEVEN 7. 47
Take seven blocks. Take two of them away. How many
are left?
Eive blocks and two blocks are blocks.
Now take three blocks from the seven. How many in
each pile?
Cut out a strip of paper seven inches long. Cut off an
inch from one end. What is the length of the part left?
This line on the blackboard is four feet long. Make
it seven feet long. How long is the line you have drawn?
Draw a line seven inches long on the blackboard. Helen
may rub out one inch of her line. How long is the part
left?
Tom may rub out two inches of his line. How much
of the line is left?
Hester may erase three inches of her line. Tell me
something about the part left.
Name two numbers whose sum is seven. Two other
numbers.
How many are □ □ and □ □ and □ □ and □ ?
Can you name three numbers that together make seven?
Show me the number of blocks these figures stand for:
6, 7, 5, 4, 3.
Make the figures that stand for the number of balls I
hold up.
62. Copy, complete and read:
6 + l = (). 5 + () = 7. 7-l = (). 7-3-().
6 + 2 = (). 3 + () = 7. 7-6 = (). 7-4 = ().
4 + 3 = (), l + () = 7. 7-2 = (). 7-() = 6.
48 SCHOOL AJUTHMSnC.
Add quickly:
5 6 4 12
2 13 6 5
Subtract at sight:
7 7 7 7 7 7
16 2 5 3 4
63. You come to school five days each week. How
many days do you stay at home?
What two pieces of money make seven cents?
There are half a dozen eggs in one nest and one in
another. How many eggs in both?
Tell a story about 7 — 1 = 6.
Four boys and three girls are how many children?
How many sides have a triangle and a square?
Seven boys went to town, but only five returned. How
many stayed in town?
This is Tuesday. How many more days in this week?
There were seven windows in a room, and two of them
were open. How many were shut?
How many quarts are a gallon and three quarts?
Eight
BIGHT
8.
•
•
•
•
•
•
•
•
49
8
64. How many dots are on this card?
How many large dots? How many small dots?
Eight dots are one more than what?
Here are six blocks. Give me enough to make eight.
Now make two piles of them with the same number in
each. How many blocks in each pile?
Take one block from one pile and place it on the other.
Now how many in each pile?
Take one block from the smaller pile and place it on
the larger. Now how many in each pile?
Make eight dots on your slate.
Albert may erase one and tell how many are left.
Carrie may erase two and tell how many she has left.
Jack may erase three and tell us about the others.
Jill may erase four and tell us how many she did not
rub out.
Count to eight, then back to one.
Count to eight by twos. How many twos in eight?
Show me one half of eight blocks.
How many fours in eight?
Two blocks are what part of four blocks?
65. Here are eight stars.
it
t
Into how many parts are they divided?
•4
50 SCHOOL ABITHMETIC.
Has each part the same number of stars?
One of the four equal parts of anything is called
one-fourth. (Fourths are often called qtoarters,)
One fourth of eight stars is stars.
Make eight tents. Draw a ring around one fourth of
them.
Make eight dots. Call them pigs. Put one fourth of
them into a pen.
Now put another fourth of them into a pen.
How many pigs are not in a pen?
What part of the eight pigs are not in a pen?
How many fourths of the eight pigs are penned up?
Are two fourths of the pigs as many as one half of them?
Ask your mamma to show you a fourth of a dollar, and
tell me all you can about it to-morrow.
One fourth (:J) of eight cents is cents.
A quart is what part of a gallon?
Ask your papa to-night what measures are used tg
measure potatoes, and tell me something about them
to-morrow.
Make the figure that stands for the number eight — <f;
66. Copy, complete and read:
7 + l = (). 5 + 3 = (). 8-l = (). 8-4 = ().
6 + 2 = (). 4 + 4 = (}. 8-2 = (). 8-3 = ().
1 + = 8. 3 + () = 8. 8-0 = 1. 8-() = 4.
2 + = 8. 4 + = 8. 8-0 = 2. 8-0 = 3.
iof8 = (). iof4 = (). iof8 = ().
EIGHT 8. 61
67. How many pints are there in a gallon of milk?
If you drink two pints of it, how much will be left?
What part of the gallon will be gone?
Six rats were caught in one trap and two in another.
How many rats were caught?
Tell a story about 5 + 3^8.
Dick has four marbles and John has four. How many
have they both?
How many fourths of this square iire black?
Is one half of the square white?
One square is what part of four squares?
Two squares are what part of four squares?
Which is more — one half of four apples, or one fourth
of them? Draw the picture.
One half of anything is as much as fourths of it.
Tell a story about 8 — 5 = 3.
A boy has eight rabbits. Four of them are white. The
rest are black. How many are black?
This line on the blackboard is two yards and two feet
long. What is its length in feet?
Kay has eight cents and Elsie has a nickel. Ask a
question and answer it.
52
SCHOOL ARITHMETIC.
68. Have you ever seen these measures? Which
measure is the largest?
Clyde may tell me some of the things he has seen
measured by them. Who can tell me something more
about them?
The bushel basket is full of corn. Find how many
times you can fill the peck measure from it.
Find how many times you can fill the peck measure and
empty it into the bushel measure.
In one bushel there are pecks.
4 pecks make 1 bushel.
When you buy a bushel of potatoes, how many pecks
do you get?
A peck is one of a bushel.
How many pecks will fill the half -bushel?
If a bushel basket is half-full of potatoes, how many
more pecks of potatoes will it hold?
Fill the peck and the half-bushel with apples, and
empty them into the bushel basket. Is the basket full?
How much more will it hold?
How many half-bushels does it take to fill the bushel?
Two pecks are what part of a bushel?
NINE 9. 63
When nuts are a dollar a peck, how much does a bushel
cost?
If plums are worth two dollars a bushel, How much
must I pay for a half-bushel?
There are eight pecks of wheat in a sack. How many
bushels are in it?
If we eat a peck of apples each week, how long will a
bushel last?
How many half -pecks will fill the bushel?
A peck is one fourth of a bushel.
Two pecks are fourths of a bushel.
Three pecks are fourths of a bushel.
A half-bushel and a peck are pecks, or
fourths of a bushel.
Papa bought a bushel and a half of beets. How many
pecks did he get?
How much must you pay for four bushels of clover
seed at two dollars a bushel?
Nine
• • •
• • •
• • •
9
69. How many more than eight dots are on this card?
Eight dots and one dot are dots.
There are three dots in one row. How many in two
rows? In three?
How many splints are needed to make three triangles?
How many threes in nine?
64 SCHOOL ARITHMETIC.
This line on the board is seven ijiches long, and this
6ne is two inches long. What is their combined length?
Put five blocks in one pile and four in another. Put
the piles together. How many blocks?
Take tfhree blocks away. How many now in each pile?
Six blocks and three blocks are blocks.
Make nine tents with splints. Take away two. How
many are left?
Cover three of the dots on the card. How many can
you see?
Here are nine beans. Take away all but four. How
many have you taken?
Use blocks to find answers:
Two blocks from nine blocks leaves blocks.
Seven blocks from nine blocks leaves blocks.
Three blocks from nine blocks leaves blocks.
Six blocks from nine blocks leaves blocks.
Four blocks from nine blocks leaves blocks.
Five blocks from nine blocks leaves blocks.
Make the figure that stands for the number nine — f.
70. Into how many equal parts are these nine dots
divided? i:#i:#i:#
One of the three equal parts of anything is called
one third.
One third of nine dots is dots.
One third of six stars is stars. T ^ T
NIKE 9. ^5
Into what is this circle divided? (^
What part of it is black? How many thirds of it are
white?
One third of the circle and two thirds of it are how
much of the circle?
In anything there are thirds.
Make 9 dots. Draw a ring around one-third (i) of
them.
* of ••• = . * of ••• = .
^ ••• ^ •••
Draw a line i of 9 inches long.
Draw a line S of 9 inches long.
Show me i of six splints.
Show me f of six splints.
Show me -I of six splints (all of them).
One third of six dollars is dollars.
Two thirds of six dollars is dollars.
Here are some squares. DOD DDD DDD
Henry may make 3 squares at a time for 3 times.
How many squares has he made?
How many squares, then, are 3 times 3 squares?
How many are 3 times 3, or 3 threes?
How many times is 3 squares found in 9 squares?
Draw a line 9 inches long. Measure it with a 3-inch
measure.
How many times does it contain the 3-inch line?
S6
SCHOOL AJUTUtfKTIO.
m
i
D
How many times does C contain A?
C is how many times A?
How many times does D contain B?
D is how many times B?
B IS what part of D?
A is what part of C?
D is how many times A?
A is what part of D?
C is what part of D?
71. C'opy, complete and read:
8 + l = (). 4 + () = 9. 9-l = (), 9 — 4 = ().
7+.2 = (). 2 + () = 9. 9-8 = (). 9-6 = ().
6 + 3 = (). l + () = 9. 9-2 = (). 9 — 3 = ().
5 + 4-(). 3 + () = 9. 9-7 = (). 9-() = 4.
3 times • • • = —
3 times 3 = —
OO =iof ( ).
2 times A A A A
2 times 4
i^^ = ioi{ ).
2 times D D D = -
2 times 3 = —
AAA = iof( ).
KINE 9. 67
72. Make a story for 8 + 1 = 9.
Seven days and two days are how many days?
There are six eggs in a dish. If I put in three more,
how many will be there?
Bertha came to school five days last week and four days
this week. How many days did she come?
Albert had nine marbles but lost two. Ask a question
and answer it.
Ada broke three of her nine e^s. How many had
she left?
Homer had nine dimes. He gave six dimes for a book.
How much had he left?
Mamma bought nine pairs of gloves, and gave Susie
four pairs. How many pairs did she keep?
Papa had nine dollars; he spent all but two dollars for
shoes. How much did the shoes cost?
Three girls wear six shoes. How many does one girl
wear?
Mamma took nine yards of cloth to make three dresses
for Bessie. How many yards in each dress?
Frank walked nine miles in three days. How far did
he walk in one day?
Tell a story about i of 9 ^ 3.
58
BOHOOL ABITHMETIO.
Zero
78, How many dots do you see on this card?
If your two hands were cut off, how many would you
have left?
Draw a line four inches long on your slate. Kub out
four inches of the line. How much of it is left?
Ida had two pennies. She spent them for a pencil.
How many pennies had she left?
Albert had four apples. He ate one and gave three
to John. Ask a question and answer it.
Make a picture of no stars.
Make the figure that stands for none — ^.
The figure is called zeroy naughty or cipher.
When it stands alone it means 7ione to count; but we
shall soon make it work hard in a " double team."
Tell a story about 5 — 5 = 0.
Ten
• • • •
• • • •
10
74. How many more than nine dots are on this card?
Nine dots and one dot are dots.
How many fingers and thumbs have you?
How many fives do you see on the card?
Put eight pegs in one pile and two in another. How
many pegs in both piles?
TEN 10. 59
Put one peg from the larger pile into tlie smaller. Now
how many in each pile? In both?
Five pegs and five pegs are pegs.
Lay ten blocks in a row. Take one away. How many
are left?
Use the ten blocks to find these answers:
Two blocks from ten blocks leaves blocks.
Eight blocks from ten blocks leaves blocks.
Three blocks from ten blocks leaves blocks.
Seven blocks from ten blocks leaves blocks.
Four blocks from ten blocks leaves blocks.
Six blocks from ten blocks, leaves blocks.
Five blocks from ten blocks leaves blocks.
Make ten dots, thus:
How many times did you make five dotGf
Two times 5 dots are dots.
How many times did you make two dots?
Five times 2 dots are dots.
Divide ten blocks into piles, putting 2 blocks in each
pile. How many times have you found 2 blocks in 10
blocks?
Then 10 blocks contains 2 blocks times.
10 blocks divided by 2 blocks = 5.
10 blocks divided by 5 blocks = 2.
60
SCHOOL ARITHMETIC
Show me ten splints. Tie them in a bundle.
How many splints in the bundle? How many ones
in it? How many tens?
Ten ones^nake one ten.
One ten and one ten are
tens.
How many are 5 tens and 5 tens?
It takes more than one figure to stand for the number
ten. We must now make go to work. Ten is written
thus: ^^.
Make ten dots. Draw a ring around one-half of them.
How many are in the ring?
75, Copy and complete:
S+2=( ). 1+ 9=( ). 7+( )=10. 10-2=(
6+4==( ). 4+( )=10. 5+( )=10. 10— 4=(
7+3=( ). 6+( )-=10. 2+( )=10. 10— 6=(
5+5=( ). 3+( )=10. 8+( )=10. 10— 3=(
10— 5=( ). 10— 0= 7. 10— ( )= 8. iof 10=(
76. Wri
te with proper signs:
From 10 take 3; 5;
From 9 take 4; 3;
To 3 add 4; 6; 5;
To 2 add 5; 8; 7;
Find one-half of 10;
Find one-third of 9;
Find one-fourth of 8;
7; 6; 8; 4.
6; 8; 5; 7.
7; 2; 3.
6; 4; 0.
8; 6; 4; 1.
6; 3; 1.
4; 1.
TEN 10. 61
77. Dan walked 8 miles on Monday and 2 miles on
Tuesday. How far did he walk in both days?
Tell a story about 10 — 2 = 8.
The white hen has seven chicks and the black hen has
3. How many have they both?
Give a story for 10 — 3 = 7.
George worked 6 days last week and 4 days this week.
How many days did he work?
Sadie bought 10 yards of gingham. She used 4 yards
for aprons, and had yards left.
How many nickels are worth 10 cents?
If you wish to pay me 10 cents, how many times must
you give me 5 cents?
Two times 5 cents = cents.
How many 5-cents in 10 cents?
If I give you 2 cents five times, how much money will
you have?
Five times 2 cents = cents.
ooo ooo ooo ooo
A A A A
If one hat costs 3 dollars, three hats will cost
dollars.
How much will five 2-cent stamps cost?
For 9 cents I can buy 2-cent stamps, and I sliall
have ^ left.
How many 2-cents in 10 cents? (Make the picture.)
10^ divided by 2^ means, how many 2j are there in lO^f
SCHOOL ABITHMETIO.
How often can you cut 2 yards of silk from a piece 10
yards long? 10 yd. divided by 2 yd. = ( ).
Mamie went to the store with 10 cents in her pocket.
She spent one-half of it. How much money had she left?
Tens.
78. How many cents equal a dime?
Then how many ten-cents is a dime worth?
How many ten-cents are the dimes on the left-hand
card worth? On the right-hand card?
Two ten-cents and three ten-cents are ten-cents.
Eight dimes and two dimes are dimes.
Oi
Two dimes are worth twenty cents.
Place ten blocks in a column as in the picture.
Make another column of ten blocks. How
many blocks in both columns?
10 blocks and 10 blocks are blocks.
One ten and one ten are
write twenty thus — ^^.
tens, or twenty. We
Make another column of ten blocks. How many tens
have you now?
2 tens and 1 ten are tens, or thirty.
20 blocks and 10 blocks are blocks.
Twenty means two tens; what does thirty mean?
TENS.
In 20 the figure 2 stands for two tens, the for no ones.
Now who can write thirty, or three tens and no ones?
Let me see who can write forty, or four tens and no
ones?
rr\
[2]
3
[T]
5
6
7
8
9
ilO
|_J
= one ten.
= one ten.
= one ten.
3 tens = 30.
79. Supply the figures needed:
One ten and no one is written thus — 10. Ten.
Two tens and no ones is written thus — 20. Twenty.
Three tens and no ones is written thus — 30. Thirty.
Four tens and no ones is written thus — Forty.
Five tens and no ones is written thus — Fifty.
Six tens and no ones is written thus — Sixty.
Seven tens and no ones is written thus — Seventy.
Eight tens and no ones is written thus — Eighty.
Nine tens and no ones is written thus — Ninety.
Ten tens and no ones is written thus — 100. One hundred.
Sixty means six tens. What does seventy mean?
Eighty? Ninety?
80. Count by tens to one hundred.
How many tens make 100?
How
many cents in a dollar? How many dimes?
How many tens make fifty?
64
80H00L ARITHMETIO.
How many dimes are worth 50 cents?
Six ten-cent pieces are worth -- — cents.
Four dimes and three dimes are dimes, or
cents.
Five tens and four tens are tens, or .
Ten tens less two tens are tens, or .
Three tens from eight tens leaves -
One-half of 6 tens is tens, or
tens, or
We gave 2 ten-dollar bills for our cow. How many
dollars was that? (Twenty dollars is written thus — $20.)
This book is worth 4 dimes, or cents.
Dora had 10 dimes. She spent 4 of them, and had
left dimes, or cents.
20 No ones and no ones are how many ones ? 2 tens and 3 tens
30 are how many tens ? Then 20 + 30 = 5 tens and no ones, or 60.
50
81. Add:
2 dimes
20^
4 dimes
40fS
3 dimes
30fS
4 dimes
40fS
5 dime?
50^
2 dimes
20^
1 dime
10^
5 dimes
50(>
3 dimes
30^
3 dimes
30^
3 dimes
30^
4 dimes
40^
4 tens
40
5 tens
50
2 tens
20
3 tens
30
TENS.
65
30 days
10 ft.
$40
$60
30 days
60 ft.
$50
$40
70 bushels $50
70
7d. 20
30 bushels $50
20
yd. 60
82. Subtract:
4 dimes
40^
7 dimes 70^
1 dime
10^
1 dime 10^
6 dimes
60^
7 dimes 70^
3 dimes
30^
2 dimes 20^
8 tens
80
10 tens 100
4 tens
40
5 1
tens 50
$60
80 ft.
90
pecks $100
$20
20 ft.
80
pecks $ 10
88. Copy and
complete:
10 + 10 = ( )
. -20 + 20 =
= ( ).
50 + 30 = ( ).
20 + 10 = ( )
. 30 + 20 =
— ( )■
60 + 30 = ( ).
30 + 10 = ( )
. 40 + 20 =
= ( ),
70 + 30 = ( ).
40 .+ 10 = ( )
. 50 + 20 =
— ( )
40 + 40 = ( )•
50 + 10 = ( )
. 60 + 20 =
= ( )
50 + 40 = ( );
60 + 10 = ( )
. 70 + 20 =
= ( )
60 + 40 = ( ).
70 + 10 = ( )
. 80 + 20 =
= ( )
. 50 + 50 = ().
80 + 10 = ( )
. 30 + 30 =
= ( )
20 + 10 = ( ).
90 + 10 = ( )
. 40 + 30 =
:=( )
. 30 + 10 = ().
•5
66
SCHOOL ABITHMETIO.
Review and DrilL
84. Copy and add:
$3 4 gal. 3 ft. 1 ten
$1 2 gal. 4 ft. 2 tens
10
20
2 gal.
3 gal.
3 in.
2 in.
2^
4 tens
3 tens
40
30
$7
$1
6 doz.
1 doz.
5 in.
4 in.
8 tens
2 tens
80
20
86, Copy and subtract:
7 ft. 6 doz. 5^
3 ft. 4 doz.
2^
6 tens
2 tens
60
20
$5
7 in. 8 gal. 5 tens 50
4 in. 6 gal. 3 tens 30
9 yd. $9
6 yd. $4
10 qt. 10 tens 100
7 qt. 8 tens 80
86. Copy and complete:
3+2=(
4+l=(
l+5=(
2+4=:(
3+3=(
6+l=(
2+5=(
3+4=(
7+l=(
2+6=(
5+3=(
4+4=(
l+8=(
7+2=(
3+6=(
5+4=(
9+l=(
2+8=(
7+3=(
4+6=(
5+5=(
6— 2=(
5— 3=:=(
7-5=(
6— 4=(
8— 5=(
7— 3=(
8— 6=(
BEVIEW AND DRILL.
67
5+( )=8,
7+( )=9,
3+( )=7
4+( )=8
6+( )=9
2+( )=7
8=2+( )
6=4+0
9=6+0
7=3+( )
9=7+( ),
8=6+( )
7=2+(
9=5+(
6=4+(
8=3+(
10=6+(
10=3+(
87. Add quickly:
88. Subtract quickly:
10-( )=7.
10-( )=2.
10— ( )=6.
10-( )=4.
10-( )=8.
10-( )=1.
4 of 4=(
iof 8=(
iof 8=(
4 of 6=(
i of 10=(
iof 9=(
4
2
1
3
4
2
6
4
3
2
3
4
3
3
5
1
4
5
6
1
2
1
3
7
4
1
2
2
7
7
8
6
2
5
9
8
3
4
5
5
6
6
6
6
7
1
2
2
3
2
4
3
5
1
7
7
7
7
7
8
8
8
8
6
2
5
3
4
4
2
3
5
8
8
9
9
9
9
10
10
10
6
7
2
7
3
4
4
6
7
68
SCH(X)L ARITHMETIC.
89. Add the number in the center to each of the other
numbers in the same square. Name results at sight:
9
7
4
8
4
5
6
4
7
6
1
8
1
2
3
1
3
2
3
5
2
6
2
7
6
3
90. Subtract the number in the center from each of
the other numbers in the same square. Name results
quickly:
7
4
3
6
8
4
5
6
8
6
2
10
10
3
7
9
4
9
9
8
6
5
3
9
4
10
7
D D
D
D
D D
D D
Q Q
Q
91. Rob made 5 squares and Roy made 3. How many
did both make? Draw the picture.
Dick had six marbles. He gave 2 to Ned. How many
had he left? Draw the picture.
There are 5 boys and 4 girls in a class. How many
children?
May had 7 apples. She ate 2. How many had she left?
Draw the picture. r
WRITING AND BBADINa NUMBERS TO 100.
69
How many feet are there in 3 yards?
How many 2-dollar bills should I get for a lO-doUar bill?
A man had ten sick sheep. One-half of them died.
How many got well ?
A lady sold 8 pounds of butter, 2 pounds in a roll. How
many rolls?
It is 2 miles from Harry's home to school. How far
does Harry walk each day? How far in two days?
Two wagons and a bicycle have how many wheels?
A farmer has 9 acres of wheat. One-third of it is cut.
How much has he to cut yet? How many thirds?
Bert has a dime. How can he give me ^ of it?
At two cents each, what will 5 oranges cost?
If $4 is i of my money, how much have I?
Two years is i of John's age. How old is he?
Writing and Beading Numbers from 1 to 100.
• ••
•• ••
••
•• ••
••
••
•• ••
••
••
••
•• ••
11
12
13
14 15
92. Look at the number picture on the left. What
do you see over the 1 at the right in this picture? (1 one,)
Over the one at the left? (1 ten.) Then It means 1 ten
and 1 one. (The figures 11 stand for the number eleven.)
What do you see over the 2 in the second number pic-
ture? (2 ones.) Over the 1? Then 12 means 1 ten and
2 ones. (The figures 12 stand for the number twelve.)
70
aCHClOL AfilTfiMETlC.
What does 13 mean? 17? 18?
How would you write one ten and three ones ({hirteen)i
One ten and four ones (fourteen)? Qne ten and five ones
(fifteen)?
How many figures do you write for each number?
What does the figure on the left show?
What does the figure on the right show?
In which place do we .write the ones? The tens?
If we call the number expressed by 16, sixteeny what
shall we call the number expressed by 17? By 18? By 19?
93. Read, supplying blanks:
11 = 1 ten and 1 one.
12 = — ten and — ones.
13 = — ten and — ones.
14 = — ten and — ones.
15 = — ten and — ones.
16 = — ten and — ones.
17 = — ten and — ones.
18 == — ten and — ones.
19 = — ten and — ones.
20 = — tens (and no ones).
a
I
1
3
4
5
6
7
8
9
10
J_
= 1 ten.
= 1 ten.
= 1 one.
94. Y^>u have already learned that two tens and no
onei? is written thus — 20.
Try to write two tens and one one.
Now write two tens and two ones.
What do we call 2 tens?
If we call two tens and one one, twenty-one, what shall
we call two tens and two ones?
Wbat shali wc call two tens and three ones? Two tens
and four oiKiiii Two tens and five ones? Two tens and
WBITING AND READING NUMBERS TO 100.
71
six ones? Two tens and seven ones? Two tens and eight
ones? Two tens and nine ones?
Copy and complete this table:*
10
«
20
30
40
60
60
70
80
90
1
11
21
31
2
12
22
3
13
4
5
6
1
7
8
9
95. How many numbers are in each column?
How many columns are there?
Name the numbers in the second column, beginning at
the top.
What does 16 express? (One ten and ones.)
What does 14 express? 18? 15?
*The pupils should be able to complete this table without help.
When they have it finished, they should learn the number names—
that is, count to one hundred.
72
SCHOOL AEITHMETIC.
Name the numbers in the third column.
What does 21 express? 23? 25? 29?
What do we call 3 tens? What then is the number made
up of 3 tens and 1 one? (Thirty-one.)
Now name the numbers in the fourth column-
What does 31 express? 32? 36? 38?
Name the numbers in the fifth column.
What does 41 express? 43? 44? 49?
Name the numbers in each of the other colunms.
Coimt to one himdred without looking at the table.
What number is written at the right of 14? At the
left of it?
What number is written at the left of 25? At the right
of it?
Begin at the number 2 and name each number to the
right of it.
Begin with 6 and read across to 96.
Name all the numbers in the table that end in 8. In
4. In 7. In 9.
What does 99 express? Who can write 9 tens and 10
ones?
A
B
—
The Sign x.
C D
E
■
96. How many squares in A? B is how many times A?
A is 2. How many 2's in B? 2 2's are .
2X2 = 4. This is read, 2 2's are 4, or 2 times 2 are 4.
(The sign X stands for the word times.)
THE SIGN X.
73
How many 2'8 in C? How many ones?
Eead this: 3X2 = 6.
How many 2's in D? How many ones? How many
fours?
Complete and read: 4 X 2 = ( ). 2 X 4 =*( ).
How many 2's in E? How many ones? How many
fives?
Complete and read: 5X2 = ( ). 2X5 = ( ).
• • •
• • •
• • •
• •
How many twos on the card to the left?
How many threes on the other card?
Are 3 2^s as many as 2 3's?
Show with blocks that your answer is correct.
Read these: 3X2 = 2X3. 3X2 or 2X3 = 6.
Call the dots on the first card cents. How many of
them will pay for a 2-cent stamp?
How many of them will pay for 3 stamps?
97.
1X2=2
2X1=2
2X2= 4
2X2= 4
3X2= 6
or
2X3=6
4X2= 8
2X4= 8
5 X 2 = 10
2 X 5 = 10
How many are 2 2'8?
3 2'8? 5 2's? 4 2's?
2 4's?
Copy and complete:
2X( ) = 4 2X( ) = 2
3X( )=6 4X( )=8
2X( ) = 8 2X( ) = 6
2 X ( ) = 10
5 X ( ) = 10
3X( )= 9
74
SCHOOL ABITHMETIO.
98. How many dots on the card at the left? How
many 3's?
How many 3's do you see on the second card? On the
third card?
Two S's are how many ones? 2 X 3 = ( ).
Three 3's are how many ones? 3 X 3 = ( ).
Nine dots are how many times 3 dots?
Call each dot on the middle card a foot. How many
of them are a yard? How many yards in 6 feet? In 9 feet?
3X2 = (). 2X() = 6. 3X() = 9.
An orange costs 3 cents. How much must I pay for
3 of them?
How many sides have three triangles? Three squares?
The Sign -^.
99. Here are 6 cents. How many 2-cent stamps can
I buy with them?
How many 2^ do you see in the 6^'i How many 3^?
How often must 2^ be taken to make 6^?
Then 6^ divided by 2^ = 3 times. This may be writ-
ten, 6^ -f- 2^ = 3.
It means that 2 cents are found in 6 cents 3 times.
6ff divided by 3^ = ( ). 6ff -r- 3^ = ( ).
What may stand for the words divided by?
THE SIGN -h.
Y5
Here are 8 stars. ^Zl^Tl^Tl^ To how many girls
can I give 2 stars each? 4 stars each?
8 stars -r- 2 stars = ( ). 8 stars -r- 4 stars = ( ).
If I divide the stars into two equal parts, how many
stars will be in each group?
Then 8 stars H- 2 = 4 stars. 8 stars -f- 4 = ( ).
How many 2's in 4? In 6? In 8? In 10?
How many 3's in 6? How many in 9?
How many 4's in 8? How many 5's in 10?
How often are 4^ contained in 8^?
times.
jMne quarts con
4^2 = ( ).
caius quarts
6^2 = ( ).
8-j-2 = ( ).
6 H- 3 = ( ).
10^2 = ( ).
9 ^ 3 == ( ).
4^^2=-( ).
$6 -J- 3 = ( ).
iof4 = ().
i of 6 = ( ).
8-4 =
5 = ()
() = 4
in.--2 = ( )
4of 8 = ( )
10
8
An orange costs 3^. How many can I buy for 9^?
If I must pay 5^ for a quart of milk, how many quarts
will I get for this dime?
Hettie had 9 buttons, 3 in a row. How many rows
were there?
How many 2-cent tops can you buy for 8 cents?
Cut a stick 9 inches long and one 3 inches long. Com-
pare them.
The longer stick is times as long as the other.
The shorter stick is — ■ — as long as the other.
How many times can a 2-inch line be measured off on
a 10-inch line?
76
SCHOOL ABITHM£TIO.
NUMBERS TO 20.
Eleven.
ITTTi
^
I
11.
100. Ten dotfi and one dot are
Eleven is made up of 1 ten and -
- dots,
one.
How many splints are in the bundle? How many loose
splints are there?
What figure will tell the number of bundles, or tens?
The number of single splints, or ones?
Take 11 pegs. Place them in two piles, putting 9 in
one pile.
How many pegs in each pile? How many in both?
What is the sum of 9 pegs and 2 pegs? Of 9 and 2?
Put one peg from the larger pile on the smaller. Now
how many in each pile?
The sum of 8 pegs and 3 pegs is pegs.
Take another peg from the larger pile and place it on
the smaller. Now tell me about the two piles.
Show me with the pegs how many 6 and 5 are.
Take one peg away from the 11. How many are left?
Show me with the pegs how many 2 from 11 leaves.
3 from 11. 4 from 11. 5 from 11. 6 from 11. 7
from 11.
Cut a string a foot long. Cut off 1 inch of it. Measure
the piece that is left.
Mary may tell us all she can about 11.
TWELVE.
101. Copy and complete:
10 + 1= 11 — 1= 11 — 6 =
ll-()= 8
9 + 2= 11 — 2= 11 — 8 =
7 + () = ll
3 + 8= 11 — 4= 11 — 7 =
4 + () = ll
7 + 4= 11 — 3= 11 — 9 =
ll-()= 6
5 + 6= 11 — 5= 11 —10=
ll-()= 4
77
102. Make a story for 5 + 6.
A stick of candy costs a cent. How many sticks can
you get for a dime and a cent?
What two pieces of money make 11 cents?
How much must you pay for three 3-cent stamps and a
2-cent stamp?
If you have been at school two weeks and one day this
month, how many days have you been at school?
Three yards and two feet are how^many feet?
We have 2 bushels and 3 pecks of apples. How many
pecks have we?
If we use 3 pecks of them, how many pecks will we
have left? How many busBels?
A rail 11 feet long was cut in two. One part was 7
feet long. What was the length of the other part?
There are 11 eggs in two nests. In one nest there are
6 eggs. How many in the other?
Twelve.
• •
• • • • • •
• • • • • •
103. Ten dots and 2 dots are
Twelve dots are 1 more than —
— dots,
dots.
78 SOHOOL ARITHMETIC.
There are 12 dots on the card at the right. Call them
pigs. How many are in each pen?
Six and six, or two sixes, are . How many 6's
in 12?
Put one little pig into the pen with the big ones. How
many pigs in each pen now?
Seven and five are how many?
Put another little pig in with the big ones. Now how
many pigs in each pen?
Eight and four are how many?
When 9 of them are in one pen, how many are in
the other?
When only two little pigs remain in one pen, how many
are in the other?
Who can name three numbers that added together
make 12?
Write twelve and tell what each figure stands for.
Use your foot rule to find these answers:
One inch from 12 inches leaves inches.
Two inches from 12 inches leaves inches.
Four inches from 12 inches leaves inches.
Eight inches from 1 2 inches leaves inches.
Three inches from 12 inches leaves inches.
Five inches from 12 inches leaves inches.
Six inches from 12 inches leaves inches.
How many triangles can you make with 12 splints?
How many squares?
Measure your rule with a stick 2 inches long. How
many 2-iiiches make 12 inches?
0X2 inches = inches.
TWELVE. 79
How many times could you cut 2 inches off your rule?
How many 2's in 12?
12 inches -r- 2 inches = .
Use splints to show me i of 12. i of 12. f of 12.
104. Measure with the foot rule:
The length of this book.
The width of your desk.
The length of this chart.
The height of this boy.
The length of this yardstick.
Measure with the yardstick:
The length of this room.
The width of this room.
The length of this house.
Your foot rule is marked off into 12 equal parts. What
is each part called?
In 1 foot there are inches. In ^ of a foot there
are inches.
How many inches in ^ of a foot? In i of a foot?
Draw a line on the board 12 inches long, without
measuring.
Now measure it and find out how long it really is.
Who can draw a line a yard long without measuring it?
Draw a rectangle (an oblong) four inches long and
three inches wide.
Draw lines across it, as in the picture.
Draw them an inch apart.
What is a square 1 inch on a side
called?
80
80HOOL ABITUMETIO.
How many square inches are there in the upper row?
How many rows are there? Then how many square
inches in the three rows?
3X4 square inches = square inches.
How many square inches in the left-hand row? How
many rows are there?
Then how many square inches in the four rows?
4X3 square inches = square inches.
Cut out a square inch and find how many of them will
cover your rectangle.
Draw a rectangle 6 inches long and 2 inches wide. Find
how many square inches there are in it.
106. Copy and complete:
10 + 2 =
11 + 1 =
9 + 3 =
4 + 8 =
7 + 5 =
6 + 6 =
2X6 =
3X4 =
12-
12
12-
12
12-
■2 =
1 =
4 =
-3 =
5 =
12 — 6^
12^2
12 -V- 6 =
12 —
12 —
12 —
12 —
12 —
12 —
12-^
12 -^
■■%
4
3
5
9+ 2^
7+ 4^
i of 12 :
f of 12
i of 12 :
iof 9 =
i of 12 :
fof 12:
106. There are 9 quarts of milk in one pail and 3
quarts in another. How much milk?
Tell a story about 8 + 4 = 12.
How many days are a week and 5 days?
Seven cents and a nickel are how much money?
npnry had 12 goats. A bad boy stole 4 of them. Ask
a question and answer it.
JIake a story about 12 — 5 = 7.
TWELVE. 81
A boy who had 12 cents gave two nickels for a book.
He had left cents.
How many cows have 12 tails? How many have 12
horns?
Six girls wear shoes.
How many shoes do 3 horses wear?
In 1 yard there are feet. In 4 yards there are
feet.
Twelve pecks of plums are how many bushels?
A log is 12 feet long. How many yards is that?
If you divide 12 nuts equally among 4 boys, how many
will each have?
How many quarts of milk in 12 pints?
If we had a dozen eggs, boys could have 2 apiece.
107. Name the months of the year.
In a year there are months. In half a year there
are months.
What is the first month? The second? The twelfth?
What is the name of the present month? In what
month is your birthday?
During what months is school held?
March, April, and May are called the spring months.
Name the summer months. The fall or autumn months.
The winter months.
JIow many seasons in a year? Then how many months
in a season?
What part of a year are the spring months? The
summer months?
What part of a year are the spring and summer months
together?
H
83
SCHOOL ABITHMEnO.
108. Some things to remember:
Jan. stands for January. Sept. stands for September.
Feb. stands for February. Oct. stands for October.
Mar. stands for March. Nov. stands for November.
Aug. stands for August. Dec. stands for December.
12 inches nmke 1
12 things nmke 1
12 months nmke 1
foot.
dozen.
year.
Ct. or ^ stands for cent.
Qt. stands for quart.
Gal. stands for gallon.
In. stands for inch or inches.
Ft. stands for foot or feet.
Doz. stands for dozen.
Sq. in. stands for square inch.
Yd. stands for yard.
Bu. stands for bushel
109, It is noon at 12 o'clock. Look
at the clock face and tell how many
hours it is from noon to midnight.
Show me to what the short hand
points at 1 o'clock. At 2 o'clock.
What stands for one on the clock
face? For two? For three? For
fivei For teni
I stands for 1.
V stands for 5.
II stands for 2.
X stands for 10.
Ill stands for 3.
What stands for 4?
In Roman notation IV always stands for 4 except on
clock faces, where IIII is commonly used.
You know that 5 — 1 means 4, or 1 less than 5. When
I is written before V, the two letters (IV) mean one less
than five, or 4.
THIBTEEN.
83
What do you think IX means?
What does 5 + 1 mean?
When I is written after V, the two letters (VI) mean
one more tha/n five^ or 6.
What do you think VII means? VIII? XI? XII?
IV stands for 4.
VI stands for 6.
VH stands for 7.
VIII stands for 8.
X stands for 10.
IX stands for 9.
XI stands for 11.
XII stands for 12.
If we eat dinner at 12 o'clock and supper at 6 o'clock,
how long is it between meals?
Look at a nickel to-night and tell me to-morrow what
shows the number of cents it is worth.
• •
f@S^
Thirteen.
UO. What number follows 12?
One ten and 3 ones are .
Name two numbers less than 10 whose sum is 13. Two
other numbers. Now two others. (Use splints to find
the numbers.)
Take 13 splints. Show how many are left when 4 are
taken away. When 5 are taken away. When 6 are taken
away.
This line on the board is 13 inches long. How much
longer is it than your foot rule?
How many splints are m the bundle? How many tens?
How many loose splints, or ones^ do you see?
84
80HOOL AKITHMETIO.
Write on the board the figures that stand for the
number thirteen.
Which figure stands for the tens? Which for the ones?
Three and ten are . (The word thirteen means
three and ten.)
HI. Copy and complete:
10 + 3= 13 — 4= 11 + 2= 8 + 2 + 3 =
9 + 4= 13 — 6= 13 — () = 9 5 + 4 + 4 =
5 + 8= 13 — 7= 13 — () = 7 4 + 3 + 6 =
7 + 6=^ 13 — 5= 13 — () = 5 5 + 3 + 5 =
112. Add quickly:
7 9 5 3
2
6
7
8
4
6
6 4 8 10
11
5
5
3
5
4
Subtract at sight:
13 13 13 13
13
13
13
12
12
12
4 6 5 7
8
9
10
3
5
4
Subtract each number in the rim of the
wheel from the 13 in the center.
113, Three bushels and a peck are how
many pecks?
There are 8 qt. of milk in one pail and 5 qt. in another.
How much milk in both?
FOURTKEN.
86
Look at the flag and tell a
story about 7 + 6.
How many 4'8 in 13, and
how many left over ? Draw the
picture, using dots.
A log is 4 yd. and 1 ft. long.
It is feet longer than a pole
ten feet long.
Fourteen.
• • • • • •
• • • • • •
• • • • • •
• • • • • •
114. One ten and 4 ones are
How many squares do you see in the figure?
How many more than 10? How many more
than 9? Than 8? Than 7?
If 5 were taken away, how many would be left?
Take six away from 14. How many remain?
Count by twos to 14. J J J J J J J
How many dots are in each row? How many
rows?
Two times 7 dots are dots.
Show that 7 times 2 dots are as many as 2 X 7 dots.
One-half of 14 dots is dots.
How many 7's make 14? How many 2's?
Take 9 splints and 5 splints and show that they are as
many as one ten and four ones.
Write the figures that stand for the number fourteen.
Which figure stands for the ones? On which side of
the 1 must it stand?
86 SCHOOL ARITHMETIO.
US. Copy and complete:
9 + 5= 14 — 6= 5 + () = 14 2X7 =
6 + 8= 14 — 7= 8 + () = 14 7X2 =
7 + 7= 14 — 8= 14 — ()=9 14--2 =
14 — 5= 14— ,9= 14 — ()= 6 14^7 =
^ qt. + 1 pt. = pt. 3 ga.. +2 qt. = qt.
7 bu. + 3 bu. = $10 + $4 =
1 ft. +2 in. = in. 5 qt. +3 pt. = pt.
3 yd. 4- 5 ft. = ft. i doz. +5 =
116. James earned 8 cents on Friday and 6 cents on
Saturday. On both days he earned cents.
How much will 6 eggs cost at 14 cents a dozen?
In 14 there are 3's and over.
Make a story for 7 + 7 = 14.
How many days are there in two weeks?
How many gloves are 7 pairs of gloves?
Fourteen months are how many more months than a
year?
A boy had a ten-cent piece and four pennies. He spent
5 cents for peanuts. How much had he left?
A spider has 8 legs. A spider and a fly together have
14 legs. How many legs has a fly?
Three gallons and 2 quarts of milk are how many quarts?
How many half -bushels of oats make 7 bushels?
If a milkman has 7 qt. of milk, to how many persons
can he sell a pint each?
A man has 14 miles to travel. When he has gone 8
miles, how far has he yet to go?
BISTBBK.
87
Fifteen.
• • •
117. One ten and 5 ones, or one ten and 1 five, are .
Lay 10 blocks in one row and 5 in another, as in the
picture above. Use them to find the missing number in
the following:
15=9+( ). 15= 8+( ). 15=6+( ). 15=7+( ).
15— 6=( ). 15— 8=( ). 15— 7=( ). 15— 9=( ).
15=3 X ( ). 15=5X(). 15-v-5=( ). 15--3=( ).
How many dots are on the card? What part of them
are on the right of the line? On the left of the line?
Are 3 fives as many as 5 threes? Show with counters.
118. This circle is divided into
equal parts.
What do you think one of these parts is called?
What part of the rectangle is dark?
One of the 5 equal parts of anything is called one-fifth
To find one-fifth of anything we must divide it
into equal parts.
How many small squares are there in the rectangle?
Are the 3 dark squares one of the 5 equal parts of the
rectangle?
88 SCHOOL ARITHMETIC.
Then i of 15 squares is — — squares.
One-fifth of 5 cents is cent.
One-fifth of 10 feet is feet.
Make 15 dots. Draw a line around i of them. Now
draw a line around another fifth of them.
How many fifths have lines around them? How many
fifths have no lines around them?
How many dots in one fifth? How many in two fifths?
119. Copy and complete
l\J\tO,
9+6— 15—6—
7+( )=15.
3X5=
7+8= 15—7=
9+( )-15.
5X3:
i of 15— 15—9—
15— ( )— 10.
15-^5=
1 of 15= 15—8=
15— ( )— 6.
n-i-Z-
i of 15— f of 15—
f of 15—
i of 15:
120. A man has 3 five-dollar bills. How much money
has he?
What two pieces of paper money make $15? What 3
pieces?
Fifteen eggs are how many more than a dozen?
Tell a story about 9 boys + 6 girls = 15 children.
Pimch has 8 dimes and Judy 7. Ask a question and
answer it.
J( unic^ has 5 yd. of cloth for a dress. How many feet
long is the cloth?
Tell a story about 15 — 6 = 9.
Stella liad 15 jacks. She lost 7 of them. She had
left.
Harry may tell all he can about 15.
Find (mt at home to-night how many ounces make a
pound*
SIXTEEN.
Sixteen.
• •••••
• •••••
121. One ten and six ones are
Show with blocks how many 9 and 7 are.
How many ones do you see on the card? How many
8's? How many 4's? How many 2's?
Show with blocks how many 16 — 7 are.
How many times 4 dots make 16 dots?
How often does the card contain 8 dots?
If the dots were shoes, how many pairs could you take?
If they were quarts, how many gallons would you have?
What part of the dots is on each side of the line?
What part of the 16 dots are large?
How many fourths of them are small?
Sixteen means six and — "—.
122. Copy and complete:
9 + 7 = i of 16 = 2X8:
8 + 8= fofl6= 8X2 =
10 + 6= iofl6= 4X4 =
16 -r- 8:
16-^2 =
16 -r- 4:
123. Tom had 9 cents and Sam had 7 cents. They
both had cents.
They gave ten cents of it for a dime. How many
pennies had they left?
Cora carried 2 gallons of water and Delia carried 8
quarts. How much did both carry?
We have 4 cows. Each cow gives 4 quarts of milk.
They all give • quarts.
90
SCHOOL ARITHMETIC.
Mr. Brown had 16 sheep, but one-half of them died.
Ask a question and answer it.
How many wheels have 8 bicycles?
I have 16 apples. To how many girls can I give two
apples each?
124. Where have you seen these weights used?
Which is the largest weight? The smallest?
How many of the smallest are equal to the largest?
How many ounces make a pound?
16 ounces (oz.) make 1 pound (lb.)-
What stands for the word ounce or ounces? For the
word pound or pounds f
How many ounces in i of a pound? In i of a pound?
What part of a pound are 8 ounces? 4 ounces?
How many ounces in a quarter of a pound of starch?
How many 4:-ounce weights are equal to the 1 -pound
weight? How many 2-ounce weights?
When butter is 16 cents a pound, how much must I
pay for 8 ounces? For 4 ounces? For 12 ounces, or J
of a pound?
Seventeen.
• • •
f
125, Ten and seven are how many? How many more
Would iiaakc -1 tens?
'bat doe^ tlie word seventeen mean?
SEVENTEEN.
91
How many dots are on the card? How many on each
end of it?
Nine dots and eight dots are dots.
If 8 dots were taken off the card, how many would
remain? How many if 9 dots were removed?
Count 12 by twos. What other numbers can you count
by twos? Can you count 9 by twos?
Numbers that can be counted by twos are called even
numbers; all others are called odd numbers.
Did you ever play " Odd or^ven"? How do you play it?
Is 5 odd or eve^i ?
Name all the odd numbers less than 17.
Tell at sight what nmnber put with
each of the outer numbers will make 17.
126. Add:
9 10
8 7
10
8
14
12
17
1
15
11
9
8
9
11
6
5
12
13
4
3
14
15
2
Subtract:
17 17
8 10
17
9
16
8
16
9
16
16
7
15
127. Is 9 odd or even? How many 2's in
13^4 =
14
2 =
2 =
5 =
17^4 =
17-^5 =
and
and
and
and
and
and
left over,
left over,
left over,
left over,
left over,
left over.
SCHOOL AKITHMETIC.
128. Nine cents + eight cents = 1 dime H — cents.
rive yards and 2 feet are how many feet?
My brother is 17 years old. How old was he 8 years
If sugar is 5^ a pound, how many pounds can you buy
with a dime and a nickel?
A string 17 ft. long was cut in two in the middle. Wbat
was the length of each part? Find by measuring.
How many gallons of oil at 8 cents a gallon can you
buy with 17 cents? How many cents left over?
Eighteen.
• • • • • •
• • • • • •
• • • • • •
129. Ten and eight, or 1 ten and 8 ones, are .
Nine dots and nine dots are how many dots?
If- nine dots are taken from 18 dots, how many will
remain?
How many small dots are on the card? How many sixes
do you see on it? How many threes? How many nines?
Find how many twos make eighteen.
One-half of 18 dots is dots.
One-third of 18 dots is dots.
Two-thirds of 18 dots are dots.
Make dots for the following: 18, 6, 12, 9, i of 18.
Count to 18 by 2's. By 3's. By 6's.
Is 18 an even or an odd number?
How many 2's in 18? How many 3's? How many 6's?
How many 9's can you take from 18? Then how many
9's are in 18?
EIGHTEEN.
93
Take 18 sticks and find how many 8's in 18, and how
many left over.
What part of 18 is 9? What part of 18 is 6?
• • • • • •
• • • • • •
130. The circle is divided into
me one-sixth (i) of the circle.
equal parts. Show
— equal
To find i of anything we must divide it into —
parts.
Show me i of the dots on the card.
i of 12 dots = dots.
How many sixths of the dots are large?
f of 12 dots = dots.
I of 12 dots = dots.
Is i of the rectangle as much as f of it?
Is i of 12 dots as many as |^ of them?
Find i of 12 dots and compare it with f of them.
Which is larger, i of 12 or i of 12?
Show me i of 18 blocks, i of 18 =
What part of 12 is 2? Of 6 is 1?
131. Copy and complete:
9+9= 9X
2
= 18 -=- 6 =
18-( ) = 9
2X9= 18 -i-
3
= 18 -=-9 =
8 + 8 + 2 =
18 — 9= 18-T-
2
3X6 =
6X ( ) = 18
3 + 5 + 10 =
i of 18 =
1 of 18 =
2 + 7+ 4 =
i of 18 =
1 of 18 =
4 + 4+ 6 =
f of 18 =
1+ i =
2 + 9+ 5 =
1 of 18 =
*-|-
94: SCHOOL ARITHMETIC.
132. A boy bought 2 books at 9 cents apiece. They
cost him — — cents.
Barnet put 18 nuts on a fence. A squirrel carried off
2 of them each day for days. Then all were gone.
How many days are 2 weeks and 4 days?
Four bushels and 2 pecks, or 4|^bu., are — — pecks.
Draw a line 18 in. long. Show that it is ft. long.
Mary sold eggs at a cent apiece. How much did she
get for a dozen and a half?
Find the cost of a gallon of milk at 4^ a quart.
If 1 orange costs 2 cents, what will 9 oranges cost?
How many yards in a piece of cloth 18 feet long?
I want to buy a book for 18 cents. I have a dime. I
need — — cents more.
Maud has 18 jacks. She gave i of them to Jane. How
many had she left?
How many squares can you make with 18 splints? How
many triangles?
Nineteen.
133, One ten and 9 ones, or 10 and 9, are .
How^ many dots are 2X9 dots, and 1 dot?
How many dots are 6 X 3 dots, and 1 dot?
Nineteen dots are how many more than 3X6 dots?
How many tens in 19? How many ones left over?
How many 2's in 19, and how many ones left over?
How many 9's in 19, and how many left over?
BBVIEW AND DRILL. 95
Show that 10 is less than .19.
Nineteen is how many more than 11?
Show that 12 and are 19.
Show that 19 is more than 13.
To each of the following add the nimiber that will make
the sum 19: ' 8, 11, 7, 9, 15, 17, 16.
134, Copy and complete:
10+9= 9 + 9 + 1= 8 + 8 + 3 =
19—9= 2X9 + 1= 2X8 + 3 =
19^10= 19-7-9 = 19-^-8 =
Review and Drill.
135. a
h
c
11 + 1 =
12 + 2 =
13 + 3
11 + 3 =
12 + 4= ■
13 + 5
11 + 2 =
12 + 6 =
13 + 6
11 + 5 =
12 + 3 =
14 + 5
11+4 =
12 + 5 =
14 + 4
11 + 7 =
12 + 7 =
14 + 2
11 + 6 =
13 + 2 =
14 + 3
11 + 8 =
13 + 4 =
15 + 2
d
e
/
15 + 3 =
9 + 3 =
8 + 9
15+4 =
9 + 5 =
9 + 9
16 + 3 =
9 + 4 =
8 + 5
16 + 2 =
9 + 6 =
8 + 8
17 + 2 =
9 + 7 =
8 + 4
96 80HOOL AKITHMETIC.
9
h
i
8 + 3
=
6 + 2 =
5 + 5 =
8 + 7
=
6 + 4 =
4 + 4 =
8 + 8
=
6 + 6 =
4 + 2 =
7 + 4
=
6 + 3 =
4 + 3 =
7 + 6
=
6 + 5 =
3 + 4 =
7 + 5
=
5 + 4 =
3 + 2 =
7 + 3
=
5 + 2 =
7 + 9 =
7 + 7
=
5 + 3 =
8 + 7 =
;■
fc I
m
2X2 =
2X
8= 3X 5-
= 5X
3
2X3 =
2X
9= 3X6 =
= 6X
2
2X4 =
2 X 10 = 4X2
= 6X
3
2X5 =
3X
2= . 4X 3-
= 7X
2
2X6 =
3X
3= 4X 4:
= 8X
2
2X7 =
3X
4= 5X2-
= 9X
2
n
p
9
9 — 2 =
8 —
2= 7— 5-
= 10 —
2
9 — 7 =
8 —
6= 7— 3 =
= 10 —
8
9 — 3 =
8 —
3= 7— 4 =
= 10 —
3
9 — 6 =
8 —
5= 6— 2
= 10 —
7
9 — 4 =
8 —
4= 6— 4 =
= 10 —
4
9 — 5 =
7 —
2= 6— 3:
= 10 —
6
r
s
i
«
10 — 5 =
12 —
2= 13-2 =
= 14 —
2
11 — 2 =
12 —
10= 13 — 11 =
= 14 —
3
11 — 9 =
12 —
3= 13—3 =
= 14 —
4
11 — 3 =
12 —
9= 13— 4 =
= 14 —
5
11 — 8 =
12 —
4= 13— 9 =
= 14 —
9
11 —4 =
12 —
8= 13—5 =
= 14 —
6
11 — 7 =
12 —
5= 13—8 =
= 14 —
8
11 — 5 =
12 —
7= 13—6 =
= 14 —
7
11 — =
12 —
6= 13—7 =
14 —
10
BBVIEW AND DBIIX.
97
2 =
9-J-2 =
2 =
8-7-2 =
10
2 =
12^2 =
w
a;
'
V
U-h 2 =
12 -T- 6 =
18-
-
3
16-^ 2 =
18-^ 6 =
10-
-
5
18 H- 2 =
6H- 3 =
15-
-
5
4^ 4 =
9-f- 3 =
12-
-
6
8-h 4 =
12 -^ 3 =
18-
-
6
12 -f- 4 =
15-^ 3 =
14-
-
7
136. A farmer has 7 Jersey cows and 8 Durham
cows. How many cows has he?
Willie caught 1 trout and Harry caught 9 trout. How
many did both catch?
School begins at 9 o'clock in the morning, and continues
3 hours. What time is it when school is dismissed?
In a game of baseball 9 persons play on each side. How
many players are there in the game?
A table is 6 feet long and 3 feet wide. What is the
number of feet around it?
From a dozen and a half cans of peaches 3 cans were
used. How many cans were left?
A farmer had 19 lambs and sold 7 of them. How many
lambs had he left?
One sash of a window has 2 rows of panes, and 3 panes
in a row. How many panes are there in the sash?
Hunter has 8 rabbits; Jack has half as many. How
many rabbits have both together?
How man^ l^s have 6 three-legged stools?
From a brood of 19 chickens, 6 were sold, and half a
dozen were eaten. How many chickens were left?
How many times does the sun rise and set in 1 week?
Divide 18 peaches among 6 girls. How many peaches
does each receive?
98
80HOOL ABITHMETIO.
A plank is 18 inches long. If you saw ojBE a half foot,
how long is the plank then?
Make a rectangle 5 inches long and 3 inches wide, and
divide it into inch squares. How many square inches in
the rectangle?
How many quart bottles will it take to hold 16 pints?
If you have J of a dollar and spend i^ how many fourths
have you left? How many quarters?
Nineteen ounces are how many more ounces than one
pound?
Draw a line 17 inches long. How many more inches long
is it than 1 foot?
How many strokes will a clock make in striking 8 and 9?
Twenty.
i
Z
3
4
5
2
S
4
187. Ten and ten, or two tens, are .
How many squares in the upper row? How many
rows are there? How many squares in all the rows?
Then 4 times 5 squares are squares.
Show that 5 times 4 squares are 20 squares.
Two tens are as many as fives or fours.
Find from the card how many twos in twenty.
What does the figure mean in the number 20?
What figure shows that there are two lO's in twenty?
Show that 20 is more than 10.
TWENTY. 99
Show that 16 is less than 20.
Show that — ^ is 5 less than 20.
One-half of 20 dots is dots.
Two dots are found in 20 dots times.
One-fourth of 20 squares is squares.
Two-fourths of 20 squares are squares.
Three-fourths of 20 squares are squares.
138. One-half of anything is one of its two equal parts.
One-third of anything is one of its equal parts.
What is meant by i of anything? i?
Divide 10 blocks into 10 equal parts. How many
blocks in each part?
What is one of the equal parts called? (One-tenth.)
One-tenth of 10 blocks is block.
How many ones make one ten? Then one one is what
part of one ten?
Show me one-tenth (^) of 20 dots.
One cent is what part of 10 cents? One is what part
of 10?
Draw a line 10 inches long. Under it draw a line -^
as long.
Into how many equal parts is this circle
divided?
What is each part called?
How many tenths are dark? How many '
are light?
•^ of the circle + -j^^ of the circle = of the
circle, or the whole circle.
How many tenths are y^^ and -^ ?
Make two rows of 10 dots each. Draw a ring around
-^jf of the dots. Draw a ring around ^ of the 20 dots.
100 BOHOOL ARTTHMBTia
Which 18 more, | of 20 dots or ^ of 20 dots ?
If you take ^ of anything away, how inany tenths
remain}
One of the ten equal parts of anything is called one-tenth.
What are 3 of the parts called? Four of the parts?
Seven of the parts?
How many tenths are there in anything? How many
halves? Show that I = A-
One tenth means one out of ten. What does ^ mean?
A? i*?
How many dimes make a dollar? A dime is what part
of a dollar?
What part of a dollar are 3 dimes? 5 dimes?
Is one half-dollar as much as 5 dimes?
Is one-half as much as 5 tenths?
Twenty things are sometimes called a score. How many
139.
in half a score?
In iV of a score i
Complete the
process:
10 + 10 =
20 — 10 =
20 = 10 +
18+2 =
20—2 =
20 = 18 +
16+ 4 =
20—4 =
20 = 16 +
17+3 =
20— 3 =
20 = 17 +
16+5 =
20—5 =
20 = 15 +
14+6 =
20—6 =
20 = 14 +
12+8 =
20—8 =
20 = 12 +
13+ 7 =
20—7 =
20 = 13 +
2X10 =
20 ^ 10 =
i of 20 =
10 X 2 =
20^ 2 =
i of 20 =
4X 5 =
20-^ 5 =
i of 20 =
5X 4 =
20-T- 4 =
A of 20 =
k
I. «,.*«> •* •*
TWENTY.
IQl
140.
10 is contained in 20
9 is contained in 20
8 is contained in 20
7 is contained in 20
6 is contained in 20
5 is contained in 20
3 is contained in 20
4 is contained in 20
2 is contained in 20
times and
times and
times and
times and
times and
times and
times and
times and
times and
over,
over,
over,
over,
over,
over,
over,
over,
over.
141.
Count by fives to 20.
Count by twos to 20.
Count by fours to 20.
Count by threes to 18.
Count by sixes to 18.
Count by tens to 10^.
- fives are 20.
- twos are 20.
• fours are 20.
■ threes and 2 are 20.
- sixes and 2 are 20.
• tens are 100.
142. How many shoes will be required to shoe 5
horses? 10 men?
If you had 10 cents and your mother gave you a ten-
cent piece, how much money would you have?
A farmer owns 3 horses, 8 cows, and 9 sheep. How
many animals has he?
If a strip of paper is 5 inches long and 4 inches wide,
how many square inches does it contain?
Two dimes equal how many nickels?
If 20 bananas were divided equally among 4 girls, how
many would each have?
If a strip of paper contains 20 square inches, and it is
5 inches long, how wide is it?
Marvin had 20 cents and spent i of them for ink, and
the rest for paper. What did the paper cost?
.X0%.
'SCHOOL ARITHMETIO.
How many school days in 4 weeks?
If I cut 5 apples into quarters, to how many children
can I give a piece?
Is 20 odd or even? How much must you add to it to
make it odd?
Take 20 cents and give -^ of them to each of 6 of your
classmates. How many have you left ?
Draw 11 vertical lines 2 inches apart on the blackboard.
How far apart are the two outside lines?
Harry had 20 marbles. He put i of them into one pile,
i of them into another pile, and the rest in the third pile.
How many in each pile?
Eggs are 10^ a dozen. How many dozen can be bought
for 20y?
We have found out that X stands for 10. What do you
think XX stands for?
How many years are 3 score years?
How old is a man who is 3 score and ten years of age?
Numbers to 100.
10+10+1=21.
2< + lo=21o.
10+10+5=26.
2^ + 50=25 o.
10+10+10=30.
3^ = 30 0.
10+10+10+4=34.
3« + 4o = 34o.
143. Here / stands for the tens. What does o stand for?
Draw squares like these to represent 23, 27, 36, 39.
Draw squares to represent 2/ + 6o, 3^ + 8 0, 2^ + 2^.
NXnCBEBS TO 100.
103
Complete:
20 + 1 =21
2< + lo = 21o
20 + 2 =
2t + 2o =
20 + 4 =
2t + 4:0 =
20 + 6 =
2t-\-6o =
20 + 8 =
2< + 8o =
30 + 1 =
3t + lo =
30 + 3 =
Zt + 3o =
30 + 5 =
3« + 5o =
2< + 5o
22 =
26 =
29 =
32 =
36 =
37 =
39 =
St + 3t = 8t = 80 6o + 5o = llo = l< + lo, or 11
4t + 5i==
3« + 4< =
7i + 2t =
6< + 4< =
7o + 6o-
9o + 6o =
12o + 8o =
20o + 7o:
I
10+10+10+10+3=43.
4e + 3o = 43o.
10+10+10+10+10+6=56.
6< + 6o = 56o.
144. Draw squares to represent 45, 57, 52, 64, 66.
Draw squares to represent 4f+6o, 5< + 8o, 6 <+l t.
104:
SCHOOL ABITHMETIO.
Complete:
40 + 1 = 41
4t + lo=41o
41 = 4< + lo
40 + 4 =
4< + 4o =
44 =
40 + 8 =
4< + 8o =
48 =
50 + =
5t + 0o =
50 =
50 + 5 =
5< + 5o =
55 =
50 + 9 =
5< + 9o =
59 =
60 + 3 =
6t + 3o =
63 =
60 + 8 =
6< + 8o =
68 =
42 = 4< + 2o
18 + 3 = 21
= 2 < + 1 0, or 21
45 =
14o + 4o =
47 =
15o + 5o =
53 =
20o + 4o =
56 =
30 + 2 =
58 =
40o + 7o =
64 =
50 + 4 =
67 =
60 + 5 =
10+10+10+104-10+10+10+5=75.
7e + 5o = 75o.
Draw squares to represent 73, 84, 89, 92.
Draw squares to represent 7 t + 4cOy 8t + 10 o, 9t+9o.
KUMBBfiS TO 100. 105
145. Complete:
70+ 1 = 71 7< + lo = 71o 7l = 7* + lo
70+ 7= 7/ + 7o= 77 =
80+ 3= 8< + 3o= 83 =
80+ 8= 8t + 8o= 88 =
90+0= 9/ + 0o= 90 =
90+5= 9« + 5o= 95 =
60 + 20= 6i + 2/= 80 =
76 = 7^+60 70 0+ 4:0 = 74:0 = 7 t+4:0, or 74
79= 70o+ 7o =
81= 80o+ 5o =
87= 80o + 10o =
93= 90o+ 3o =
96= 90 + 10 = 100 =10 t, or 100
Idime + 5ff=15^ lt+ 5 o=15 12^=1 dime + 2^
2 dimes + 5^= 2 ^+ 5 o= 15^= •
4 dimes + 2^= 4<+ 2o= 17^=
5 dimes + 8^= 5 t+ 8 0= 25f^=
7 dimes + 5^= 7 ^+ 5 o= 38^=
8 dimes + 7^= 8 /+ 7 a= 53^=
9 dimes + 9^= 9 t+ 9 o= 81^=
9 dimes +10^= 9 ^+10 o= 98^=
146. Write and read the numbers to 100.
Count backwards from 20 to 0. From 50 to 20.
Count by 2's to 50; then backwards to 2.
Count by lO's from to 100; then backwards to 0.
Count by lO's from 1 to 91. From 2 to 92.
In 25 wihat does the 2 stand for? The 5?
In 33 the figures are alike. Do they mean the same
thing?
106
SCHOOL ARITHMETIO.
Complete:
24=20 + 4
46 =
74 =
88
27 =
48 =
77 =
89
22 =
52 =
79 =
67
31 =
55 =
82 =
94
34 =
68 =
85 =
96
39 =
71 =
87 =
99
^
^
I—
J
24 + 3 =
32 + 4 =
25—3 =
=
37—
147.
Add:
24
32
24
32
21
33
33
3
4
4
5
3
4
5
34
26
35
46
44
51
62
2
3
3
2
4
7
6
65
62
74
83
77
86
94
4
7
3
6
2
2
5
smaoEsa to 100.
107
Snbtiaet:
25
3
87
4
26
45
3
47
4
36
2
Name results quickly:
21 + 1 =
31 + 1 =
41 + 1 —
51 + 1 =
71 + 1 =
91 + 1 =
61 + 1 =
81 + 1 =
21 + 2 =
31 + 2 =
51 + 2 =
71 + 2 =
22 + 2 =
32 + 2 =
42 + 2 =
52 + 2 =
21 + 3 =
31 + 3 =
41 + 3 =
51 + 3 =
22 + 3 =
32 + 3 =
42 + 3 =
52 + 3 =
35
3
19
29
39
49
59
69
79
4
4
4
4
4
4
4
28
38
48
57
67
77
87
6
5
5
3
3
3
3
21+4:
31 + 4:
41+4:
51 + 4:
22 + 4:
32 + 4:
42 + 4:
52+4:
If you add 1 to numbers ending in 1, with what figure
does the sum end?
If you add 2 to numbers ending in 1, with what figure
does the sum end?
If you add 2 to numbers ending in 2, with what figure
does the sum end? '
If you add 3 to nimibers ending in 1, with what figure
does the sum end?
If you add 3 to numbers ending in 2, with what figure
does the sum end?
108 SCHOOL ABITBMETIO.
«
If jou add 4 to numbers ending in 2; with what figure
does the sum end?
If you add 4 to numbers ending in 3, with what figure
does the sum end?
When you increase 31 by 2, do you add 2 to the 1 or
to the 3?
21 + 5 =
21 + 6 =
21 + 7 =
21 + 8 =
31 + 5 =
31 + 6 =
31 + 7 =
31+8 =
41 + 5 =
41 + 6 =
41 + 7 =
51 + 8 =
51 + 5 =
51 + 6 =
51 + 7 =
71 + 8 =
22 + 5 =
22 + 6 =
22 + 7 =
73 + 6 =
32 + 5 =
32 + 6 =
32 + 7 =
84 + 5 =
42 + 5 =
42 + 6 =
42 + 7 =
92 + 7 =
52 + 5 =
52 + 6 =
52 + 7 =
65 + 3 =
If you subtract 1 from numbers ending in 2, with what
figure does each answer end?
If you subtract 1 from numbers ending in 3, with what
figure does each answer end?
Add 3 to numbers ending in 5. What is the ending
figure?
Subtract 5 from numbers ending in 8. What is the
ending figure?
Find the value of :
24 — 1
26 — 3
87 — 4
49 — 7
16 — 5
34 — 1
46 — 3
18 — 5
79 — 7
26 — 5
74 — 1
86 — 3
28 — 5
88 — 6
66 — 5
15 — 2
17 — 3
48 — 5
58 — 6
18 — 8
25 — 2
27 — 3
19 — 6
39 — 8
28 — 8
35 — 2
57 — 3
29 — 6
28 — 3
49 — 9
65 — 2
77 — 4
39 — 6
47 — 4
86 — 6
16 — 3
97 — 4
89 — 7
56 — 5
99 — 7
ADDITION AND SUBTBACTION.
109
Add numbers in center of each square to each of the
other numbers. Subtract central number from each of the
others.
Addition and Subtraction.
20+15 =
14 + 22
31 + 26
148, If we put these splints all together, how many
loose splints will we have? How many bundles, or tens?
14 = 1^ + 40
22 = 2t+2o
36 = 3^ + 60
20 = 2 ^ +
15 = 1^+5
35 = 3 ^ + 5
Sl = 3t + lo
26 = 2 t+6o
57 = 5 < + 7
Four ones and 2 ones are 6 ones. One ten
and 2 tens are 3 tens. Where is the 6
written? The 3? Which then is the ones*
place? The tens* place?
No ones and 5 ones are ones. Two
tens and 1 ten are ^— tens. Show me the
5 ones in the picture. The 2 tens. The 1
ten. The 3 tens. Which do we add first —
the ones or the tenaf
Show me the 6 ones in the picture. The
7 ones. The 3 tens. The 2 tens. The 5 tens.
110 60HOOL ABITHMBTIO.
1. Add:
13 12
20
16
21
10
15
23
24 13
11
22
16
12
23
14
24
27
18
25
32
30
26
34
14
31
31
42
24
10
32
33
43
41
20
51
62
75
17
54
26
28
40
31
25
23
82
35
64
45
17
50
73
69
40
26
23
53
42
40
16
20
50
72
150. Find the value of:
32 + 26 12 + 14 34 + 25 15 + 10
54 + 15 36 + 23 17 + 50 25 + 10
67 + 21 60 + 15 24 + 34 35 + 10
23 + 70 54 + 33 31 + 51 12 + 12
42 + 27 62 + 17 63 + 25 24 + 12
36 + 12 41 + 24 56 + 42 36 + 12
11 + 11 70 + 16 40 + 21 22 + 11
40 + 40 60 + 31 24 + 12 33 + 11
A boy has 30 hens and 12 roosters. How many chickens
has he?
A man paid a barber 25^ for a hair-cut and 10^ for a
shave. For both he paid — — ^.
A farmer drove 14 miles to town and then drove home.
How far did he drive?
Helen's papa gave her 50^ and her mamma gave her
a quarter, S^e then had cents.
ADDITION AND SUBT^RAOTION.
Ill
There are 24 hours in a day. In two days there are
— hours.
There were 20 cents in a box, when George put in 14
cents, and Ada 5 cents. How many cents were in the
box then?
How many days in May and June together?
There are 45 pupils in one school and 42 in another.
In both schools there are pupils.
Hallie's book has 23 pages more than there are in Odie's.
There are 42 pages in Odie's book. How many pages are
there in Hallie's book?
There are 33 frogs in one pond, and 24 in another. How
many are there in both?
^..^L^ i—
25—5 =
i — 4 =
151, Here are 24 splints (2 tens and 4 ones). Take
4 away. How many are left?
Did you take the 4 from the loose splints (the ones)
or from the tens? How many ones were left?
24 = 2/ + 4o
4= 4o
25 = 2^ + 5
5= 5o
20 = 2*+0o
20 = 2 ^ -I-
Show with splints how many 16 — 6 are.
Draw squares to represent 18 — 8.
112
SCHOOL ABITHMEnO.
Show me 3 tens and 5 ones with splints. Take 3 away
and tell me what you have left.
From what did you take the 3 splints? How many
ones were left? How many tens?
35 = 3f+5o
3= So
36 = 3^ + 60
4= 4o
32 = 3i+2o
32 = 3 < + 2
Show with splints how many 17 — 4 are.
Draw squares to represent 24 — 3.
152.
Subtract:
16
26 36
46
18
28
38
48
4
4 4
4
5
5
5
5
18
8
27
3
26
2
37
4
49
7
68
8
75
6
%
36 — 12 = 24.
158. Here are 36 splints. How many tens? How
many ones?
Take away 12 splints (2 ones and 1 ten).
ADDITION AND SUBTBAOTION. 113'
How many ones are left? How many tens? How many
splints?
36 Two ones from 6 ones leaves ones. One ten from 3 tens
^^ leaves tens. Two tens and 4 ones are . Which do
24 we subtract first— the ones or the tens?
When 12 is subtracted from 36, what is the remainder?
Show me the squares that represent it.
Take 25 splints (2 tens and 5 ones.) Take away 13
splints (1 ten and 3 ones). How many ones remain? How
many tens? How many splints? 25 — 13 =
Draw squares to represent 25 — 10.
154.
Subtract:
13
16
26
34
45
24
27
30
2
4
14
14
12
12
15
10
37
44
56
63
58
76
69
76
14
12
24
21
33
25
36
50
86
93
77
68
84
50
95
98
41
21
34
58
62
30
70
23
80
72
97
48
59
76
81
99
«»
5t
60
18
21
41
31
44
114 BOHOOL ABITHMETIO.
23
^2 ^ ones, 2 ones, and 3 ones are ones.
14 1 ten, 4 tens, and 2 tens are tens.
— The sum is tens and ones, or .
Find the sum:
12 14 11 20 30 25 13 21
24 31 42 45 27 40 35 16
51 23 45 13 32 14 40 51
23
27
18
25
32
30
26
34
31
42
54
26
28
20
17
64
24
30
21
11
31
13
2
10
Jane had 3 dimes and a nickel. She gave a dime and a
nickel for a slate. How much money had she left?
William earned 45 cents on Friday and 30 cents on
Saturday. On both days he earned cents.
There are 24 hours in a day. If you work 10 hours,
how many hours do you have for rest?
If you cut 12 feet from a fish line 36 feet long, how
many feet of line will be left?
This week there are 69 pupils in school; last week there
were 48. How many new pupils have come this week?
Eobert had 40 cents, Mack had 30 cents, and Clyde
had 10 cents How many more cents did the three boys
need to make a dollar?
Goorge has 14 marbles and Tom has 10 more. They
both have marbles?
The white hen has 15 chicks, and the black hen has 5
less. They both have chicks.
John had a knife worth 45 cents, which he traded to
Walter for his knife and 2 nickels. What was Walter^s
knife worth?
KUMBEBS TO 30.
116
Numbero to 30.
f
33333333
1S5. What is tlie name of the number made up of 2
tens and 1?
2 tens and 2? 2 tens and 3? 2 tens and 4? 2 tens
and 5? 2 tens and 6? 2 tens and 7? 2 tens and 8? 2
tens and 9?
How many squares in the rectangle? How many
threes? Then 8 threes are .
How many squares in the upper row? How many
rows? Then 3X8 squares = squares.
Show that 8X3 squares = 3X8 squares.
The dark row is what part of the rectangle? One part
out of 8 parts is called one .
Show how many eighths of the rectangle make i of it.
i of 24 squares = squares.
-I of 24 squares = squares.
squares.
i of 24 squares = -
i of the rectangle = •
-squares.
The upper row is what part of the rectangle?
i of 24 squares = squares.
§ of 24 squares = squares.
How many light squares are there? How many 3's
make 21? How many 7's?
i of 21 squares = squares.
f of 21 squares = squares.
116 SCHOOL ARITHMEnO.
Make 4 dots six times. How many dots have you?
• • • • • How many 4's make 24?
• • • • • Arrange 5 rows of 6 dots each in a square,
• • • • • as in the nmnber picture at the left. Tell
• • • • • how many 5's in 25.
• • • • • Count by 5's to 25. 5X5= .
Make 3 dots 9 times. How many
dots have you? How many 3's make *
27? How many 9's? •••••••
Show by the picture at the right that
4 X 7 dots = 7 X 4 dots.
How many 4's in 28? How many 7'8 in 28?
Count by 3's to 30. How many 3's make 30?
156, Complete and memorize:
1X3 = 3. 3X 1=3.
2X3= 3X 2 =
3X3= 3X 3 =
4X3= 3X 4 =
5X3= 3X5 =
6X3= 3X 6 =
7X3= 3X 7 =
8X3= 3X8 =
9X3= 3X9 =
10 X 3 = 3 X 10 =
157. 3 squares are found in 18 squares times.
3 squares are found in 24 squares times.
3 squares are found in 30 squares times.
3 squares are found in 21 squares times.
What added to 2 tens makes 22? 23?
Find i of 22 splints. ^ of 22 = .
How many elevens make 22?
Find how many 12's make 24?
KVMBEBS TO 30.
158. Find the value of:
9-t-3
15-^3
12
18 -r- 3
24 -f- 3
21 H- 3
3
30
27 H- 3
12 -f- 2
18
16 -J- 2
14
2
20-^2
24 -J- 2
22 -T- 2
20-^3
16-r-3
22-^3
117
20
40
60
50
30
80-
10
10
10
10
10
10
4X6 =
4X7 =
5X5 =
6X4 =
21 -r- 7 =
24-^8 =
20-^-5 =
24-^6 =
28 H- 7 =
25
24
28
24
5 =
4 =
4 =
2 =
20-^4 =
i of 21 =
i of 24 :
i of 27 =
iof 24 =
iof 28 =
iof 25 =
iof 24 =
28 = 18 + -
28 = 20 + ■
27 = 21 + -
26 = 22 + •
29 = 21 + ■
30 = 20 +
25 = 19 +
159. Find the cost of 10 pints of milk at 34 a pint.
A boy walks 3 miles a day. In 7 days he walks
miles.
A man who had 24 bushels of potatoes sold i of them.
How many had he left?
Mr. Jones had 27 sheep but 3 of them died. He then
had sheep left.
What will 2 dozen eggs cost at a cent apiece?
How many ounces in i of a pound? In f of a pound?
A blacksmith has 24 horseshoes. He can shoe •
horses with them.
With 25 cents I can buy 3-cent stamps, and I shall
have left.
A man had $30. He gave iV of it for a pair of shoes.
Find the cost of the shoes.
118 SCHOOL ABTTHMETIO.
A room is 27 feet long. How many yards long is it?
Divide 21 apples equally among 3 boys. How many
apples will each boy have?
If you have 25 oranges, how many times can you give
away oranges if you give 5 each time?
If it takes 4 men 7 days to dig a certain ditch, how long
will it take 1 man to dig the ditch?
How many weeks are there in 28 days?
If you sleep 8 hours every day, what part of the whole
day do you sleep? In 1 day there are hours.
How many days has February? When a week of this
month has passed, how many days of it will be left?
T
I
J
4
5
6-
7
How many squares in the upper row of this rectangle?
How many rows?
3X7 squares = squares.
Draw a rectangle 7 inches long and 3 inches wide. Draw
lines to divide it into square inches.
How many sq. in. in 1 row? How many rows?
3 X 7 sq. in. = sq. in.
Find how many square inches in each of the following:
A square, 5 inches on a side.
A rectangle, 6 inches by 4 inches.
A rectangle, 7 inches by 4 inches.
A rectangle, 10 inches by 3 inches.
NUMBERS TO 30. 119
m
I
160. In this picture the line ah is a vertical line.
Which other lines are vertical?
The line mn is a horizontal line. Point out the other
horizontal lines.
Draw on the blackboard a square 3 feet on each side.
Draw two horizontal lines to divide it into 3 equal parts.
Then draw two vertical lines to divide it into 9 equal
parts. How long is each of the 9 parts? How wide?
What is the shape of each part?
A square that is a foot on each side is called a square
foot (sq. ft.).
How many square feet are there in your large square?
Measure the large square with the yardstick. What is
the length in yards? The width?
A square that is a yard on each side is called a square
yard (sq. yd.).
Now who can tell how many square feet in a square
yard?
In 3 square yards there are square feet.
A rug is 5 ft. square. How many square feet in it?
A strip of carpet is 9 yards long and 1 yard wide. It
contains square yards.
There are 4 strips of carpet on our bedroom. Each
strip is 5 yards long and a yard wide. How many square
yards of carpet are there?
120
SCHOOL ABITHIISTIO.
I
Numbers to 40.
5 3 4 5l^tl8ldh(«
4444444444
10
10
10
10
16L What is the name of the number made up of 3
tens and 1? 3 tens and 2? 3 tens and 3?
Read the numbers: 34; 35; 36; 37; 38; 39.
In 5 rows of 6 dots each there are dots.
6X6 =
X5=:
30-^5 =
— dots.
In 5 rows of 7 dots each there are —
6 times 7 are . 7 times 5 are
Show by the dots at the right how many 7's in 35. How
many 5's in 35?
How many squares in this rectangle? How many tens?
How many fours?
Show that 4 X 10 squares = 10 X 4 squares.
The upper row is what part of the rectangle? Then
J of 40 squares is squares.
The left-hand column is what part of the rectangle?
then -^ of 40 squares is squares.
162. How many squares are there in 7 columns? Then
7X4 squares are squares.
Make 4 rows of 7 dots each. How many dots?
How many 4's make 28? How many 7's?
Draw a ring around i of the dots, i of 28 ^ .
KUMBBBS TO 40. 121
168. How many squares are there in 8 columns? Then
8X4 are squares.
Here are 32 blocks. Give me i of them, i of 32 = .
Now divide these 32 blocks into 4 equal parts. How
many in each part? i of 32 = .
164. How many squares in 1 column? How many
columns are light? How many squares are light?
9X4 squares = squares. 9X4= .
Divide 36 splints into 4 equal piles. How many splints
in each pile?
36 splints -=- 4 = splints.
Separate 36 splints into 9 equal piles. How many
splints in each pile?
36 splints -r- 9 = splints.
Lay 36 blocks in 3 equal rows. How many 3's make
36? How many 12's?
Hake a square of dots, having six dots on each side.
In 6 rows of 6 dots each there are dots.
Count by 4's to 36. Count by 6's to 36.
Count by 4's to 40. How many 4's make 40?
166. Complete and memorize:
1X4 = 4.
4X 1 =
2X4 =
4X 2 =
3X4 =
.4X 3 =
4X4 =
4X 4 =
5X4 =
4X 5 =
6X4 =
4X 6 =
7X4 =
4X 7 =
8X4 =
4X 8 =
9X4 =
4X 9 =
10X4 =
4X10 =
122
SCHOOL ARITHMETIO.
4 squares are contained in 24 squares
4 squares are contained in 32 squares
4 squares are contained in 28 squares •
4 squares are contained in 36 squares
166. 4 squares are contained in 24 squares times.
- times.
- times.
- times.
Show by dots how many 3's make 33. How many ll's?
i of 33 dots = dots.
What added to 3 tens makes 34? 37?
Count by 3's from to 36, then backwards to 3.
Count by 4's from to 40, then backwards to 4.
Count by 3's from 1 to 37, then backwards to 1.
Count by 4's from 1 to 41, then backwards to 1.
Count by 4's from 2 to 38, then backwards to 2.
167. Find the value of:
8-
-4
32 -r
-4 28-^2
30^3
16-
-4
36^
-4 26 -r- 2
40-7-2
12-
-4
40 -^
-4 34-7-2
iof40
20-
^4
32-^
-2 24 ^ 2
iof36
28-
!-4
36-7
-2 33-7-3
iof40
24-
-4
30 H
-2 36 -^ 3
iof36
5X6 =
30-
-6 =
i of 30 = 37 =
() X 4 +
5X7 =
32-
1-8 =
* of 30 = 31 =
()X 4 +
6X6 =
35-
r-7 =
i of 35 = 34 =
()X4-}-
5X5 =
36-
^9 =
iof36= 38 =
= ()X4-}-
168. Our hens lay 4 eggs a day. How many will they
lay in 10 days?
How many quarts in 6 gal. ? In 9 gal. ?
How many months in 2 yr.? In 3 yr.? In i of a year?
I have 4 rows of peach trees, 8 in each row. How many
trees have I?
Mr. Wilson has 11 barrels of apples, 3 bushels in each
barrel. He has bushels of apples.
NUMBEB8 TO 60. 123
In 35 days there are weeks.
How many cents are 6 five-cent pieces?
How many eggs are there in 3 dozen eggs?
From the 8th to the 29th of May there are days,
or weeks.
How many inches long is the yard-stick?
A line is 3 feet 2 inches long. How many inches is it?
John took 36 pecks of potatoes to the store. How many
bushels was that?
How many 6-cent ctamps can you buy for 30 cents?
A farmer has 32 horses. How many 4-horse teams can
he form?
At 5 cents a ride, how many street-car rides can be
taken for 30 cents?
Mr. Henry gave 30 cents to his children. Each child
got a dime. How many children has he?
A bushel of oats weighs 32 pounds. How much does
a peck weigh?
Eight quarts make a peck. How many quarts in a
bushel? 4 X 8 qt. = qt.
Numbers to 50.
169. How many dots do you see here? How many
fives?
10 X 5 dots = dots.
5 X 10 dots = dots.
Find from the picture how many 5 times 5 dots are.
6 times 5 dots. 8 times 5 dots. 7 times 5 dots. 9 times
5 dots.
Count by 5's from 5 to 50, then backwards to 6.
124
BOBOOL ABITBMBTIO.
Complete and memorize:
1 five =5.
2 fives =
3 fives =
4 fives =
5 fives =
6 fives =
7 fives =
8 fives =
9 fives =
10 fives =
Find the value of:
1X6 = 5.
2X5 =
3X6 =
4X5 =
5X5 =
6X5 =
7X5 =
8X6 =
9X5 =
10X5 =
4X5 + 5
S X 5 + 3
7X5 + 1
8X5 + 2
5X4 + 6
7X4 + 2
8X3 + 5
9X4 + 2
iof24
iof20
}of20
iof21
170. Show how many times —
5 blocks are contained in 15
blocks.
5 blocks are contained in 25
blocks.
5 pegs are contained in 30
pegs.
5 inches are contained in 10 inches.
5 is contained in 5
5 is contained in 10
6 is contained in 20
5 is contained in 25
5 is contained in 40
5 is contained in 50
6 is contained in 45
one
time.
times.
times.
times.
times.
times.
times.
X
X
X
X
X
X
X
X
1 = 6.
2 =
3 =
4 =
5 =
7 =
8 =
5X 9 =
5X10 =
6
10
16
20
26
80
86
40
46
10
50
5-f-5=-
10-f-5=-
20-^5=-
25-^5=-
40-T-5 = -
50h-5 = -
45h-5 = -
Point out one of the 5 equal parts of 50 dots.
IfUMBBBS TO 50.
125
171. Is i of 50 dots the same as 50 dots -r- 5? Prove it.
How much is i o£ 25 cents? f of 25 cents?
•>#-•'•'••#•
• •••••••• •••••!
• »••••••• •••>••!
• ••••*••• •••••!
How many dots in each row of dots at the left?
How many rows are there?
In 6 rows of 7 dots each there are dots.
7X6= . 6X7= .
Add to 42 by 6's. How many 6's in 42?
Add to 42 by 7^s. How many 7's in 42?
In 6 rows of 8 dots each there are dots.
By aid of the middle picture, complete:
6X8= . 8X6= . 48-^6= . 48-^8=-
In a square made of dots, 7 dots on each side, there
are dots.
I /\
< .
tV-r- 1
•
172. Copy
and complete:
50 H- 5 =
35^5 =
50 -MO =
TVof50 =
30-^5 =
15-4-5 =
30 -T- 10 =
Aof50 =
40-^5 =
17^5 =
40 -=-10 =
1 of 50 =
20 H- 5 =
21 H- 5 =
20 -r- 10 =
V^of50 =
25-^5 =
28^5 =
25 ^ 10 =
i of 50 =
45 -f- 5 =
32 -=-5 =
45 ^ 10 =
1 of 60 =
40-^-8 =
6X 7 =
42-4-7 =
ftX 8 =
46-^9 =
7X 7 =
43H-6 =
7X 6 =
40 H- 4 =
8X 5 =
48-f-8 =
4X10 =
48^6 =
4X 9 =
49^-7 =
41-^ 5'=
12d SCHOOL ABTTHMETIC.
178. How many cents are 6 nickels worth?
Our cow gives 10 quarts of milk a day. In 5 days she
gives quarts.
How many flags at 5 cents apiece can I buy for 17 cents?
How many cents shall I have left?
9^999 ^^^^^ ^^999 99
n n n
For 17 cents I can buy flags. I shall have
cents left.
How many 5-cent stamps can I buy for 30^? Draw
the picture.
Forty pecks of onions are how many bushels?
A house is 12 yards long. It is feet long.
At 6 dollars a ton, how many tons of coal can be bought
for 42 dollars?
What will 7 yards of cloth cost at 7 cents a yard?
A pansy has five petals. How many petals do 9 pansies
have?
How many times can a 5-inch line be measured off on
a line 40 inches long?
Ben had 30 cents and gave i of it for candy. How much
money had he left? Show by drawing.
What are 3 dozen eggs worth at 1 cent apiece?
What will a pound and a half of butter cost at 16 cents
a pound?
Draw a rectangle 10 inches long and 4 inches wide.
Divide it into square inches. How many are there?
How many rows are there running lengthwise?
How many inch squares in each row?
How many square inches, then, are 4 times 10 square
inches?
ADDITION AND SUBTEAOTION. 127
Find the nixmber of square inches in the following:
A square, measuring 7 inches on a side.
A rectangle, 10 inches by 5 inches.
A rectangle, 10 inches by 4 inches.
A rectangle, 9 inches by 5 inches.
9 square feet make 1 square yard. How many square
yards are there in 45 sq. ft. ?
Addition and Subtraction.
1< + 9o + lo = 2< + Oo
19 + 1 = 20
174. Take 19 splints. Make a bundle of 10. How
many do you need to make another ten?
19 = 1^ + 90 29 = 2^ + 90
1 = lo 1 = lo
20 = 2< + 0o 30 = 3^ + 00
Show with splints how many 39 and 1 are. 49 and 1.
Add:
49 59 79 89 69 99
111111
How many splints must you put with 18 to make 2 tens?
With 28 to make 3 tens?
18 = lf+8o 28 = 2* + 8a
2 = 2o 2 = 2o
198 loWMH. AxmnoncL
^ffv Thk sptzcts kya- 1
BUJ
3»aai
SatCL 48 a^
Ai&i:
3S 4S IS
^S
SS
CS
93
3 3 3
3
3
a
3
Xaat iwol^ qakklr:
» -r 1 i> — 3
** — 1
75^J
S -r 3 3:> -r 1
5S — 3
S»-i-l
19 — 1 5S — 3
(» — 1
SS — 3
15-2 4* — 1
*> — 3
9* — 1
2*^-1 -IS -r 3
r* — 1
96 — 3
Etw maiiT MS}' m ome i-jjinL^fC* How ssnj pm^
BaLf a amuLbecl Hew maiLT .xdk^!
i of !»» = ttiifiy. or
) ^ 2 = 19 ^ 2 -r
/
ITSi yine ^ORV^ And ± ^vlinriy ^re <pait6Sw.
Nineteen ^linns- and ± splin:^^ ire spIinCSw
Take one splint from the r^o ind pat :t with, the
Y'ja now have I ten and 1 one* or ^.
Take one ^^lint Tyjm the other r*'o ^nd out it wxj^
"he nine. Ym nuw have tens and one. or w
Show by :fDiint& how manv i*) -anKi i are. '59 aad i
4rl> md ^.
3 ID 20 :39 « 59 »j9 79
__^_ — ~ — ~
ADDITION AND SUBTRACTION. 129
176. Take 11 splints (a ten and a one). How can you
take 2 splints away from the 11? How many must you
take from the ten? How many will be left?
Take 21 splints — 2 tens and a one. Take away 2 splints.
How many must you take from one of the tens? How
many tens and how many ones will be left?
Show by splints how many 31 less 2 are. 41 — 2.
51 — 2. 61 — 2.
11 21
31 41
51 61
71 81
2 2
2 2
2 2
2 2
~9 ~
177. Find the value of:
9 + 2
8 + 2
11 — 2
10 — 2
19 + 2
18 + 2
21 — 2
20 — 2
39 + 2
48 + 2
41 — 2
30 — 2
49 + 2
28 + 2
61 — 2
50 — 2
29 + 2
68 + 2
31 — 2
60 — 2
69 + 2
38 + 2
51 — 2
40 — 2
89 + 2
58 + 2
71 — 2
70 — 2
79 + 2
78 + 2
81 — 2
90 — 2
59 + 2
98 + 2
91 — 2
80 — 2
Add by 2's from 2 to 50.
Subtract by 2's from 40 to 18.
Add by 2's from 9 to 61.
Subtract by 2's from 49 to 9.
^9
130
SCHOOL ABITHMETIO.
8 + 3
72
—
1
-1
L_i_J
m
,._
\J\
18 + 3
17 + 4
19 + 3
178. Show with blocks that 8 + 3 = 1 ten and 1
one, or 11.
Show that 18 + 3 =
Show that 28 + 3 = -
Show that 17 + 4 = -
Show that 19 + 3 =
tens and
tens and -
tens and
tens and
- one, or .
- one, or .
- one, or .
- ones, or .
179. How many squares do you see in the picture at
the left? How many of them will be left if you take
away the 3 dark ones?
How many squares in the next picture? How many
light ones?
Showthat 21 — 3 =
Show that 31 — 3 =
Show that 21 — 4 =
Show that 22 — 3 =
ten and
tens and
ten and -
ten and -
8 ones, or 18.
8 ones, or
■ ones, or
Add; also, subtract:
11
3
21
3
31
3
41
3
61
3
81
3
71
3
51
3
ADDITION AND SUBTBAOTION.
131
21 31
41 51
71 61
91
81
4 4
4 4
4 4
4
4
22 32
42 62
52 72
82
92
3 3
3 3
3 3
3
3
180. Ifame
results at sight:
8 + 3
7 + 4
11 — 3
11—4
18 + 3
17 + 4
21 — 3
21—4
28 + 3
27 + 4
31 — 3
31—4
58 + 3
37 + 4
51 — 3
41—4
48 + 3
67 + 4
61 — 3
61—4
68 + 3
87 + 4
41 — 3
81—4
38 + 3
47 + 4
81 — 3
71—4
88 + 3
57 + 4
71 — 3
51 — 4
78 + 3
77 + 4
91 — 3
91—4
Add hj 3's from to 51.
From 2 to 50
Subtract by
4's from 48 to 0. From 45 to 1.
181. Name results at si
ght:
8 + 4
9 + 4
12 — 4
13 — 4
18 + 4
19 + 4
22 — 4
23 — 4
28 + 4
29 + 4
32 — 4
43 — 4
38 + 4
49 + 4
42 — 4
53 — 4
48 + 4
39 + 4
62 — 4
33 — 4
68 + 4
79 + 4
82 — 4
73 — 4
88 + 4
89 + 4
52 — 4
93 — 4
78 + 4
69+4
72 — 4
63—4
58 + 4
59 + 4
92 — 4
83 — 4
Add 5 to 16, 26, 36, 46, 56, 66, 76, 86.
Subtract 5 from 21, 31, 41, 51, 61, 71, 81, 91.
132
SCHOOL AKITHMETIO.
+
15 + 7 - 19
182. Find the sum of 16 and 7.
15 =
Write 15 and then write the 7 ones under the 5 ones.
7 ones and 5 ones are ones, or 1 ten and 2 ones.
Write the 2 ones in one^ place under 7.
What shall be done with the ten ? Add it to the 1 ten in
15. 1 ten and 1 ten are tens.
In what place do we write the tens?
Find the sum of 19 and 15.
6 ones + 9 ones =■ 14 ones, or 1 ten and 4 ones.
1 ten + 1 ten + 1 ten = tens.
19
15
34
15
7
22
Copy and add:
18 38 29
32
63
42
78
69
4 4 15
19
28
39
14
24
25
35
27
64
43
57
68
34
56
48
16
18
32
25
17
38
63
42
74
31
28
36
43
54
28
39
17
49
64
58
37
39
ADDITION AND SUBTRACTION. 133
26 57 44 87 65 39 76 58
58 27 37 15 26 47 18 37
15
16
23
14
26
32
29
40
23
34
42
37
38
18
29
27
47
26
18
25
14
47
30
19
183. Find the value of:
36 + 14 25 + 45 33 + 49 26 + 35 + 18
33 + 17 81 + 19 62 + 28 17 + 23 + 46
42 + 18 46 + 37 71 + 29 35 + 18 + 26
82 + 18 34 + 58 80 + 18 24 + 39 + 27
47 + 14 76 + 17 46 + 35 31 + 17 + 46
184. There are 31 days in May and 30 in June. In
both months there are days.
Mr. Jones has 58 sheep in one field and 37 in another.
In both fields he has sheep.
Ella is 18 years old and her mother is 36 years older.
How old is her mother?
Our black horse cost $65 and our red cow cost $25.
How much did both cost?
If a room is 18 feet long and 16 feet wide, how many
feet is it around the room?
A Christmas tree held 13 dolls; 27 balls. 37 flags, and
17 bags. How many articles were there in all?
Edith paid 35 cents for a book, 15 cents for paper, and
3 cents for a ruler. How much did they all cost her?
Mr. White's wagon cost $42. His buggy cost $29 more
than the wagon. How much did the buggy cost?
How many days are there in October, November, and
December?
134
SCHOOL AKITHMETIC.
2t +
2o — 5o
22 — 5
185. Take 22 splints (2 tens and 2 ones). How many
ones can you take away without taking any from a bundle ?
If you wish to take 5 splints away, how many ones must
you take from one of the tens? How many ones will be
left? One ten and 7 ones are .
Take 32 splints (3 tens and 2 ones). How can you take
7 splints away? Can you take 7 ones from the 2 ones?
Take the string from one of the bundles. Now how
many ones have you? Take 7 splints away. How many
ones are left? How many tens?
22 = 2^ + 2 = 1^ + 12 0.
5 = 5 = 5 0.
32 = 3^ + 2 = 2^ +12 0.
7= 7o= 7o.
17 =
1/+ 7o. 25 =
= 2t+ 5 a.
How many squares do you see in the picture?
How many tens? How many ones?
We cannot take 5 squares from the 3
squares, so we must take one of the tens and
and put it with the 3 ones, making 13 ones.
We then have 2 tens and 13 ones. What is
left when 5 ones are taken away?
Show with splints how many 23 less 5 are.
31 less 7.
ADDlTtOK AN1> 6OBTIIA.OTI0M.
135
Subtract:
24 25
32
26
21
7 6
7
8
5
34
36
^ P fl p c
\J \l \J \J \J
It)
We cannot take 6 from 1, so we put one of the tens with
the 1, and take 6 from 11. There are only 2 tens left,
so we take the 1 ten from 2 tens.
31
16
15
20 + 11
10+ 6
10+5
Note. — Of coarse, as soon aa the pupils understand the process,
they should do the work without any change of figures.
Show with splints how to subtract 12 from 31. 15 from
32. Use splints to show how many 25 less 15 are. 45
less 20.
186. Copy and subtract:
23 31 34 42 63
6
16
25
34
54
28
36
19
75
47
V
>
60
91
40
53
68
90
84
93
29
16
25
15
35
50
30
48
44
55
64
45
74
80
100
100
28
37
26
28
24
51
50
80
136 SCHOOL ARITHMETIC.
187. Find the value of:
34 — 16 44 — 19 52 — 27 41 — 16
42 — 15 50 — 38 75 — 36 52 — 27
61 — 24 72 — 22 44 — 18 63 — 38
83 — 15 67 — 28 63 — 45 74 — 49
21 — 12 83 — 38 81 — 50 85 — 56
75 — 54 62 — 43 27—9 96 — 67
92 — 65 91*— 56 50 — 13 43 — 15
188. How many more days are there in this month?-
A man wants to buy a watch for $32. He has only $25.
How much more does he need?
Julia bought a doll for 29 cents, and gave the store-
keeper a half-dollar. How much change did she get?
In a school there are 45 pupils. There are 26 boys.
How many girls are there?
^hat number must you add to 14 to get 21?
What number must you subtract from 32 to get 24?
A man paid $94 for a horse and cart. He paid $18
for the cart and $ for the horse.
Grandma is 83 years old, and Lizzie is 7 years old. How
much older is grandma than Lizzie?
If your mamma had 2 dozen eggs, and used all of them
at Easter but a half-dozen, how many did she use?
How many days from the 11th of June to the 9th of
July?
A barrel of oil contained 53 gallons but 5 gallons leaked
out. There were gallons left in.
Mrs. Hill had 62 hens. She sold 27 of them and had
left.
Tom weighs 96 pounds and Warren 78 pounds. How
many more pounds does Tom weigh than Warren?
KtnOEBS TO SIXTY.
187
Numbers to Sixty,
189. How many dots in the picture? How many rows
of 10 dots each?
6 X 10 dots = dots.
How many large dots do you see? How many sixes are
there?
10 X 6 dots = dots.
In 60 there are tens or sixes.
How many times can you take 10 dots from 60 dots?
60 dots -^10 dots = times.
The large dots are what part of the 60 dots? yV ^^ ^^
dots =
dots.
How many tenths of the 60 dots equal i of the 60 dots?
Ten dots are what part of 60 dots? ^ of 60 dots =
dots.
How many sixths of 60 equal i of 60?
In 60 there are twelves.
In 60 there are fives.
190. How many small dots in the picture? How many
rows of 9 dots each? How many columns of 6 dots each?
6X9 dots = dots. 9X6 dots == dots.
Draw a rectangle 9 inches long and 6 inches wide, and
draw horizontal and vertical lines to di\'ide it into square
inches.
138
SCHOOL ARITMMETIO.
How many squares inches does it contain? How many
times 6 sq. in.? How many times 9 sq. in.?
How many sq. in. in one-sixth of the rectangle? i of
54 = , 54 gq, in. -^• 6 = sq. in.
In ^ of the rectangle how many sq. in. ? |of 54 =
54 sq. in. -r- 9 =
sq. m.
Show how many sixths of the rectangle equal i of it.
Count by 4's to 60. By 5's. By 6's.
191. Complete and memorize:
1 six =6
1X6 = 6.
6X
1 = 6
2 sixes =
2X6 =
6X
2 =
3 sixes =
3X6 =
6X
3 =
4 sixes =
4X6 =
6X
4 =
6 sixes =:
5X6 =
6X
5 =
6 sixes =
6X6 =
6X
6 =
7 sixes =
7X6 =
6X
7 =
8 sixes =
8X6 =
6X
8 =
9 sixes =
9X6 =
6X
9 =
sixes =
lOX 6 =
6X10 =
192. Find how many times:
6 dots are contained in 18 dots.
6 squares are contained in 30 squares
6 eggs are contained in 48 eggs.
6 blocks are contained in 36 blocks.
6 inches are contained in 42 inches.
6 beans are contained in 54 beans.
6 feet are contained in 24 feet.
9 sq. ft. are contained in 36 sq. ft.
9 sq. ft. are contained in 54 sq. ft.
9 dollars are contained in 45 dollars.
NUMBEES TO SIXTY.
139
193. In 7 rows of 8 squares each
there are squares.
How many times 7 squares make 56
squares?
Show that 7X8 squares = 8X7
squares.
How many times are 8 squares found in the 56 squares?
7 squares?
56 squares -r- 8 squares = times. 56 squares
-f- 7 squares = times.
What part of the rectangle is found in the upper row?
Two rows are what part of the rectangle? Three rows?
Four-sevenths of 56 squares are squares.
Seven squares are what part of the 56 squares? 14
squares?
Compare •§ of the squares with i of them.
66 squares -S- 8 = squares. 56 squares
squares.
How many 9's in 56, and how many oyer?
How many 6's in 56, and how many over?
How many lO's in 56, and how many over?
•7 =
Find the value of:
12 -T- 6
4X7
^of 60
30^6
6X8
|of 60
48^6
TXY
|of 60
42^6
4X8
iof 60
54-7-6
3X9
|of 21
36-7-6
5X8
^of 40
24^6
7X5
|of 60
60 -J- 6
5X9
|of 60
60 = 7 X 8 4- ( )
53 = 10X 5-l-( )
54-= 7X7-|-( )
58= 8X74-( )
55 = 6 X 9 + ( )
59 = 11 X 5-1- ( )
51= 8X6-|-( )
52 = 6 X 8 -I- ( )
140
SCHOOL ARITHMETIC.
194. Here is a picture of a watch
face.
When the pointer in the little
circle has gone round once, how many
minutes have passed ?
The little circle is divided into how
many spaces?
Sixty seconds muke a minute.
When the longer hand in the large circle has gone round
once, what time has passed?
Into how many spaces is the large circle divided?
Sixty minutes make an hour.
Which is the hour-hand? Which the minute-hand?
The second-hand?
How often does the hour-hand go round from midnight
to midnight?
Then how many hours make a day?
What time of day is shown on the watch-face?
How many minutes in a half of an hour? In a quarter
of an hour?
What part of an hour are 30 minutes? 15 minutes? 10
minutes?
From noon to midnight is what part of 48 hours?
In half a minute how many seconds?
What part of a minute are 15 seconds? 10 seconds?
6 seconds?
In what time does the hour-hand go round four times?
How many hours in a half of a day?
How many hours is it from 6 A. M. on Monday till
6 A. M. on Tuesday?
NUHBEBS TO SIXTY. 141
196, How much money will buy 10 pounds of sugar
at 6 cents a pound?
Five boys bought a ball for 50 cents. No one gave
more money than another. How much did each give?
In 8 weeks there are days.
We had 48 eggs on Sunday. On Monday we got a
dozen more. How many eggs had we then? How many
dozens?
9 quarts of milk at 6 cents a quart will cost cents.
Maud had 11 nickels. She gave 50 cents for a doll, and
had cents left.
A house is 30 feet long and 18 feet wide. What is the
distance around the house?
A rug is 9 feet long and 6 feet wide. It contains
square feet, or square yards.
There are 52 weeks in a year. How many weeks in
half a year?
A bushel of wheat weighs 60 pounds. What is the
weight of a peck? A half -bushel?
Six windows contain 48 panes of glass. How many
panes are there in each window?
If each of 7 boys makes 8 balls of snow, how many will
they have together?
Eoy borrowed 60 cents from his brother, and paid him
back 6 cents of it every week. How many weeks did it
take to pay the whole?
If a man works 8 hours a day, what part of the day
does he work?
If a horse walks a mile in 15 minutes, how many miles
at that rate will he walk in an hour?
If a railway train runs one mile in 2 minutes, how many
miles will it go in an hour?
142 SCHOOL ARITHMETIO.
Numbers to Seventy.
196. We have rows of 10 dots each; there are
dots in all the rows. 7 X 10 dots = dots.
There are 10 columns of dots each. 10 X 7 dots
= dots.
We see that there are tens or sevens in 70.
70 ~- 10 = 70 -^ 7 =
The large dots are one of the 70 dots, ^i^ of 70 =
The small dots are nine of the 70 dots, ^of 70=
On one side of the vertical line there are tenths
of the 70 dotsj on the other side we find i of the 70 dots.
One side has as many dots as the other, {i = y^.)
197. There are small dots in the picture — seven
rows of dots each. 7X9 dots == dots.
There are 9 columns of dots each. 9X7 dots =
dots.
We can take 7 small dots away times; we can
take away 9 small dots ^ times.
63 dots -^ 7 dots = times. 63 dots -5- 9 dots =
times.
Show by a drawing that 9 sevens = 7 nines.
Count by 6's to 70, 3y lO's. By 7^8,
KTTMBERS TO SETENTT.
143
198. Complete and memorize:
1 seven = 7.
2 sevens =^
3 sevens =
4 sevens^
5 sevens =
6 sevens =^
1 sevens =
8 sevens =
9 sevens =
10 sevens =
1X7 = 7.
2X7 =
3X7 =
4X7 =
5X7 =
6X7 =
7X7 =
8X7 =
9X7 =
10X7 =
7X
7X
7X
rx
7X
7X
7X
7X
7X
1 = 7.
2 =
3 =
4 =
5 =
6 =
7 =
8 =
9 =
7X10^
times.
199. 7 dots are contained in 21 dots
7 days are contained in 70 days times.
7 pints are contained in 35 pints times.
7 yards are contained in 63 yards times.
9 sq. ft. are contained in 36 sq. ft. times.
9 eggs are contained in 63 eggs times.
7 pounds are contained in 66 pounds times, and
3 pounds over.
200. Here is a square. How
many small squares in the upper
row? How many rows?
8X8 squares =^ squares.
How many times can 8 squares
be found in the 64 squares?
In one-half of the large square how many small squares?
i of 64 squares = squares.
64 squares -t- 2 = squares.
T
T
T
[T
5
6
1
8
64 squares H- 8 =
squares.
144 SCHOOL AKITHMETIC.
The upper row is what part of the large square?
How many eighths of the large square are on each side
of the dark line?
i of 64 squares = squares.
■| of 64 squares = squares.
201. Find the value of:
14-7-7 7X6 iof64 64= 9X 7 + ()
28-^7 9X5 i-of64 62= 7 X 8 + ()
35 -f- 7 8X7 I of 64 69 = 8 X 8 -h ( )
21H-7 7X9 ^oi70 68= 7X 9 + ()
70 ^ 7 8X8 tV of 70 61 = 8 X 7 + ( )
42 H- 7 6X7 iV of 70 67 = 10 X 7 — ( )
49^7 9X6 -iVofTO 65=6X10 + ()
56-T-7 6X8 |of70 66=7X10 — ()
63 -V- 7 9X7 ^ of 70 7o = 8 X 8 -}- ( )
202. In 10 weeks there are days.
Tom has 65 cents. How much more than 50^ is that?
Maria has 40 cents and Martha has a quarter. How
much have they both?
At 8 cents a quart how much will 8 quarts of chestnuts
cost?
How much will 3 yards of wire cost at 7 cents a foot?
10 cents is i of my money. How much have I?
A nickel is i of my money. How much have I?
I gave YW of my money for a 5-cent stamp. How much
had I?
7 children give 9 cents each to a Children's Aid Society.
How much money is given by all together?
NUMBERS TO EIGHTY.
145
In a school-room there are 63 seats arranged in 7 rows.
How many seats in each row?
Robert has 56 cents. How m^ny quarts of peanuts can
he buy at 7 cents a quart?
How old is a man who has lived 3 score and 10 years?
Numbers to Eighty. '
10
8
203. How many squares in this rectangle? How many
rows of 10 squares each? How many columns of 8 squares
each? 8 X10= lo X 8 =
Find how many squares in 9 columns. 9X8= 8X9==
How often do 80 squares contain 10 squares? 80-^10=
How many times are 8 squares contained in 80 squares?
How many tens make 80? How many tens make i of 80?
iV of 80 =
I of 80 =
How many 8's make 80? How many 8's make i of 80?
Which is more, -^ of 80 or ^ of 80 ?
Make 6 rows of 12 dots each, and tell how many six
12's are. 12 X 6 =
Show that 9 X 8 = 6 X 12.
In 50 there are 5's; in 25 there are 5^8.
Count by 6's to 78. By 7's to 77.
Count by 8's to 80, By 5's to 80,
146 SCHOOL ARITHMETIO
204. Complete and memorize:
1 eight =8 1X8 = 8 8X1 = 8
2 eights =
2X8 =
SX 2
3 eights =
3X8 =
8X 3
4 eights =
4X8 =
8X 4
6 eights =
5X8 =
8X 5
6 eights =
6X8 =
8X6
7 eights =
7X8 =
8X 7
S eights =
8X8 =
8X 8
9 eights =
9X8 =
8X 9
10 eights =
10X8 =
8X10
205. Find how many times:
8 squares are contained in 24 squares.
8 squares are contained in 40 squares.
8 squares are contained in 72 squares.
9 squares are contained in 72 squares.
6 pegs are contained in 66 pegs.
7 days are contained in 77 days.
8 pounds are contained in 64 pounds.
206.
Find the value of:
16-
-8
5X7
iof36
75 =
7 X 10 + ( )
32-
-8
4X9
|of 36
72 =
9X 8 + ( )
40-
-8
6X8
iof40
76 =
8X 9 + ( )
80-
-8
7X9
§of40
71 =
8X 8 + ( )
72-
-8
8X8
fof40
74 =
• 50 + 20 -F( )
24-
-8
6X7
iof44
79 =
:40 + 25 + ( )
48-
-8
9X8
fof44
77 =
7 X 10 + ( )
64-
-8
8X7
4 of 80
. 73 =
50 + 14 + ( )
66-
-8
7X7
iof80
78 =
7 X 11 + ( )
NUKBBES TO EIGHTY.
147
Tbianglb
Square
Rectangle
o
Hexagon
207, If each side of the triangle is an inch long, what
is the distance around the triangle? (The distance around
it is called the perimeter.)
How many sides make the perimeter of the square?
What is the perimeter of a square inch?
A table is 2 feet square. The perimeter is feet.
If the rectangle is 1 inch long and i inch wide, its
perimeter is inches.
How many sides has the hexagon? If each side is half
an inch long, the perimeter is half inches, or
inches.
A rectangle is 3 feet long and 2 feet wide. What is
the perimeter?
The perimeter of a square is 4 feet. What is the length
of a side? What is the figure called?
The perimeter of a triangle is 15 feet. One side is 8
inches, another is 5 inches. How long is the third side?
Find the perimeter of this room. Of this table.
Find the perimeter of a room 16 feet long and 16 feet
wide.
208. In 8 dimes there are
cents.
I gave 50ff for a book and 22^ for a slate. How much
did I give for both?
Mattie had 8 dimes. She gave 5 cents for candy, and
then had cents left.
148 SCHOOL AKITHMBnC.
A bushel of wheat weighs 60 pounds. A bushel and a
peck weigh pounds.
How many gallons must be added to 65 gallons to make
78 gallons?
If I have 70 cents, to how many boys can I give a dime
each?
Uncle Henry is 50 years old. How old will he be in 24
years ?
The perimeter of a square is 12 inches. Draw the
square and show how many square inches it contains.
If you had 65 cents and each of 5 boys gave you 2
cents, how many cents would you have?
Wilbur earns 53 cents in a day and Oscar 44 cents.
How much more does Wilbur earn than Oscar in 8 days?
Numbers to One Hundred.
209. Draw a square 9 inches on a side. Mark it off
into square inches.
How many squares inches are there? How many in 1
row? How many rows?
9X9 square inches = squares inches.
81 square inches contains 9 square inches times.
10 X 9 sq. in. = sq. in. 9 X 10 =
90 -f-10 = 90 -^■ 9 = yV of 90 =
Make 7 rows of 12 dots each, and tell how many seven
12's are. How many are twelve 7's?
How many 12's make 84? How many 7's?
Add by 7's to 84. By 8's to 96. By 9's to 99. By
lO's to 100.
NUMBERS TO ONE HUNDRED.
149
Write a number which has 9 in the ones' place. Can
you write a number which has ten in the ones' place?
What is the smallest number that is written with two
figures?
What is the largest number that can be expressed by
two figures?
210. Complete and memorize:
1 nine = 9
1 X9 = 9
9X
1 = 9
2 nines ^
2X9 =
9X
2 =
3 nines =
3X9 =
9X
3 =
4 nines =
4X9 =
9X
4 =
5 nines =
5X9 =
9X
5 =
6 nines =
6X9 =
9X
6 =
7 nines =
7X9 =
9X
7 =
8 nines =
8X9 =
9X
8 =
9 nines =
9X9 =
9X
9 =
10 nines =
10X9 =
9X10 =
11 nines =
11X9 =
9X11 =
Multiply 10 by 3, 7, 5, 4, 8, 6, 9, 10.
How many lO's in 50, 30, 70, 90, 60, 100?
How many 9's in 36, 45, 63, 72, 90, 81?
How many 8's in 40, 56, 64, 80, 72, 88, 96?
211. Find the value of:
90-
-9
80-
-10
77 H- 7
72-
- 9
36^
-9
60-
-10
63 -T- 7
64-
- 8
63-
-9
30-
-10
84^7
56-
- 7
45-
-9
90-
-10
66-^6
54-
- 6
54-
-9
88-
-11
72 H- 6
49-
- 7
72-
-9
99-
-11
88 -r- 8
42-
- 6
81-
-9
84-
-12
96^8
60-
-12
99-
-9
96-
-12
72^8
72-
-12
160 SCHOOL ARITHMETIO.
212. How many 10-cent dishes can I buy for a dollar?
A bath room is 9 feet square. It contains square
feet.
Mr. Hall has 12 bushels of turnips. To how many
persons can he sell 1 peck each?
A milkman has 9 gal. 1 qt. of milk. He can sell 1 qt.
to each of customers.
What are 7 dozen eggs worth at a cent apiece?
How many days are there in 11 weeks?
Twelve men paid 2 dollars apiece to hire a sail boat. How
much did they all pay?
If a boy's suit costs 9 dollars, how much will 10 such
suits cost?
A man paid 81 dollars for a horse and -J as much for
a saddle. How much did the saddle cost him?
If the whole of anything costs 81 cents, how much
does -| of it cost ?
At his last birthday Edward had lived 96 months. How
many years old was he?
Add the days in the month in which Thanksgiving comes
to those in the month after and the month before.
Slate Work.
213. How many dollars are $32 and $32 and $32^ or
3 X $32?
1^^ ^^^ Three times 2 ones are 6 ones. Write the 6
^^" 3 in ones* place Three times 3 tens are 9 tens.
Z^ ioA Where do we write the 9 1
$96
SLATE WOBK.
Multiply:
42 23
34 31 44
21
32
2 3
2 3 2
3
2
151
The perimeter of a square room is 48 feet. What is the
length of each side?
4 ) 48 feet 'EiAch side is J of the perimeter. J of 4 tens is 1
12 feet ^^f ^^^ J of 8 ones is 2 ones. J of 48 feet is 12 feet.
Find i of $84, i of 66 yd., i of 46 gal., i of 96^.
How many 3's in 36?
3 ) 36 3 ) 36
In 3 tens there are 10 threes. In 6 ones
there are 2 threes. 10 threes and 2 threes
are 12 threes.
10
2
12
12
Find how many:
2's in 28.
3's in 96.
Divide :
2 )68 3)69
2) 86 3) 96
3's in 63.
4's in 88.
2 )64
9)99
4 )44
4)88
4's in 48.
2's in 84.
5 )55
6) 66
7 )77
8)88
214. This is a cube. How
many sides, or faces, has it ?
What is the length of each
face ? The width ?
Are the faces all of the same
size ? Each face is a inch.
A cube that is an inch long.,
an inch wide, and an inch thick
is called a cubic inch (cu. in.).
162 SCHOOL ARITHMETIC.
Find a block that is a cubic inch.
Place 4 such blocks in a row. How many cubic inches
in the row?
Place 4 more cubes beside these. How many cubic
inches in the 2 rows?
Place 8 more cubes on top of these. How X/0'^> ^^
many cubic inches in each layer? How LI— i-J ^
many in both layers?
215. With one-inch cubes build a cube 2 inches on
each side.
How many layers are there? How many rows in each
layer? How many one-inch cubes in each row?
How many cubes in both rows? In both layers?
How many cubic inches in the cube you have built?
A cube 2 inches on a side is a two-inch cube. It con-
tains cubic inches.
A one-inch cube is what part of a two-inch cube?
A two-inch cube is how many times a one-inch cube?
Point out i of a two-inch cube. \ of it.
How many fourths of the two-inch cube equal i of it?
How many eighths of the two-inch cube equal i of it?
One-fourth is what part of one-half?
One-half of one-half is one .
216. Build a cube having 3 layers, 3 rows in each
layer, and 3 one-inch cubes in each row.
This cube is inches on each side, and contains
cubic inches.
It is a three-inch cube and contains one-inch cubes.
Nine one-inch cubes are what part of the 3-inch cube?
18 one-inch cubes are what part?
BEVIEW AND DRILL WOKK.
153
How many square inches in each face of the 3-inch cube ?
In 3 faces? In all the faces?
How many inch cubes will be needed to make a pile 6
in. long, 3 in. wide, and 2 in. high?
217.
Review and Drill Work.
a b
fghijklmn
1.
4
8
7
4
9
6
8
5
4
7
6
8
9
6
2.
7
4
8
6
2
5
2
7
8
4
5
3
2
7
3.
5
6
7
8
7
4
6
4
3
5
7
8
9
6
4.
6
5
4
3
5
7
5
6
8
7
5
4
2
4
5.
8
4
5
6
4
5
7
3
4
3
8
9
8
8
6.
4
6
8
7
6
4
3
8
7
9
5
4
6
7
7.
6
7
9
4
8
7
8
6
6
2
8
7
5
6
8.
9
5
6
8
<
6
5
4
5
6
7
8
6
8
Add the numbers in each line.
Add the numbers in each column.
Multiply the numbers in each column by 3, 4, 5, 6, 7,
8, 9.
Multiply the numbers in column li by 8, and those in
column m by 7, and find the sums and differences of each
two corresponding results.
218. Complete:
12 -f- 2 =
49 -V- 7 =
42-
h6 =
63-
r- 9
32^4 =
48^8 =
27-
H3 =
54-
1- 9
60 -f- 5 =
84 -V- 7 =
28-
-4 =
81-
- 9
15 -J- 3 =
18 -f- 3 =
40-
-4 =
66-
- 7
64-^9 =
33^3 =
63-
-7 =
84-
-12
21 -T- 3==
64 -f- 8 =
72-
-8 =
45-
- 3
164 SCHOOL AEITHMETIC.
219. How many —
yards in 30 ft.? dimes in 90^?
pecks in 24 qt.? gallons in 28 qtJ
feet in 96 in.? dollars in 30 dimes?
bushels in 32 pk. ? pints in 44 qt. ?
weeks in 49 days? yards in 27 feet?
ounces in 2 lb.? half -pecks in 2 bu.?
quarts in 48 pt.? shoes in 30 pairs?
dimes in SSfi tens in 35 ones?
220. Find the cost of:
9 lb. of sugar at 6^ a pound.
4 quires of paper at 10^ a quire.
8 qt. of peanuts at 6^ a quart.
9 yd. of silk at $4 a yard.
1 dozen papers at 3^ each.
2 bu. of salt at 4f^ a quarter-peck.
221. Find the perimeter and area of:
A rectangle, 7 inches by 4 inches.
A rectangle, 8 inches by 3 inches.
A rectangle, 9 inches by 4 inches.
A rectangle, 12 inches by 5 inches.
A square, measuring 3 inches on a side.
A square, measuring 4 inches on a side.
222. Take inch cubes and build a pile 4 blocks long,
3 blocks wide, and 2 blocks high. Then fill out the
following:
BEVIBW AND DBILL WORK. 155
Length of one side = inches.
Height of one side = inches.
Area of one side = sq. in.
Width of one end = inches.
Area of one end = sq. in.
Area of the top = sq. in.
Area of all six sides = sq. in.
Number of cubes in the pile = .
22^. Draw a square that contains 49 square inches.
Draw a rectangle that contains 30 square inches.
James is 10 years old. His age is i of his father's age.
How old is his father?
When oil is worth 20 cents a gallon, how much can be
bought for 5 cents?
If you take 2 quarts of milk a day at 6ff a quart, how
much will your milk cost you for a week?
How much must you pay if you buy 7 yards of cloth
at 9ff a yard?
H there are 4 sq. in. in the face of a cube, how many
square inches are there in all the faces?
24 sheets of paper make a quire. Find how many
sheets there are in a quire and a half of a quire.
Nanje all the months of the year that have 31 days.
From 7 o'clock in the morning until nine o'clock in
the evening is how many hours?
If your oil can holds 2 gal. and your lamp holds 2
quarts, how many times can you fill your lamp from your
can?
Show by lines that ^, f , and f are the same in value.
166 SCHOOL ABITHMETIO.
Hundreds.
one ten hundred
224. How many ones make 1 ten? How many tens
make 1 Imndred ?
Show me 10 tens with splmts. Put a band around them.
How many ones are in the bundle?
Make another bundle of 100. How many ones are in
both bundles? How many hundreds?
One himdred and 4 hundreds are hundreds.
Four hundreds and 5 hundreds are hundreds.
How many cents make 1 dime ? How many dimes make
a dollar? How many cents make a dollar?
One hundred cents make a dollar.
How many cents in 5 dollars? In 8 dollars?
In what place, counting from the right, do we write the
figure for the number of tens?
In what place do you think we should write the hundreds
of a number?
225. Supply the figures needed:
One hundred is written thus — 100.
Two hundred is written thus — 200.
Three hundred is written thus —
HUNDBEDS.
157
Four hundred is written thus — •
Five hundred is written thus —
Six hundred is written thus —
Seven liundred is written thus —
Eight hundred is written tlius —
Nine hiuidred is written tlius —
Ten hundred is written thus — 1000.
One ihxmawnd.
5826. Copy and complete:
10 tens make
20 tens make
30 tens make
40 tens make
50 tens make
100,
100
500
300
400
200
10 tens.
— tens.
— tens.
— tens.
— tens.
60 tens make
80 tens make
70 tens make
90 tens make
100 tens make
600 =
800 =
700 =
900 =
1000 =
tens,
tens,
tens,
tens,
tens.
227. Add:
$5
500^
300^
$4
400^
500^5
4 hundreds
3 ''
40 tens
30 ''
400 ones
300 ''
100 miles
300 ''
500 "
200 sheep
400 ''
300 "
$100
600
200
168
SCHOOL AJOTUMETIO.
228. Subtract:
$6 600^
60 dimes
$2 200^
20 "
7 hundreds
70 tens
700 ones
3 "
30 "
300 "
900 700
600 800 900
200 400
100 500 700
229. Copy and complete:
100 + 300 =
500 + 100 =
300 + 600 =
200 + 400 =
400 + 300 =
500 + 400 =
400 + 200 =
700 + 200 =
100 + 800 =
600 + 300 =
100 + 600 =
300 + 500 =
300 + 200 =
200 + 500 =
400 + 600 =
Hundreds and Tens.
t
h
t
h
t
1
1
1
1
230. In writing ten in figures, why do we put in ones^
place?
In writing one hundred in figures we put in two
places. Why?
How many ones can be written with one figure? How
many tens? How many hundreds?
How do you write 1 ten and 1 one in figures?
How do you think 1 hundred and 1 ten should be
written?
HUNDBE»)6 AND TENS. 159
One hundred and one ten is written thus — 110.
One hundred and two tens is written thus — 120.
One hundred iand three tens is written thus — 130.
One hundred and ten tens is written thus — 200.
Two hundreds and one ten is written thus — 210.
Three hundreds and five tens is written thus — 350.
231. Copy and complete:
1 hundred + 1 ten =110. 1 hundred +9 tens=^
1 hundred + 3 tens = 2 hundreds + 3 tens =
1 hundred + 7 tens = 2 hundreds + 6 tens =
1 hundred + 5 tens = 2 hundreds + 5 tens =
1 hundred + 4 tens = 3 hundreds + 1 ten =
1 hundred + 8 tens = 3 hundreds + 4 tens =
100 + 80 = 300 + 40 =
One hundred and two tens, or 120, is read one hundred
twenty.
How then should 140 be read? 250? 230? 360?
510? 740?
Count by lO's from 100 to 300. From 300 to 500.
From 500 to 1000.
How many hundreds and how many tens in 240? In
360? In 580?
282* Copy and complete:
260 =
2h + %t
430 = 4 ^ + 3 <
320 =
680 =
410 =
740 =
630 =
590 =
540 =
860 =
720 =
770 =
810 =
990 =
950 =
870 =
160
SCHOOL ABITHMETIO.
What numter contains 4 hundreds and 3 tens? Two
hundreds and 5 tens?
Count by lO's from 300 to 600, and write the numbers
as you count.
Show with sticks what is expressed by each figure in
140. In 250.
How many tens in 100? In 200? In 500? In 250?
In 120? In 210?
233. Read:
150, 180, 210, 320, 430, 540, 360,
280, 470, 390, 760, 920, 650, 870.
234. Write in figures :
One hundred forty.
One hundred sixty.
Two hundred thirty.
Two hundred twenty.
Three hundred eighty.
Five hundred ninety.
Four hundred fifty.
Six hundred ten.
Eight hundred seventy.
Seven hundred eighty.
Nine hundred forty.
Nine hundred ninety.
Hundreds, Tens, and Ones.
h
t
1
1
h
t
1
2
4
235. In writing 1 hundred and 1 one, or 1 more than
100, what do we write in the ones' place? In the tens'
place?
In writing 124 what do we write in ones' place? In
tens' place?
Count from 100 to 200, and write the numbers as you
count.
HUNDBBDSj TENS, AND ONES.
161
Numbers from 100 to 1000 are written as follows:
One hundred, 100.
One hundred one, 101.
One himdred two, 102.
Two himdred one, 201.
Two hundred twelve, 212.
Two hundred forty-six, 246.
Nine hundred ninety-nine, 999.
One thousand, 1000.
How many hundreds in 132? How many tens? How
many ones?
How many hundreds, tens, and ones in 245? In 328?
In 612?
236. Eead:
25 42
30
90
81
325 542
130
290
781
16 23
17
84
10
216 423
217
484
810
37 66
36
3
98
437 666
336
303
898
237. "Write in figures
Forty-one.
Eleven.
Two hundred forty-one.
Five hundred eleven.
Sixty-four.
Thirty-six.
Six hundred sixty-four.
Three hundred
thirty-six.
Eighty-nine.
Ninety.
Four hundred eighty-nine.
Nine hundred ninety.
•^n
162 SCHOOL ABITHMBTIC.
238. Copy and complete:
Hundreds tens ones
1 _^ 3 + 2 = 132. 100 + 30 + 2 = 132
1 + 2 + 5 =
100 + 20 + 5 =
2 + 1 + 6 =
200 + 10 + 6 =
2 + 4 + 7 =
200 + 40 + 7 =
5 + 3 + 8 =
500 + 30 + 8 =
4 + 5 + =
300 + 60 + 4 =
6 + 6 + 6 =
400 + 40 + 4 =
8 + 3 + 9 =
700 + 80 + 1 =
3 + + 5 ==
600 + 20 + =
9 + 7 + 1 =
800+ + & =
lars dimes cents ceilts
Dollars dimes cents cents
1 + 5 + 5 =155
2 + 3 + 1 = 231
1 + 4 + 2 =
3 + 5 + 4 =
3 + 2 + 8 =
6 + 7 + 6 =
4 + 6 + =
6 + 9 + =
2 + + 6 =
7 + + 8 =
5+0 + 0= 4+4 + 4 =
In 325 cents, the 5 represents centSy the 2 represents
dimes, and the 3 represents dollars, or hundreds of cents.
"What does each figure in 427 cents represent?
In 555 cents, which five represents the greatest value?
Which represents the least value?
Wliich 5 represents 50 cents? Which represents 5
cents?
Then the middle 5 represents 10 times as much as
which 5?
Which 5 represents 10 times as much as the middle 5?
ADDITION AND SUBTRACTION. 163
Show how many dollars, dimes, and cents there are in
215 cents.
How many hundreds, tens, and ones are there in 348?
In 592? In 402?
How many figures are needed to write hundreds? How
many to write hundreds, tens, and ones?
Addition and
Subtraction.
239. Add
:
1
2
3
4
5
6
24
92
57
68
90
27
87
87
86
94
76
46
68
69
75
76
84
84
96
34
68
45
59
■ 68
7
8
9
10
11
12
49
94
84
65
7
92
74
87
76
29
84
37
98
39
18
84
68
48
65
65
54
76
42
51
83
56
63
• 17
79
76
13
14
15
16
17
18
28
81
63
37
97
28
46
63
81
96
2
84
92
9
5
42
85
61
74
27
37
88
46
79
19
45
19
4
58
46
37
76
46
73
39
37
164 SOHOOL ARITHMETIO.
18
20
21
22
23
24
76
64
95
76
12
74
32
93
26
90
37
29
23
89
7
39
45
83
67
46
80
68
79
28
51
57
78
85
28
45
24
54
38
42
55
45
86
36
47
36
84
83
45
79
62
7
83
37
240. Subtract 286 from 763.
753 We cannot take 6 ones from 3 ones, so we add 10 ones to
286 the 3 ones, and take 6 from 13. Where do we get the 10
ones? How many tens are left?
467 CJan we take 8 tens from 4 tens ? Then we must add 10
tens to th'e 4 tens, and take 8 from 14. Where do we get
the 10 tens? How many hundreds are left? 2 hundreds from 6
hundreds leaves 4 hundreds.
Add 467 and 286. If the sum is 763, the subtraction
is correct.
Subtract and prove:
1 2
IP
3
4
5
6
714 635
582 .
745
827
610
362 271
175
476
572
247
7 8
8
10
11
12
921 824
732
.672
523
624
478 547
435
48
149
258
ADDITION AND SUBTRACTION.
lU
13
362
57
U
521
412
15
607
278
16
300
27
17
815
726
18
935
786
19
20
21
22
23
24
872
360
706
982
617
308
375
97
418
387
419
199
241. Copy and
1. 475+65=
2. 582+78=
3. 368+53=
4. 729+94=
5. 647+85=
6. 768+74=
7. 526+59=
8. 395+67=
complete:
9. 248+376=
10. 426+187=
11. 519+183=
12. 372+439=
13. 582+276=
14. 766+180=
15. 647+273=
16. 504+396=
17. 527—348=
18. 716—297=
19. 432—186=
20. 666—378:
21. 500—275=
22. 807—508=
23. 431—276=
24. 760—498=
242. 1. How much will a span of horses cost if one
horse costs 85 dollars and the other 105 dollars?
2. In a box were 85 oranges. If the box would hold
125, how many more oranges would it take to fill it?
3. A boy shoots one arrow 97 yards up the road, and
another 65 yards down the road. How many yards apart
are the two arrows?
4. Mr. Thomas paid $625 for a lot, and sold it for
$900. How much did he make?
5. Three men have $980. One has $145, another
has $321. How much has the third man?
6. I can buy a candy store for $825, but I have only
$688. How much more do I need?
166 SCHOOL ARITHMETIC.
7. Mr. Johnson raised 345 bushels of corn, 475 bushels
of oats, and 128 bushels of wheat. He raised
bushels in all.
8. One week a milkman sold 284 qt. of milk, the next
week 296 qt., the next week 318 qt., and the next week
72 qt. In the four weeks he sold quarts.
9. Martin weighs 128 lb., Frank 96 lb., Jack 116
lb., Eob 87 lb., and Will 131 lb. How much do all five
boys weigh?
10. A storekeeper had 970 bushels of potatoes. One
week he sold 265 bu., and the next week 325 bu. How
many bushels had he left?
11. On Monday morning a freight train started to run
962 miles. The first day it ran 316 miles, the second day
it ran 373 miles. It still had miles to run.
12. September, April, June, and November each has
30 days. February has 28 days except in leap years, when
it has 29. All other months have each 31 days. How
many days in all the months, or in a year?
Multiplication and Division.
243. Multiply:
243
2
321
3
434
2
233
3
212
4
211
6
322
4
423
3
534
2
412
4
Take 46 splints, 4 tens and 6 ones. How many would
you have if you had 4 times as many?
MULTIPLIOATION AND DIVISION. 167
Four times 6 splints = 24 splints. How many tens and.
how many ones in the 24 splints.
Four times 4 tens = 16 tens. 16 tens and 2 tens are
18 tens. You would have 18 tens and 4 ones, or 184
splints.
46= 4?5 + 6<?
4 4
184 = 16^ + 24^ = 18^ + 4<>
Multiply 246 by 4.
246' 246 = 2A + 4^ + 6o
246 4 4
246
246
984
984 = 9A + 8^ + 4o
We can find the result by adding, but there is a snorter process.
4 times 6 ones = 24 ones. We write the 4 ones under the 6 ones,
and * 'carry" the 2 tens to add with the tens. 4 times 4 tens =: 16
tens. The 2 ones we had to carry make 18 tens, or 1 hundred and 8
tens. We write the 8 tens under the 4 tens, and carry the 1 hundred.
4 times 2 hundreds are 8 hundreds and the 1 hundred makes 9 hun-
dreds. Where is the 9 hundreds written ?
Multiply
1
2
3
4
5
6
45.
36
25
35
143
125
3
4
5
3
4
5
7
8
9
10
11
12
216
117
228
170
280
181
4
5
3
2
3
4
168 SOHOOL ARTTHMETie.
13
U
15
16
17
18
242
162
136
172
196
167
5
6
6
5
4
5
19
20
21
22
23
24
152
138
126
119
137
128
6
7
8
7
7
7
26
26
27
28
29
30
108
107
117
163
69
76
8
9
8
6
8
9
31
32
33
34
35
36
35
24
32
51
62
44
12
12
11
11
12
12
244
Examine carefully
:
5
multiplied by
10 =
50.
10 X 7 =
70.
8
multiplied by
10 =
80.
10 X 2 =
20.
10
multiplied by
10 =
100.
10 X 9 =
90.
12
multiplied by
10 =
120.
10 X 20 =
200.
15
multiplied by
10 =
1-50.
10X50 =
500.
Annexing to a number multiplies it by 10,
Announce results at sight:
10 X 7
10 X 25
10X60
10X11
10X30
10X66
10X14
10X36
10X70
10 X 18
10X40
10X75
10X20
10X48
10X87
10X24
10X50
10X98
MtTLTIPUOATION AND DIVISION.
169
246. Divide:
-
^
(a)
2)486
2)682
2)348
3) 636
3)369
(!>)
4)844
4)480
5)555
6)660
8)888
(«)
2)100
2)128
3)126
3)150
3) 189
(d)
4)168
4)204
4)284
4)320
4)368
(e)
5)105
5)150
5)200
5)355
5)550
W
6)126
6)240
6)366
6)420
6) 546
(&)
7)140
7)217
7)280
7)357
7)630
(h)
8)160
8) 248
8)400
8)560
8)728
(i)
9)639
9)720
9)810
9)909
9)990
246. Examine carefully
50 -^ 10 =
30-^10 =
80 -^ 10 =
100 ^ 10 =
= 5
- 3
= 8
= 10
120 -T- 10 =
150-7-10 =
200 -^ 10 =
250 -^ 10 =
= 12
= 15
= 20
= 25
Annexing a cipher to a number multiplies that number
by 10. Show that cutting off zero divides a number by 10.
247. Name results at sight:
50-
-10
140-
-10
400-
-10
70-
-10
180-
-10
460-
-10
40-
-10
200-
-10
510-
-10
60-
-10
270-
-10
680-
-10
110-
-10
300-
-10
790-
-10
130-
-10
320-
-10
940-
-10
170 SCHOOL ABITHMBTIO.
248. To find i of 75 splints, take 7 tens and 5 ones, and
divide them into 5 equal piles. Each pile mil contain
i of the 75. How shall we proceed to make the 5 piles?
5) 76 i of 7 tens = 1 ten for each pile, but there are 2 tens
~ left out. 2 tens and 5 ones = 26 ones, i of 26 ones = 5
ones for each pile. Hence each pile has 1 ten + 5 ones,
or 15 splints.
15
1. Divide 738 by 6.
6) 738 7 hundreds h- 6 = 1 hundred, and 1 hundred remain-
1 9^ ^^^
The remainder 1 hundred equals 10 tens, which with
the 3 tens makes 13 tens.
13 tens -r- 6 = 2 tens, and 1 ten remaining. 1 ten and 8 ones = 18
ones. 18 ones -t-6 — S ones.
Explain this division by using splints.
2. Divide 375 by 5.
Since 3 does not contain 6, we take the 3 hundreds or
5) 375 ^ ^^^ ^^^ P^t them with the 7 tens, making 37 tens.
— — Then 37 tens -j- 5 = 7 tens, and 2 tens remaining.
* ^ The 2 tens or 20 ones put with the 5 ones make 26 ones.
25 ones -4-5 = 6 ones.
Divide
3
4
5
6
7
8
2)236
2)112
2)154
2) 178
2)192
2)254
9
10
11
12
13
14
2)176
2)452
2) 634
2)816
2)412
2)630
15
16
17
18
19
20
3)168
3)195
3)351
3)642
3)975
3)678
21
22
23
24
25
26
3)426
3) 753
3)826
3) 525
3)432
3)528
MULTIPLICATION AND DIVISION. 171
27
28
29
30
31
32
4)452
4)896
4)568
4)604
4)720
4) 956
33
34
35
36
37
38
5)625
5)675
5)720
5)835
5)960
5)985
39
40
41
42
43
44
6)132
6)198
6)252
6) 618
6)714
6)804
45
46
47
48
49
50
7)154
7)112
7)105
7)714
7)798
7)861
51
52
53
54
55
56
8)176
8)104
8)256"
8)736
8)984
8)992
67
58
59
60
61
62
9)117
9)198
9)288
9)657
9)765
9)846
249. 1. What number multiplied by 7 is equal to 84?
2. What number divided by 6 is equal to 72? To 720?
3. Find one of the 4 equal parts of 96. Of 2^0.
4. Of what number is 25 one-fourth? One-eighth?
5. Fifty is i of what number? yV ^^ what 'number?
6. If 24 is t of some number, what is i of the number?
7. If $20 is f of my money, how much money have I?
8. A train runs 315 miles in 9 hours. How far does
it run in 1 hour?
9. If 3 organs cost $180, how much does one cost?
10. If 1 organ costs $60, how much will 10 cost?
11. At the rate of 2 for 5 cents, what will a dozen
lemons cost? (12 = how many 2's?)
12. What will 10 books cost if 2 books cost $3 ? 10 is
•how many times 2? The cost of 10 books will be how
many times
172
SCHOOL ARITHMETIC.
13. If you read 23 pages each day, how many pages
will you read in a week?
14. How many boxes will hold 117 pounds of candy,
if 3 pounds are put in each box?
15. In a year there are 365 days. How much more
than 52 weeks is that?
16. At $7 a barrel, how many barrels of flour can be
bought for $413?
17. A rectangle is 81 inches long and 7 inches wide.
How many square inches does it contain?
18. Three boys have 43 quarts of nuts, and they
gather 32 quarts more. If they divide them equally
among themselves, how many quarts will each receive?
19. How many inch-cubes can you put into a box that
measures in the inside 5 inches long, 4 inches wide, and
3 inches deep?
United States Money.
250. How many cents make a dime?
How many dimes make a dollar?
Then how many cents make a dollar?
10 cents make 1 dime.
10 dimes, or 100 cents, make 1 dollajr.
One dollar is written $1, or $1.00. The sign $ is called
UNITED STATES MONEY. 173
the dollar mark, and is placed before the figures express-
ing dollars. Four dollars and twenty-five cents is written
$4.25. The dot after the $4 in $4.25 means that the two
figures on the right stand for cents, and the figures on the
left stand for dollars. This dot is called the decimal point.
251. Eead the following:
$4.75
$6.20
$8.10
$2.05
$5.05
$4.50
$2.84
$1.90
$3.60
$4.40
$3.25
$7.15
$5.35
$9.01
$8.16
Write the following:
Two dollars and fifty cents. One dollar and twenty-five
cents. One dollar. Five dollars and forty cents. Eight
dollars and five cents. Ten dollars and seventy-five cents.
Six dollars and two cents. Nine dollars and fifteen cents.
252. When there are no dimes or cents we do not need
to use the dot unless we write ciphers in the place of dimes
and cents.
Read the following:
$5 $10 $50
$100
$125
$500
$1 $25 $75
$110
$206
$640
$4.00 $2.00 $8.00
$105
$30.00
$75.00
When there are no dollars to write we place the dot
between the dimes and the dollar mark.
Eead the following: .
$.25 $.75 $.10 $.01 $.07 $.09
$.50 $.90 $.05 $.20 $.85 $.99
174
SCHOOL ABITHMEnO.
Write in figures:
Thirty dollars. One hundred five dollars. Four hun-
dred ten dollars. Five hundred dollars. Twenty-five cents.
Sixty cents. Ten cents. Five cents. Thirty cents. One
cent. Eighty-eight cents. Seven cents. Twelve cents.
Five dollars and five cents.
253. Write as dollars and cents :
0^ 175^
225^
360f!
105f!
310^
0^ 500^
713fS
609^
220^
666^
Complete and read:
Dollars
Dimes
Cents
3
2
5
= $3.25
5
1
6
=
7
=
2
4
8
=
8
8
=
4
=
4
=
5
2
=
9
6
7
=
254. Dollars, dimes, and cents are added just as hun-
dreds, tens, and ones are added.
Dol.
2
4
7
Dimes
4
5
6.
6
5 = $2.45
8 = 4.58
= 7.60
14
3 =$14.63
What is written in the first
column? In the second ? In
the third?
Are the dots all in one
column?
How do we get 14 dollars
in the sum?
mnncD states homey.
176
Find the sums:
$12.15
7.06
8.29
4.80
36.94
$16.52
5.01
7.75
30.40
28.89
$21.45
8.72
6.34
6.80
10.10
$60.76
28.09
7.84
3.63
5.00
Find the differences:
•
$84.75
26.38
$70.20
8.05
$37.00
25.25
$64.03
28.85
Multiply:
$14.16
3
$15.10
4
$12.25
6
$24.75
3
$42.48
$51.80
6
$42.34
5
$28.04
7
$37.43
8
Divide:
2 ) $48.76 3 ) $48.51 2) $75.20 2 ) $25.00
$24.38
5^)75^ 3^)30^ 8^)72^ 6^)96^ 10^ )150^
255. 1. One month Mr. Gray paid $22.60 for rent,
$4.80 for milk, $26.78 for groceries, and $6.37 for gas.
How much did he pay for all ?
2. I owe $32.20 for coftl.. If I pay $25 now, how much
shall I still owe ?
176 SCHOOL ABITHMEnO.
3. A man bought 6 cows at $24.75 each. He paid
$ for all.
4. A dealer paid $112.25 for 5 stoves. What was the
price of one?
6. A farmer paid $328 for two horses. He sold one
for $197.50, and the other for $187.50. What was his
profit? '
6. Find the cost of 10 acres of land at $85 an acre.
7. Mrs. Brown gave $320 for 10 cows. How much
did she pay for one cow?
8. How many pounds of sugar at 5^ a pound can you
buy for 75^?
9. If I can buy 2 oranges for 5^, how many can I buy
for a half-dollar?
Oral Exercises.
256. How much money in:
a. 1 5-dollar bill, 3 2-dollar bills, 1 silver dollar, 1 half
dollar, and 1 quarter?
b. 1 10-dollar bill, 2 5-dollar bills, 3 silver dollars, 3
quarters, and 2 dimes?
c. 3 20-dollar bills, 6 5'-dollar bills, 2 1-dollar bills, 2
half dollar bills, 5 dimes, and 6 nickels?
d. 5 10-dollar bills, 10 2-dollar bills, 1 5-dollar gold
piece, 6 half dollars, 8 dimes, and 5 cents?
How many half dollars are there in $2? $5? $10? $12?
How many quarters are there in $2? $3? $5? $10?
How many dimes are there in $2? $3? $5? $15?
How many quarters are there in 2 half dollars? 5 half
dollars? 12 half dollars?
OBAL BXEBOISKS.
177
How many dimes are there in 2 quarters? 2 half dollars?
6 quarters? 3 half dollars?
. How many dimes are there in 30^? 80^? 120^? 250^5?
10 nickels?
How many dollars are there in 20 dimes? 50 dimes?
60 dimes? 75 dimes? 40 nickels? 600 cents?
267. Copy and complete:
i of $1 = 50^
i of $1 =
f of $1 =
i of $1 =
tV of $1 =
25^= i
50^ =
75^ = _
20^ =
10^ =
of $1
of $1
of $1
of $1
of $1
358. Two dollars and a half means $2.50; a dollar and
a quarter means $1.25.
Complete and read:
$1 + i of $1 =
$2 + i of $1 =
$5 + i of $1 =
$3 + i of $1 =
$4+1 of $1 =
$7 + tV of $1 =
$6 + A;of $1 =
$9 + tV of $1 =
259. Find the amount of this bill:
6 lb. steak at .... $ .15
5 yd. silk at 1.35
4 gal. milk at 30
9 doz. eggs at 14
•12
178 SCHOOL AKITHMETIO.
260. A lady bought 3 lb. of sugar for 18 cents, and
gave the grocer a half dollar. He made the " change ''
as follows:
Saying 18, he handed her 2^, and said 20; gave her a
nickel, and said 25 ; then gave her a quarter, and said 50.
Did she get the correct change?
Change is nsnally m&de by counting up from the
amount of the purchase to the amount given in pay-
ment.
Find the change by counting up:
Bought candy for S^; gave a dime in payment.
Bought sugar for 83^; gave $1 in payment.
Bought shoes for $3.25; gave $5 in payment.
Bought books for $8.12; gave $10 in payment.
NUMBERS TO MILLIONS. 179
NUMBERS TO MILLIONS.
261. Measure with the quart measure the water in
this pail. How many quarts are there? One quart is
called the unit of measure.
Measure with a ruler the length of your book. How
many inches long is it? What unit of measure did you
use?
When we say we have ten apples, the unit used in count-
ing them is one apple.
One of any kind (or any group regarded as one) by com-
parison with which we count or measure is called a xmit.
262. You have already learned that when three figures
are written side by side, the one at the right represents
ones J the second figure represents tens, and the one at the
left represents hundreds.
Can you write 10 hundred with three figures?
The number 10 hundred is called a thousand.
A thousand is written — 1,000. Then how many figures
are required to write thousands?
263. One thousand one hundred is written — 1,100.
Twenty-five thousand is written — 25,000.
Ten thousand five hundred is written — 10,500.
One hundred twenty thousand three hundred is writ-
ten — 120,300.
How many thousands and how many hundreds in
1;500? 2,600? 8,200? 3,800? 9,300? 18,700? 115,400?
180 SCHOOL ABITHMBTIC.
264, One thousand one hundred ten is written — 1,110.
One thousand one hundred eleven is written — 1,111.
One thousand twenty-five is written — 1,025.
One thousand four is written — 1,004.
How many thousands and tens in 1,130? 1,480?
2,140? 3,250? 4,890? 7,620? 6,970? 5,710?
How many thousands, hundreds, tens, and ones in 1,235?
1,346? 1,472? 2,125? 3,521? 6,275? 2,017? 12,534?
Write in figures and read all the numbers from 1,002
to 1,020; from 10,995 to 11,001; from 125,090 to 125,160.
266. Complete:
2,743 == 2000 + 700 + 40 + 3 = 2th + 7A + 4f + 3o
5,271 =
1,075 =
12,004 =
25,378 =
3000 + 500 + 60 + 2 = Zth + 5A + 6f + 2o = 3,56^.
6000 + 200 + 70 + 5 =
5000 + 800 + 20 + =
4000 + 000 + 50 + 4 =
8000 + 300 + 00 + 7 =
266. Compare 1, 10, 100, 1000.
How many ones make 1 ten?
How many tens make 1 hundred?
How many hundreds make 1 thousand?
When 1 stands alone how many ones does it express?
When it stands at the left of a cipher? At the left of two
ciphers?
NUMBERS TO MILLIONS. 181
In the number 11 which 1 expresses the greater value?
How many times as great? In the number 111?
REMEMBER: Any figure represents ten times the
v&lne it would represent in the next place to the right,
267. In counting by ones the unit is one.
In counting the tens of a number, we may regard one
ten as the unit for the tens.
May one hundred be regarded as the unit for the
hundreds of a number?
The ones of a number are called units of the first order,
or simply units; the tens are called units of the second
order; the hundreds are called units of the third order,
and so on.
268. One more than 999,999 is 1000 thousands, which
is called a million, and is written thus — 1,000,000.
When we wrote thousands, what did we put after the
last figure of the thousands?
Do we place a second comma after the figure for
millions?
Into groups of how many figures each do the commas
divide the figures?
For convenience in reading numbers the figures are
divided into groups of three figures each, beginning at the
right. Each group is called a period. The right-hand
group is called the period of units, the second group, the
period of thousands, the third group, the period of
millions.
182
SCHOOL ARITHMETIC.
269. What we have learned about the manner of
writing numbers is shown in the following
cc
^
s
§
^
JH
5
Millions
Hundred-t
Ten-thousa
Thousands
Hundreds
Tens
Ones
3 8
4
5 3 2
Y
"Y
3d
2nd
1st
Period. Period.
Period.
Millions T/umsands
Units
The number in the table is read three million^ eight
hundred forty thousand, five hundred thirty-two.
Examine the table and tell:
How many figures are required to write ten-thou-
sands ? Hundred-thousands ?
How many figures are required to write millions?
Are the tens and ones of each group read together?
How many figures has the left-hand group?
How many figures must the other groups contain?
Each period has three places — ones, tens, and hun-
dreds. The first period has ones, tens, and hun-
dreds of ones; the second has ones, tens, and
hundreds of thousands; and so on.
300
999
3,204
5,060
6,308 "
8,401
NUMBERS TO MILLIONS. J 83
270, Bead the following: „
507 101 340
2,100 1,310 2,136
6,400 3,240 1,275
12,800 15,890 12,581 16,035 14,008
234,600 616,720 321,476 695,182 999,999
3,005,008 2,452,320 1,982,200 2,879,079 1,121,001
Write in figures:
Two thousand five hundred. Five thousand eight hun-
dred. Four thousand two hundred ten. Six thousand one
hundred ninety. Three thousand four hundred forty-six.
Eight thousand seven hundred thirty-five. Four thousand
three hundred eight. Nine thousand twenty-four. Two
thousand ten. Six thousand twenty. Seven thousand five.
Ten thousand fifty-eight. Eight thousand two hundred
six. One million.
271,
You have already learned how numbers are written in
the Roman notation up to 12.
Now state what the new letters L, C, D, and M each
stand for.
I represents 1; II represents 2; X stands for 10; XX
stands for 20. Then what is the effect of repeating a letter?
V stands for 5; IV stands for 4; X stands for 10; IX
stands for 9. What then is the effect of writing a letter of
less value before a greater?
I
V
X
L
C
D
M
1
5
10
50
100
500
1000
184 SOH(X>L AUTTHHETIO.
What does XL stand for? XO?
VI stands for 6; XI stands for 11. What is the effect
of writing a letter of less value after a greater?
What does LX stand for? CX?
Complete
:
1= I
11 = XI
21=:
XXI
35 = XXXV
2 =
12 =
22 =
45 =
3= •
13 =
23 =
75 =
4 =
14 =
24 =
96 =
5 =
15 =
25 =
34 =
6 =
16 =
26 =
46 =
7 =
17 =
27 =
77 =
8 =
18 =
28 =
88 =
9 =
19 =
29 =
99 =
10= 20= 30= 101 =
Addition and Subtraction.
272. Add:
1
2
3
4
6
3,725
7,618
5,392
6,728
8,796
6,287
4,376
2,763
8,276
6,978
7,392
2,914
4,827
4,937
3,547
6
7
8
9
10
$7,246
$2769
$3486
$16.38
$70.35
3,983
8478
7615
29.15
25.97
2,762
9192
5307
85.72
64.78
6,219
7581
8590
72.40
59.24
8,768
4803
6925
69.17
91.39
ADDITION AND SUBTRACTION.
185
11
12
13
U
15
87535
29413
44777
67890
36925
62914
72694
32416
12345
81470
4728
547
87324
34251
14703
872
84062
4715
26076
69258
53389
7618
982
8907
58147
7604
385
5639
73529
3692
5881
92764
76248
982
81470
3627
8270
39571
8076
369
98376
64936
50867
93745
70487
278. Find the sum of:
16. 72384 + 2984 + 37038 + 920 + 8006.
17. 60572 + 3751 + 807 + 73092 + 46075.
18. 19283 + 47650 + 2006 + 8372 + 50098.
19. 53761 + 6807 + 924 + 7354 + 89763.
20. 40516 + 27385 + 6607 + 4481 + 90876.
21. Four thousand six, twenty thousand seven hundred
fourteen, eighty-nine, five hundred ninety-four, eighty-
four thousand nineteen.
274. Subtract:
1 2
3
4
6
7,236 5,176
4,753 2,849
8,352
5,178
6015
2376
9200
2914
6
$3520
1750
7
$7245
2754
12
6004
5706
8
9
10
$6321
4576
$4000
2545
$8007
7129
13
14
IS
7005
5717
3004
1068
45216
27089
186
SCHOOL AEITHMEnC.
16
37002
19008
21
870623
581539
17
56214
42657
18
73014
34025
19
18001
7608
22
601540
403862
23
803002
80305
20
20450
16784
24
500000
423167
275. Tlie Hinnend is the number from which another
number is subtracted; the Subtrahend is the number that
is subtracted. What is i^anT remainder f
1. The minuend is 825, the subtrahend is 368. Find
the remainder.
2. The minuend is 7215, the remainder 2345. What is
the subtrahend?
3. The subtrahend is 4527, the remainder is 1328.
What is the minuend?
4. To what number must 572 be added to make the
sum 1420?
6. If 365 be subtracted from — — , the remainder
wiU be 1824.
276. 1. There are 365 days in a common year. In
10 common years there are days.
2. In 1860 there were 177,840 people living in Boston;
in 1890, there were 448,477. What was the increase in
30 years?
3. From 1860 to 1890 the population of Baltimore
grew from 212,418 to 434,439. Find the gain.
4. In 1890 how much larger was the population of
Boston than that of Baltimore?
MULTIPUOA'nON.
189
16
17
18
19
20
3906
8
4075
9
7766
7
23
8594
8
99,888
9
21
22
24
25
5604
6
3817
8
6670
9
4096
7
124,762
6
26. Multiplier 8, multiplicand 50,725.
27. Multiplicand 23,450, multiplier 7.
280. 1. If a man earns $125 a month, how much
does he earn in 6 months?
$125 in one month.
6
$750 in six months.
In 6 months he earns 6 times
$125, or $750.
2. A grocer bought 8 barrels of sugar each weighing
284 lb. How many pounds did he buy?
Illustration. $5-f-$5 + $5 + $5 = $20. This is addition.
4 X $5 = $20. This is multiplication. $5 is the multiplicand. It is
taken 4 times, hence 4 is the multiplier. Which is the product?
The multiplicand and the multiplier are called factors
of the product. Thus, in 2 X 5 = 10, 2 and 5 are factors
of 10.
Of what number are 8 and 11 the factors? 5 and 7?
One factor of 21 is 3. What is the other factor?
What is the product of the factors 7 and 9? 10 and 12?
The product is 48, and one factor is 4. What is the
other factor?
190
SCHOOL ASITHMEnO.
281. 1. Multiply $48 by 12.
$48
12
~96= 2 X $48
480 = 10 X $48
Are 2 times $48 + 10 times
$48 equal to 12 times $48?
$576 = 12 X $48
2. Multiply $32, $54, $66, and $75 each by 12.
3. Multiply 225 by 15. By 23.
225 225
15 23
1125 = 5 X 225
2250 == 10 X 225
675 =
4500 =
3 X 225
20X225
3375 = 15 X 225
4. Multiply 314 by 13.
Find the products :
36 X 12. " 10.
45 X 13. 11.
63 X 15. 12.
72 X 18. 13.
88 X 23. 14.
5175 == 23 X 225
By 24.
124 X 22.
143 X 25.
216 X 32.
244 X 36.
326 X 43.
15.
16.
17.
18.
19.
413 X 18.
625 X 23.
842 X 26.
736 X 33.
534 X 44.
20.
Multiply 648 by 164.
648
164
2592 = 4 X 648
38880 = 60 X 648
64800 =- 100 X 648
106272 = 164 X 648
648
164
2592
3888*
648
106272
*In multiplying by Um it is not customary to put the in ones'
place. 60 X 648 = 38880 ones, or 3888 tens.
In multiplying by hundreds how many ciphers may we omit?
When we multiply by tens and omit the 0, in what place does the
MULTIPLICATION.
191
first figure of the partial product stand ? In what place when we
multiply by hundreds and omit the two ciphers?
Observe that the oneSf tenSf and hundreds of the muUxplicand^ in order ^ .
are mvMplied by the ones, tens, and hundreds of the multiplier, in order,
and that the first figure of ea^h product is put directly under the figure of
the muMpUer used in obtaining itf and thai the products are then added.
282. Multiply:
1
2
3
4
5
6
362
264
218
264
317
364
24
26
32
34
25
37
7
8
9
10
11
12
523
417
643
527
486
639
44
35
38
46
53
56
13
14
15
16
17
5247
6351
2583
4286
7465
54
68
65
73
37
18
19
20
21
22
6304
7023
5230
4076
8276
36
47
84
63
48
23
24
25
26
27
325
761
248
691
835
143
235
534
346
462
28
29
30
31
32
2317
3465
4263
6375
8729
324
125
by 1
217
264
536
33. Multiply 325
03.
826
103
If either factor is
0, what is the product?
975
Multiply 1C8 by
325
and compare the
325
producte
1.
33475
192
SOHOOL ASITHMKnO.
288. Find the
1. 7430 X 53.
2. 9625 X 49.
3. 6275 X 56.
4. 4760 X 72.
5. 3586 X 63.
6. 8274 X 76.
7. 6407 X 81.
8. 496 X 237.
9. 738 X 346.
product:
10. 2108
11. 3206
12. 4004
13. 5760
14. 3090
15. 6805
16. 7273
17. 638
18. 857
X 93.
X 57.
X 68.
X 74.
X 85.
X 39.
X 47.
X524.
X432.
19.
20,
21.
24.
25.
26.
27.
62425
23507
75310
38672
50836
40078
82036
3726
4385
X 56.
X 68.
X 39.
X 74.
X 83.
X 95.
X 78.
X485.
X724.
284. 1. Multiply 72 by 30.
72
30
72
30
or
2160
2160
Here we multiply by 3 tena
and no ones. '
Multiply:
2. 74 X 20.
3. 48 X 30.
4. 65 X 40.
5. 142 X 30.
6. 59 X 30.
7. 38 X 60.
8. 67 X 50.
9. 234 X 40.
10. 75 X 80.
11. 83 X 70.
12. 96 X 90.
13. 456 X 150.
285. 1. If a man takes 180 steps a minute, how
many steps will he take in an hour?
2. If a train runs 35 miles an hour, how far will it
run in 20 hours?
3. How much will 8 months' wages amount to at $27
a month?
4. When you know the cost of one orange, how can
you find the cost of 10 oranges?
5. A steamer sails 275 miles a dav. How far does she
sail in 9 days?
MULTIPLICATION, 193
6. In an orchard there are 18 rows and 12 trees in a
row. How many trees in the orchard?
7. My parlor is 18 feet square. How many square
yards of carpet will it require?
8. How many lines are there on this page of your
book? How many on 27 such pages?
9. There are 144 pens in a box. How many pens in
2 dozen boxes?
10. A lot is 175 feet long and 60 feet wide. How
many square feet does it contain?
11. There are 28 regiments in an army. If there are
875 men in each regiment, how many men in the army?
12. If a bushel of wheat weighs 60 pounds, what will
150 bufihels weigh?
13. An army used 48512 pounds of meat each week.
How much was used in 13 weeks?
Find the cost of:
14. 245 dozen fresh eggs at 9^ a dozen.
16. 384 pounds of sugar at 6^ a pound.
16. 18 pianos at $275 each.
17. 75 tons of clover hay at $14 a ton.
18. 286 bushels of wheat at 70^ a bushel.
19. 524 sheep at $4 a head.
20. 4 barrels of molasses, 42 gal. each, at 35^ a
gallon,
21. 65 barrels of apples, 3 bu. each, at 45^ a bushel.
22. 2 rolls of carpet, 59 yd. each, at 75^ a yard.
28. 8 loads of coal, 45 bu. each, at 8^ a bushel.
*i3
194 SCHOOL ARITHMETIC.
Division.
286, When we divide one number by another, the
result is called theftnotient; the number divided is called
the Dividend; and the number by which we divide is called
the Divisor.
In multiplicat^/m we ha/ve two factors to jmd the product.
In division we ha/ve a product and one fa^ctor to Jmd the
other factor. The dvvidend is the product^ the divisor
one factor. What is the other factor?
2 X $5 = $10. $10 -^ 2 = $5. $10 -f- $5 = 2.
Point out the factors in this example. The product.
The dividend. The divisors. The quotients.
287. Division includes —
(A). Finding one of the equal parts of a number; as, i
^f $10 = $5. $10 -^ 2 = $6.
(B). Finding how many times one number contains
.another; as, $20 -f- $5 = 4. 12 ft. -f- 3 f t. = 4.
1. What is one of the 3 equal parts of $24?
$24 -T- 3 = $8.
18. How many times is $3 contained in $24?
$24 -^$3 = 8.
In these examples $24 is the dividend. In the first 3 is the divisor
and $8 the quotient. In the second $3 is the divisor and 8 the
quotient.
3. When 50 lb. is the dividend and 5 the divisor, what
is the quotient?
What is required in this example? Do we also find the number of
pounds in each part? Is the quotient of the same kind (pounds) as
the dividend ?
DIVISION.
195
4. When 40^ is the dividend and 5^ the divisor, what
is the quotient?
Are the dividend and divisor of the same kind in this example 7
Does the quotient denote the number of times the divisor must be
taken to equal the dividend ?
6. Find by trial whether the product of the quotient
and divisor is equal to the dividend.
6. When $36 is the dividend and $4 the quotient, what
is the divisor?
7. When $7 is the divisor and 5 the quotient, what is
the dividend?
8. If you have a dozen eggs and wish to give me i of
them, you must give me one of the 3 equal parts of 12
eggs. That is, you must divide 12 eggs by 3.
9. Divide 30 gallons by 3. By 5. By 6. By 10.
10. What is i of 36 feet? i?
288. Divide:
1 2
3) 369 5) 550
i?
A?
7
4)368
8
5)400
3
6)126
9
7)427
4
5)205
10
6)540
5
4)328
11
8)720
6
6)426
12
8)818
13 14 16 16 17 18
6) 612 7) 714 5)300 9)369 8)808 9)918
19
4) 8044
20
5) 1050
21
3) 9126
22
6) 1206
23
7)14014
289. Find the quotients:
1. 3096 -T- 3.
2. 4015 -7- 5.
3. 1421 -f- 7.
4. 1224 -f- 6.
6. 1612 -^ 4.
6. 3240 -f- 8.
7. 18618 H- 6.
8. 20515 -^ 5.
9. 16812 -4- 4.
10. 14721 -T- 7.
11. 24816 -r- 8.
12. 18924 -r- 9.
13.
14.
15.
16.
17.
18.
305100
180120
363636
281435
271836
321632
196 SCHOOL ARITHMETIC.
19. What is the diflFerence between i of 824 and 824
^ 4?
20. Which would you rather have — i of $1200 or
$1200 -T- 3?
290, Are 5 tens and 6 ones equal to 4 tens and 16 ones?
Complete:
34 = 3 tens + 4 ones = 2 tens + ones.
78 = 7 tens + 8 ones = 6 tens H ones.
42 = 4 tens + 2 ones = 3 tens 4 ones.
87 = 8 tens + 7 ones = 6 tens -^| ones.
95 = 9 tens + 5 ones = 5 tens H ones.
126 = 12 tens + 6 ones = 7 tens H ones.
1. Divide 34 by 2, or find i of 34.
2 ) 34 = 2 tens + 14 ones. j of 2 tens= 1 ten.
17 = 1 ten + 7 ones. * ^^ ^"^ ^^®« = ^ ^°^«-
Complete:
2. i of 78= 6. 1 of 126= 10. 76^2 =
3. i of 42 = 7. i of 52 = 11. 51 ^ 3 =
4. 4 of 87 = 8. i of 65 = 12. 80 -t- 5 =
6. iof95= 9. i of 64= 13. 78-4-6 =
291. 1. Divide 968 by 8.
8 )968 = 8h + 16< + 8o
121 = lh+ 2t + lo
Divide:
2. 568 by 4. 6. 655 by 5. 10. 516 by 3.
3. 605 by 5. 7. 968 by 8. 11. 750 by 5.
4. 847 by 7. 8. 780 by 6. 12. 684 by 4.
6. 726 by 6. 9. 648 by 4. 13. 846 by 6.
DIVISION. 197
292. 1. Divide 945 by 7.
7 )945 = 7h + 24t + 5o= 7fe + 21t + 35o
135 = lk+ 3t+ 5o ■
9 A -r- 7 = 1 A, and 2 A or 20« remaining ; 24< -5- 7 = 3<, and 3< or
30o remaining ; 35o -r- 7 = 6 o.
•Divide:
2 3 4 6 6 7
5 )625 4 )548 3 )525 6 )756 5 )725 4 )632
8 9 10 11 12 13
6 )852 3 )534 8 )984 7 )952 8 )992 6 )948
IS 16 17 18
3 ) 6471 2 ) 2756 5 ) 5620 6 ) 6804
20 21 22 23
3 ) 7260 2 ) 3674 5 ) 6705 6 ) 7344
293. 1. Divide 7356 by 12.
(a) 0)
12) 7356 12) 7356 ( 613 quotient.
14
4)
8524
19
4)
9256
613
72
15
12
73 hundreds -^ 12 = 6 hundreds,
and 1 hundred remaining.
15 tens ^ 12 = 1 ten, and 3 tens 33
remaining. og
36 ones -5- 12 = 3 ones.
A common way of proceeding is something like the following :
12 in 73 6 times and 1 over ; I'J in 15 once and 3 over ; 12 in 36 S
times.
The process as shown in (a) is called short division; as shown in
(b) is long division. Wherein do they differ? In what ways are
they alike?
2. Divide 864 by 24.
J
24) 864 (36
1
72
86 tens ^- 24 = 3 tens and a remainder. 24 X 3 1
—
tens = 72 tens. 14 tens and 4 ones are 144 ones. |
144
144
144 ones
-J- 24 = 6 ones.
24X6
ones = 144 ones.
Find the quotients:
*
3. 5670 -
- 6.
13.
3454-
-11.
23.
7072-
-52.
4. 7212 -
H 6.
14.
4565-
-11.
24.
3536-
-26.
5. 6315 -
- 5.
IS.
4851 H
-21.
25.
5346^
-22.
6. 3507 -.
- 7.
16.
9702-^
-21.
26.
14624 H
- 32.
7. 2536 -
1- 8.
17.
3844-
1-31.
27.
14616 -
r-42.
8. 9208 -
r- 8.
18.
7688-
1-31.
28.
25599 -
r-53.
9. 7452 -
-12.
19.
9963-
-41.
29.
62350 -
-25.
10. 3744 -
-12:
20.
7488-
-24.
30.
20020 -
-35.
11. 4956 -
-12.
21.
6908-
-22.
31.
10368 -
-36.
12. 6276 -
-12.
22.
9050-
-25.
32.
30576 -
-48.
294. 1. Find one half of $49.
2) $49 = $40 + $9
= $20 + $4i
} of 4 tens, or $40, = $20.
} of 9 ones, or $9, = $4}, or
$4.50.
When there is a remainder we may write the quotient and re-
mainder as a complete quotient, as $24 J above.
Find:
2. iof$25.
7. i of 45 gal.
12.
iof 127.
3. i of 10 yd.
8. 4ofl5pk.
13.
4 of 214.
4. iof45qt.
9. I of 69 bu.
14.
i of 366.
6. i of 75 bu.
10. tV of $21.
15.
i of 329.
6. iof $89.
11. i of 145 lb.
16.
T^of 501.
DIVISION. 199
296, 1. At 604 a gallon, what is the value of a quart
of molasses?
2. How many times can you fill an 8-gallon jug from a
barrel that holds 48 gallons?
3. A crate holds 1728 eggs. How many dozen eggs
are there in the crate?
4. When you know the cost of 10 apples, how can you
find the cost of one apple?
5. A cattle dealer paid $682 for 22 head of cattle.
What was the average price?
6. How many years old is a man who has lived 900
months?
7. Tommy Jones weighs 100 lb. A ton of hay weighs
as much as 20 such boys. How many pounds in a ton?
8. If there are 60,000 lb. of coal in a car, how many
tons are in it?
9. A nine-acre field produced 375 bushels of oats.
How many bushels to the acre did it yield?
10. In 4 years the President receives salary to the
amount of $200,000. What is his yearly salary?
11. There are 5280 ft. in a mile. How many yards
in a mile?
12. If a man saves $12 a month, in how many months
will he save $1440? In how many years?
13. One day the fares on a certain street car amounted
to 2450 cents. Each passenger paid 5 cents. How many
persons rode on the car that day?
14. If a man on a bicycle rides 48 miles each day in
June, how much farther will he have to travel to make
1500 miles?
15. Mr. Butler divided $19500 equally among his 3
children. The daughter divided her share equally among
her 5 children. How much did each grandchild get?
200 SCHOOL ARITHMETIC.
REVIEW WORK.
Oral Exercises.
296. 1. If 6 oranges cost 30 cents, what will 3
oranges cost?
If 6 oranges cost 30 ct., 1 orange will cost i of 30 et., or 5 ct.; and
3 oranges will cost 3 X 5 ct., or 15 ct.
2. If 9 cords of wood cost $36, what will 1 cord cost?
What will 12 cords cost?
3. If 4 knives cost 96 cents, what will 9 knives cost?
4. If ^ of a pound of candy costs 10 cents, how much
must I pay for 2 pounds?
5. If 4 of a pound of cheese costs 5 cents, how much
will 2 pounds cost?
6. If 4 men can do a piece of work in 6 days, how many
days will it take 3 men to do it?
If it takes 4 men 6 days to do the work, it will take 1 man 4X6
days, or 24 days ; if it takes 1 man 24 days, it will take 3 men i of
24 days, or 8 days.
7. If 8 men can mow a field in 9 days, how many days
will it take 6 men to mow the field?
8. If 4 men can dig a ditch in 5 days, how many men
will be required to dig it in 4 days?
9. 7 is i of what number?
10. At 10 cents a dozen, what will 60 apples cost?
11. How many oranges at the rate of 2 for 5 cents
can I buy for 20 cents?
12. How many coats can.be cut from 21 yards of cloth,
if 3 coats can be cut from 9 yards?
13. How many pounds of sugar at 6 cents a pound
must be given for 2 pounds of coffee at 15 cents a pound?
14. If you divide 36 marbles among 6 boys, how many
marbles will 2 boys have?
WRITTEN EXERCISES. 201
16. If a railroad car has 8 wheels, how many cars will
40 wheels supply?
16. A boy bought 6 lead pencils at 4^ each and ex-
changed them for erasers at S^ each. How many erasers
did he get?
17. If 7 men can do a piece of work in 9 days, how
many men will it take to do the same work in 1 day?
18. If you buy 3 dozen pencils at 20^ a dozen, and sell
them at 3^ each, how much do you gain?
19. John is 9 years old, and his father is 3 times as old
and 9 years more. How old is his father?
20. If a man pays $30 for 6 sheep, how much at the
same rate does he pay for 5 sheep?
21. How many square yards in the floor of a room 15
yards long and 9 yards wide?
22. Alice's father gave her $2 every 2 months. How
many dollars did he give her in a year?
23. If a cow gives 6 qt. of milk a day, how many
gallons does she give in six days?
24. $28 is $7 more than the cost of 3 tons of coal.
What does 1 ton cost?
25. A man pays $3 a month for his room rent and $9
a month for his office rent. How much rent does he pay
a year?
26. If 2 oranges are worth 4 apples, how many oranges
are worth 12 apples?
Written Exercises.
297, 1. A man gave $35 for a wagon, and paid $4
for repairing it. For how much must he sell it to gain
$11?
2. There are CL Psalms. When you have read XC,
how many more have you to read?
3. The earth moves in its orbit 19 miles a second. How
many miles does it move a minute?
202 SCHOOL ARITHMETIC.
4. B and C start from the same place and travel in
opposite directions. B travels 5 miles an hour, and C 4
miles an hour. How far apart are they in 15 hours?
6. A clock strikes 156 times a day. How often will it
strike in a year of 365 days?
6. A barrel of flour weighs 196 pounds. What is the
weight of i a barrel?
7. Sound travels 1120 feet a second. How far off is a
cannon, the report of which is heard in 13 seconds?
8. How many times will 500 oranges fill a fruit dish
that holds 1 dozen oranges, and how many will be left
over?
9. If you purchase a horse for $100, and pay $40 in
cash, how long must you work at the rate of $12 a week
to pay the balance?
10. If your pulse beats 4320 times in an hour, how
many times will it beat in a day?
11. In what number is 225 contained 25 times?
12. Gold was discovered in California in 1848. How
many years ago was that?
13. A farmer sold 60 bushels of apples at $2 a bushel.
How many pigs can he buy at $4 each with the money?
14. One farmer gets $200 for his wood, and his neigh-
bor gets $248. The price is $8 a cord. How many cords
do they both sell?
16. A boy takes 9 subscriptions to the " Youth's Com-
panion '' at $1.75 each. How much money does he receive
for them all?
16. A building is 240 feet long and 200 feet wide.
How many yards is it around the building?
17. A man owed $5000. He made three payments,
one of $1375, another of $964, and another of $2484.
How much did he still owe?
WBITTEN EXERCISES. 203
18. A car line is 12 miles long. If a car makes 6
round trips daily, how many miles will it run during the
month of July?
19. If 8 cords of wood are worth $32, what axe 19
cords worth?
20. America was discovered in 1492; the Pilgrims
landed at Plymouth in 1620. How many years from the
discovery of America to the landing of the Pilgrims?
21. A man paid $175 for a horse, which was 5 tinies
as much as he paid for a cow. How much did he pay
for both?
22. The multiplicand was 3962; the multiplier was
186. What was the product?
23. If the divisor is 55, and tl^ dividend is 9625, what
is the quotient?
24. The floor of a room 16 ft. long contains 192 square
feet. What is the width?
26. How many marble slabs each 10 in. by 2 ft. will
cover a floor 10 ft. square?
26. A baker has 200 loaves of bread. He sells f of
them at 6^ each, and the remainder at 5^ each. How
much does he get for his bread?
27. If 3 oranges cost 10^, how many times 10^ must
be paid for a dozen oranges?
28. A farmer clipped 1000 lb. of wool from his sheep.
If each fleece weighed 5 lb., how many sheep had he?
29. A sugar plantation produces 2000 barrels of sugar,
averaging 250 lb. in weight. At 2^ a pound, what is the
value of the sugar?
30. . A man earns $2.50 a day and pays 50^ a day for
board. If he does not work on Sundays, how much will
he have left this month after paying his board?
204 SCHOOL ARITHMETIC.
U. S. Money and Decimals.
Ten dimes make a dollar.
298. What part of a dollar is 1 dime? 2 dimes? 3
dimes? 5 dimes? 10 dimes?
How many tenths of a dollar make a dollar?
How many tenths make 1 one?
A dime is 1 tenth of a dollar. We write dimes (tenths
of dollars) in the first place to the right of dollars.
Where with reference to ones' place should we write
tenths of ones?
What do we place between the figures for dollars and
the figures for dimes?
Should we place the decimal point after ones and before
tenths?
Tenths occupy the first place to the right of the decimal
point.
The number five and three-tenths is written 5.3.
The number .3, or 0.3, is read three tenths*
299. What part of a dollar is 1 cent? 2^?
How many hundredths of a dollar are 3^? 5^? 10^?
25^? 50^?
l(2^=$.01=y^ of a dollars. 01 of a dollar.
2(2^=:$.02=-3-fg- of a dollar = .02 of a dollar.
5^=$.05=:yfg- of a dollar = .05 of a dollar.
10(2^=1.10=^ of a dollar=.10 (or .1) of a dollar.
20(2^=1.20=^ of a dollar = .20 (or .2) of a dollar.
25(2^=1.25=^ of a doUar=.25 of a dollar.
Which is easier to wrie, yot ^^ ^ dollar or .01 of a
dollar?
V. 8. MONEY AND DECIMALS. 206
The^e are two ways of writing hundredths and tenths.
Yor ai^d .01 are both read one-hundredth.
y^ir ^^d .05 are both read five-hundredths.
■^ and .1 are both read one-tenth.
j^ and .5 are both read five-tenths.
■^ and .2 are both r^ad two-tenths.
3^ and .25 are both read twenty-five-hundredths.
300. How many tenths of a dollar are 10 cents (1
dime) ?
How many hundredths of a dollar are 10 cents?
Then how many hundredths make 1 tenth?
20 hundredths make 1 tenth.
10 tenths make 1 one.
What is written between tens and
terdhsf
The places to the right of ones are
called decimal places. Compare the
names of the decimal places with
those of the corresponding places on
the left of the decimal point.
How many of each place make 1 of the next place to
the left?
Does the figure next to the decimal point express tenths
or hundredths? Which figure expresses hundredths?
When there are five hundredths and no tenths, what is
written in tenths' place?
When there are tenths and no hundredths, is it neces-
sary to put a zero in hundredths' place? Why not?
Is 1 tenth (.1) of a dollar equal to 10 hundredths of a
dollar? Is 1 dime equal to 10 cents?
M
CQ
^
©
QJ
1
1
-2
w.
I
-2 ^
1
1
1
1
. 1 1
1 1
L
1
206 SCHOOL ABITHMETIO.
801. How many dimes and cents in:
$.05 $.04 $.50 $.25 $.05
$.20 $.30 $.08 $.05 $.75
$.25 $.34 $.58 $.30 $.80-
How many tenths and hundredths in:
.04 .4 .05 -.7 .1 .45
.2 .03 .6 .05 .35 .12
.24 .43 .65 .75 .45 .57
302. Copy and complete:
4 hundredths of a dollar = 4^ = $.04.
6 hundredths of a dollar =
9 hundredths of a dollar =
3 tenths of a dollar =
7 tenths of a dollar =
2 tenths and 5 hundredths of a dollar =
25 hundredths of a dollar =
5 tenths and 8 himdredths of a dollar =
303. Write with the decimal point:
4 hundredths 4 tenths and 2 hundredths
7 hundredths 3 tenths and 6 hundredths
5 tenths 7 tenths and 5 hundredths
8 tenths 1 tenth and hundredths
36 hundredths 10 hundredths
65 hundredths 50 hundredths
304. Two dimes and 5 cents are how many cents?
Two tenths and 5 hundredths are how many hundredths?
Two dimes are how many cents? Two tenths are how
many hundredths?
How many hundredths of a dollar make a dime? .10=.l.
U. 8. MONEY AND DECIMALS. 207
A quarter is equal to how many hundredths of a dollar?
A silver dollar is worth how many hundredths of a
dollar? How many tenths of a dollar? 10 tenths =
hundredths.
How many tenths of a dollar make a half dollar? How
many hundredths? .5 = .50.
75 cents = 7 dimes and cents.
75 hundredths = 7 tenths and hundredths.
Write with the decimal point:
TUT Tuir Tinr it tot
Tot tw ttt tit tot
33^ 84 2„0„ 7 30
TUT TTir TOT TT TOT
306. What part of a dime is a cent?
One-tenth of a dime is what part of a dollar?
One-tenth of .1 of $1 is one of a dollar.
Compare $10 and $1. 10 ft. and 1 ft.
Six minutes is what part of an hour? 12 minutes?
How many tenths of an hour are thirty minutes?
What part of $500 is $50? $5?
What is .01 of $100? Of $200? Of $500?
One foot is what part of 100 feet? 10 feet?
A dollar, 3 dimes, and 2 nickels are how many tenths
of a dollar?
Two dimes, a nickel, and 3 pennies are how many hun-
dredths of a dollar?
How many ones in 30 tens? In 30 tenths?
How many Ones and tenths are there in 25 tenths?
Write it decimally.
How many ones, tenths, and himdredths in each of
these: 1.11, 1.05, .05, .44, 55.55?
208 SCHOOL AKITHMETIO.
Draw a square and divide it into 10 equal parts. Point
out .2 of the square. .5 of it. .7 of it.
Add:
(a)
(b)
(»)
(d)
(«)
37.5
26.8
62.4
81.92
25.65
25.6
34.2
13.7
34.34
43.37
47.5
51.3
45.6
56.87
68.98
btract:
(?)
Q^)
(i)
(J)
62.55
48.75
72.44
49.8
85.3
12.42
25.30
36.23
37.5
62.9
Where do we place the decimal point in the result ?
306. 1. At 5f^ each how many oranges can I buy
for .5 of a dollar?
2. A farmer who had 100 sheep sold .1 of them to a
butcher and .5 of them to a drover. How many did he
sell?
3. Mr. Hall gave .3 of $50 to his daughter and .7 of
$50 to his son. How much did each receive?
4. Clark spent $4, which was .1 of his money. How
much money had he?
6. If $15 is .3 of my cash, what is .1 of it?
6. From 2.2 take .22. Erom 4 take .45.
7. Add 7.6, 7.8, 5.9, 3.4, and 5.7.
8. Bertha gave .2 of her money for a lO-cent dolL
How much had she left?
COMMON FBACTION8.
209
COMMON FRACTIONS.
1
z
Q
H
E 4-
307. What part of A is dark? What part is light?
Into how many equal parts is A divided?
Is B one of the equal parts? What part of the rectangle
isB?
How do we find i of anything?
How does the line CD divide the rectangle E? What
part of E is to the right of CD?
What part of this half is H? What part is G?
What part of the whole rectangle is H? Then may we
find i of a thing by dividing half of it into 2 equal parts?
One-fourth is what part of a half? How many fourths
are equal to a half?
What is 2 times i? 3 times i? 4 times i?
How many times must I take i to make f ?
What part of E are G and H together?
One-half of A is how many times i of it?
What part of A is* B + O + M?
How many fourths of E is ^ of it + i of it?
V
r^
H
308. This rectangle is divided into equal parts.
Point out i of it. | of it. | of it.
»i4
210
SCHOOL AMTHMETIC.
How many eighths of it are dark? How many are light?
How many fourths of it are dark? How many are light?
One-eight is what part of a fourth? How many eighths
are equal to i? Tof? To|?
How is i obtained from i?
What is 2 times i? 3 times i? 4 times i? 6 times i?
How many eighths are there in the rectangle? How
many have letters? How many have none? f — f =
How many fourths of the rectangle have letters? These
3 fourths are equal to how many eighths? i = ^?
What part of the whole rectangle isH + A + E + F?
How many fourths? How many eighths? f = ^.
Show that i of the rectangle = f or f of it.
What part of the rectangle is O? What part is D?
What part is + D?
What is i of i? i is equal to how many eighths? f ? f '
How many eighths of the rectangle is i of it + i of it?
Six quarters are worth how many half dollars? ^ are
equal to how many halves?
'■'a
c
D
..
i \^
1
12
L.: ■ • ^^ :"^/^.-&^
309. What part of the circle is shaded? How many
thirds of it are not shaded?
The dotted line divides one of the thirds into 2 equal
parts. What is each part called?
COMMON FKAOnONS.
211
One-sixth is what part of on^third? How many sixths
are equal to J? To f ? To|?
What part of the circle is below EH? Above EH?
Then which is larger, i of the circle or ^ of it? How
much larger?
How many times must I take i of the circle to make
f of it? To make the whole circle?
What part of the rectangle isA + B + + D? 'Then
C + D is what part?
What part of the rectangle is D? Then + D = how
many twelfths? i of 3^ (or |) = ^.
How many -^^^'s are there in the rectangle ? In ^ of the
rectangle ? ^ = j^.
What part of the rectangle is A + O + R?
Which is larger, i of the rectangle or i of it? Show
how much larger.
How many ^'s of the rectangle = ^ of it + |- of it ?
Find how many -j^'s of the rectangle are equal to § of
it. To J of it.
Find how much larger i of the rectangle is than i of it.
310. Copy and complete:
i= T
1 -_
T — IT
1 _
r — TY
311. What part of this rectangle
is dark ? How many fifths are light ?
How many tenths of the rectangle
make i of it?
One-half of the dark portion is what part of the whole
figure? i of i =
i= T
i=TT
1= T
i= T
i=TT
*= T
i = TT
l=TT
i= T
i=TT
f =TT
f = TT
1 fmm^
B
C
^j^m
E
D
212 SCHOOL ABITHMETIO.
What part of the figure is on each side of AH?
Show how many tenths of the rectangle make ^ of it.
What part of the figure is E+B+C?
If D were removed, what part of the whole would
remain?
How many times C+D make up the figure? How many
times i = 1 ?
How many fifths of a nickel make a dime (two nickels) ?
How many J's in 2?
Point out i of half the rectangle. It is what part of
the whole? i of ^ =
B+C+D+E = how many i's of the figure? How
many-^'s? | = yir-
How many -^'s make f ? |? |? |?
How many -j^^'s of the rectangle = |- of it + iV ^^ ^* •
Which is larger, f of the rectangle or ^ of it? How
much larger?
Draw a 10-inch square and divide it into square inches.
Each small square is what part of the whole?
How many hundredths in the upper row? Then how
many hundredths make 1 tenth?
Find how many hundredths make -^5 or |. -j^, or i.
One-tenth is how many times as much as one-hundredth?
Find how many hundredths in i of the large square.
In f of it.
One-hundredth is what part of 1 tenth?
Point out ^ of one-tenth of the large square, and tell
what it is called.
Complete: i=:f =^ =-g- =-nr =1^ =-nnr
Complete: l=f =^ =^ =^ =t7j- = t^ =nnr
COMMON FEA0TION8.
213
1
'i.
h = fe - f tf = jsf
312. A, B, C, and D are equal squares. What part of
each is dark? Are the dark parts equal?
Into how many equal parts is B divided? How many
of the dark parts are equal to the dark part of A? Then
how do ^ and i compare in size?
How does i of A compare in size with f of C? Then
what can you say of i and f ?
Compare ^ oi A with ^ of D, and state what you learn.
Are 2 of the equal parts of B equal to 4 of the equal
parts of D ? Is i greater than | ? Is f ?
Arrange the fractions ^^ f , f , and ^ in six groups of two
fractions each. Compare each two, and tell what you learn.
In the fractions ^ and 1^, what does the 2 show ? The 1 ?
The 8? The 4?
In the fraction f , which figure indicates the number
of equal parts into which a whole is divided? What shows
us how many of the parts are taken?
The number helow the line of a fraction shows into how
many equal parts anything is divided. It is called the
Denominator.
The number above the line shows how many of the parts
are taken. It is called the Numerator.
In t of the rectangle, what does the 8 show? The 5?
Draw on the board a line 4 ft. long. Measure it with
your foot rule, which is i yd. in length. The line is how
many thirds of a yard long?
214 SCHOOL AEITHMETIO;
What does the 3 show? What does the 4 show?
Give the meaning of the numerator and of the denomi-
nator in }. In f . in. In f yd. In i.
313. What is the sum of a quarter and a half dollar?
The half-dollar = 2 quarters. 2 quarters + 1 quarter = 3 quarters.
What is the sum of i bu. and a peck?
Add i gal. and i gal. i + i = :f .
Can you add halves and fourths without changing the
halves to fourths?
Use your foot-rule to find the sum of i in. and i in.
To find the sum of i in. and i in.
T + i^'S'' "i+-s- = -s"'
What must be done with i before it can be added to
i? Withi?
Only like numbers can he added. Fractions to he added
must have the same denominator.
314. With a foot-rule complete:
iin.-f|in.=^in. i^in.+|in. =r^in. |in.+f in.=-g-in.
^in.4-|-in.=^in. |in.+^in.=r^in. |in.-f-iin.=^in.
|in.+iin.=:^in. ^in.-f |in. =^in. f in.+|in. =^in.
When one fraction is to he subtracted from another, hoth
must have the same denominator.
I^in. — ^in. =^in. |in. — |-in. =-g^in. fin. — ^in.^^in.
I^in. — ^in.=-g^in. -|in. — |^in.=^in. 1 in. — f in.=^in.
I^in. — -|^ in. = -g^ in. 1 in. — |^in. =^in. fin. — l-in. =-g-in.
1 in. — fin. =:j-in. |^in. — f in.=^in. -|^in. — f in.=-jin.
OOHHON FBAOnOKS. 215
316. Find the value of:
i + i l + l + i i-l l+i- + i
l + i i + i- + i 1-1 i + i + l
k + i f + i + ^ l-i l + l-i
l + i l + i + l i-i 4 + i-i
f+f i+i+i' i-4 i+i-i
l + i i + i- + i f-l l + l-i
316. Copy and complete:
2 times i = | or i. 3 X | = ^ ^r y.
2 times f = ^ or ^. 2 X | = -y or ^.
2 times ^ = ^ or ^. 4 X f = -g^ or ^.
2 times f = ^ or ^. 8 X ^ = Y ^^
4 times J = ^or 8x1 = :^ or
317. How many ^'s = |^? How many ^'s = ^?
|- = how many times ^ ? |- = how many times \ ?
How many times is 1 ft. contained in 3 ft ?
3 ft. -f- 1 ft. = . 3 fourths -f- 1 fourth =
6 yd. -r- 2 yd. = times. |^ -r- |^ = times.
i of 2 qt. = qt. ^ of I = :j:.
^ of 3 ft. = ft. I of I = ^.
i is contained in i times.
i is contained in i — — times.
i is contained in i how many times?
i is contained in f how many times?
f is contained in i how many times?
f is contained in i how many times?
i is contained in 1 how many times?
i is contained in 2 how many times?
216 SCHOOL ARITHMETIC.
How many i's are there inl? In2? In 5?
How many i's are there in 2? In 5? In 12?
How many i's are there in 1? In 2? In 3?
How many eighths of an inch in 4 inches? In 12 inches ?
318. Complete and read:
1 in. + ^ in. = li in. (one and one-haK inches), or
I in.
2 in. + i in. = 3 in. + f in. =
1 in. + i in. = 1 hr. + f hr. =
5 in. + f in. = 4 gal. + i gal. =
319. In li gal. how many fourths? How many quarts?
In 2i bu. how many halves? How many pecks?
In li in. how many eighths? In 2i inches?
In $3f how many fourths, or quarters?
In 2^ yd. how many halves? How many fourths?
Change to fourths:
• i H 4i I 1| V
n H ^. i ^i ^
Six half -inches = how many inches?
Twelve quarter-inches = how many inches?
Three half inches = how many inches and half -inches?
How many inches in f in.? In | in.? In ^ in.?
How many inches and half -inches in f in.? In ^ in.?
320. 1. If a horse eats three times a day^ and eats
i pk. of oats at a time, how many half-pecks will he eat
in 6 days? How many pecks? How many bushels?
2. When milk is 3^ a pint, how much must be paid
for li quarts?
COMMON FRACTIONS.
217
3. If i of a yard of cloth costs 24^, what does i of a
yard cost?
4. How many sheets of paper at i^ apiece can you
buy for 5^?
5. If f of a yard of ribbon costs 18^, what is the cost
of i of a yard? Of i of a yard?
6. Tom earned i of a dollar on Monday and f of a
dollar on Tuesday. How much did he earn?
7. A box is I yd. long and ^ yd. wide. By how much
does the length exceed the width?
8. Each side of a square is f ft. long. What is the
perimeter?
9. A lady who had f of a gallon of milk sold a quart
to a neighbor. What part of a gallon had she left?
10. A man who had $40 spent $10. What part of his
money had he left?
11. Tillie had f of a yard of velvet and gave Nell i
of it. What part of a yard had Tillie left?
12. Draw a rectangle 12 in. long and i as wide. How
many square inches in i of it? In f of it?
Common Denominator.
A B C
321. How many i's are equal to i? Then i is how
many times ^?
Multiply numerator and denominator of i by 2. What
is the result?
When i is changed to |, how is the size of the parts
changed? Are more of them taken?
218 SCHOOL ABITHMBTIO.
By what must numerator and denominator of i be
multiplied to change it to -| ?
The part on the left of OD is how many times as large
as one of the parts on the right?
The number of parts on the right of CD is times
the number of parts on the left.
Multiply numerator and denominator of i by 3, and
explain the result.
Divide numerator and denominator of f by 4. Is the
result equal to |^ ?
By what must you divide numerator and denominator
of ^ to ciiange it to i?
Show that the following is true:
If both numerator a/nd denominator of a fraction are
multiplied, or divided, by the same number, the value of
the fraction is not changed.
322. Change i, 'i, and f to 12ths.
Both numerator and denominator of i must be multi-
plied by 12 -^ 2, or 6.
Both numerator and denominator of S must be multi-
plied by 12-^3, or 4.
By what must both numerator and denominator of f be
multiplied?
Change:
1. i, i, and | to 12th8.
2. i, f 5 and ^ to Sths.
a! h h and ^ to lOths.
4. h h I, andf tol2th8.
5. h h i, and^to20th8.
6. h h h ^^^ iV to 40th8.
7. 8, ^, I, and ^ to lOOths.
8. f, A. H. a^d il to 4th8.
COMMON FEACTI0N8. 219
323. Change to smaller denominators:
9 3 4 6 4 19 6 16 12 10
• ^5 ?? TIT? TT J-^' TT9 "5T5 TT? "2T
10. ^5 -f, TIT? T2 13. if 5 H, H, tA
11 2 8 10 12 1^ 26 10 50 76
15. In 3^2^ of a dozen liow many half dozen ?
16. In f of a dozen how many ^'s of a dozen?
17. In ^ of a dozen how many ^^'s of a dozen?
18. How many more oranges are ^ of a dozen than ^ of
a dozen ? What part of a dozen more ?
19. How many 12th8 of a foot (inches) in ^ foot? In
I foot?
20. In 1^ yards how many thirds ? How many feet ?
21. How many yards in |^ yd. ? How many feet ?
22. How many ones are equal to f ? -^^ ? |-| ?
23. How many ones and thirds in |^ ? In |^ ? ^ ?
24. In f how many fourths ? In |^ how many halves ?
25. Change 1^ bu. and i bu. to pecks, or fourths (of a
bushel).
Addition and Subtraction.
324. Fractions that have a common denominator are
called Similar fractions. Only similar fractions can be
added or subtracted. Change to similar fractions and add
or subtract as indicated:
1.
i+i = ir
9.
I+T2- TS
17.
i
-i = ir
2.
t+i = ir
10.
i+^=T^
18.
1
-i = Tr
3.
*+| = ir
11.
i+TV=T^
19.
*
-i = 7r
4.
i+i = Tr
12.
l+TSr=TT
20.
i
— T^=TJ
5.
4+|-ir
13.
H-A=TT
21.
1
— tV=T7
6.
i+*=?^
14.
i+A=TT
22.
1
— TV=nr
7.
i+TV=TT
16.
i+l=TT
23.
tV
— i =TT
8.
l+T^ = TT
16.
i+TV=TT
24.
i
1T=TT
220
SCHOOL AMTHMETIO.
Find the value of:
25.
i + i
30.
i+i+iV
35.
i -tV
26.
i+iV
31.
f+l+i
36.
A-l
27.
f+i
32.
f+l+i
37.
i - i
28.
A+4
33.
i+*+ 1
38.
i — i
29.
i + i
34.
A+i+^
39.
i^-A
In the following exercises add the integers and frac-
tions separately, and then add the results:
40.
H
+ 7f
45.
6i + 2|
+ H
41.
H
+ 51
46.
n + H
+ 4A
42.
n
+ 3i
47.
8i + 7^ + 12t^
43.
If
+ 4f
48.
2| + 5^3, + 24^
44.
8A
+ 5i
49.
lOi + 9|
+ 26,2ii^„
50. Subtract 2| from 5i.
5i
2|
2f
= 5^
= 2^
=
^' ■ The fractions are first made similar. We can-
^~i not take } from f , so we take 1 one, or f , from
the 5 ones, and add it to the |. We then take |
^f from f , and 2 from 4.
f
Subtract:
51.
1\ from 10^
56. 124
from 16^
52.
3f
from
64
57. 224
from 30|
53.
5|
from
n
58. 31|
from 42:J-
54.
2*
from
n
59. 16Jir
from 20|
55.
4|
from
8A
60. 37T§i/V
from 62y8^
2
X
tV = T7 or ^
3
X
iV = TT or T
4
X
tV = T7 or ^
COMMON FRACTIONS. 221
Multiplication and Division.
325. Complete:
3 times ^ = ^ or ^
2 times ^ = ^ or ^
2 times |- = ^ or ^
3 times f=-g-or <>XiV = TT^rt
3 times ^ = ^or ^X^V^tt^^^
4 times |=^or 9XiT2- = y7or^
6 times ^ = ^or 6Xi^ = T2'^^
326. How many ^'s = ^? How many ^'s = ^?
1^ = how many times ^ ? ^ = how many -^'s ? ^'s ?
How many times is ^ contained in |^, or ^ ?
3 sixths -4- 1 sixth = times. |^ -f- ^ = times.
^ is contained in ^ times, i -r- ^ =
^ is contained in 1 times. 1 -r- ^ ^
3^ is contained in ^ times, -g- -i- tt ^"
-j^ is contained in ^ times, i -^ -o^ =
^ of 2 sixths = ^. i of |- =y.
i of i = 7- i of -^ = ^ or Y.
i of f = Y. I of ^ = 3^ or ^.
How many ^'s are there inl? In 2? In 4?
How many |-'s are there in 1 ? In 2 ? In 5 ?
How many ^'s are there in 1 ? In 2 ? In 3 ?
How many ^'s of a foot in 2 inches ? In 6 inches ?
Four inches is what part of a foot ?
How many inches = f of a foot ? f of a foot ?
222
SCHOOL ABITHMETIO.
I
6
^
Wi
i
B
I
D
327. If each third of A is divided into 2 equal parts,
as in B, how many parts will there be?
What is each part of B called? ^ of i =^.
How many fifths of E are there to the left of CD?
How many thirds of this part of E are dark?
How many fifteenths of E are dark ?
Then§off = T7- fXf = .
In finding f of S how was the 15 obtained? How was
the numerator obtained?
To multiply one fraction by another —
We take the product of the numerators for the required
numerator, and of the denominators for the denominator.
Find the product of:
1.
2.
3.
4.
5.
6.
IX f
|x i
|x f
ix|
IX i
7.
8.
9.
10.
11.
12.
i X I X I
ix l-x f
I X i X I
4 X f X i
^ X i^ X X
2 X :;■ XyT7
13.
14.
15.
16.
17.
ix
f X
IX
ix
3
S
7
18. AX
xU
i
COMMON FRACTIONS.
223
19. Multiply 3i by 6.
H
6
18 =
6
X 3
3 =
6
xi
We multiply the integral part, then the
fractional, and add the results.
21 = 6 X 3i .
Find the products:
20.
21.
22.
23.
24.
6 X 4i
9 X 2^
5 X 7|
*X 3|
3 X 9|
25.
26.
27.
28.
29.
7 X 6f
4 X 5|
8 X 3|
6X 4|
9X7^
30. 4 X 12i
31. 6 X 37i
32. 6 X 16|
33. 3 X 33i
34. 8 X 62i
328. 1. Divide 4 ft. by 2 ft. 4 thirds by 2 thirds.
2. Find ^ of 4 thirds. | ^ 2 = f .
3. How many f 's in f ? | ^ f = times.
Find the quotients:
4.
5.
6.
7.
8.
i H-2
4 -- 3
5
5 — *
8-2-9!
S
TTT
9.
10.
11.
12.
13.
2
I
8
1
T
2
s
4
•3"
14- i
15. i
16. i
17. i
18. I
1
TIT
1
TIT
2
TIT
1
T
2
"5-
19. Write these fractions in a line, placing the largest
first, the next largest second, and so on: i, i, i, i, ^,
T? T12") T5 fj f) TirU'*
224 SCHOOL ABITHMETIC.
■
329. How many sixths of A are shaded? How many
times is f contained in A ? Can you find out by inverting |^ ?
Find how many times A contains ^ (the light part).
What does A contain 6 times ? What does it contain f ,
or 2 times ?
B contains ^ how many times ? Can you tell by invert-
Invert |^ and show how many times it is contained in the
whole of B.
In B, 1^ is contained 2^ times, or f times.
Can we find how many times a fraction is contained in a
whole or 1 by inverting the fraction ?
Find how many times 1 contains i, i, i, f , -j^, f .
One-half is contained in one 2 times; in four it is con-
tained times.
How many times is i contained inl? In2? In 5?
Ini?
To divide by a fraction —
Multiply the iwverted divisor hy the dividend,
330. 1. Divide 4 by f .
f = the number of J's in 1.
4 X f = -/> or 6, the number of §*s in 4.
Divide:
2.
5 by i
8.
6 by 1
14.
10 by %
3.
3by i
9.
2 by 1
16.
3 by ^
4.
6 by i
10.
5 by f
16.
2 by 4
5.
4by i
11.
8 by 1
17.
5 by A
6.
7 by i
12.
3 by i
18.
4by 1
7.
Sby^V
13.
4byT^
19.
Sby^V
COMMON FRACTIONS.
225
20. Divide f by f .
Inverted divisor f = the number of S's in 1.
J X I = f > or IJ, the number of f's in f .
Find the quotients:
21.
22.
23.
24.
f-i
1
1
25.
26.
27.
28.
i^
2
3
T
4
1
TTT
1
T
1
¥
2
29.
30.
31.
32.
5
5
I
4
2
3
331. 1. Ella picked i gal. berries and Nora picked f
gal. They both picked gal.
2. What is the difference between i of an hour and
i of an hour?
3. How much will 3^ quarts of milk cost, if 1 pint
is worth 3 cents?
4. If carpet is f yd. wide, how wide a room will 6
widths cover?
5. If i of a yard of ribbon costs 2^, how many yards
can you buy for 32 cents?
6. If I had 1^ of a yard of ribbon, and used i of a yard,
what part of a yard have I left?
7. At Yir of a dollar a peck, how many pecks of apples
can be bought for $f ? For $1?
8. If a boy earns $f a day, in 12 days he will earn
9. How many 12's of a foot are equal to a yard?
10. At i of a dollar a pound, how many pounds of
coffee can I buy for $1? For $5?
11. James sold 2 bushels of apples at 10^ a half -peck.
How much did he get for them?
*i5
226 SCHOOL AKITHMETIC.
12. 4 horses are i of horses. (Show by dots.)
13. One-third of 12 sheep is sheep, f of 12
sheep are sheep.
14. 8 quarts are f of how many quarts? (Show by
dots or squares.)
15. Bell bought a book for 10^, which was i of her
money. How much had she?
16. There are 36 gallons of cider in a barrel which is
f full. How many gallons will the barrel hold?
17. A 3-gallon pail was full of water, but 2 quarts were
taken out. What part of the water was taken out? What
part was left?
18. If f of a yard of cloth cost 15^, what is the cost of
i of a yard? Of 1 yard? Of 2 yards?
19. If y\ of the cost of a wagon was $12, what was
the entire cost?
20. If ^ bu. of corn is worth 20^, what is the value of
2 bushels? Of2ibu.?
21. Adam's house is f of a mile south of the school-
house, and Dick's is f of a mile north. How far apart do
the boys live?
22. In a school of 48 scholars f are girls. How many
boys are there?
23. If -J lb. of coffee costs $.15, what will 2 pounds
cost?
24. How many pieces of velvet, each half a yard long,
can be cut from a piece 9i yards long?
28. I have a jointed fishing rod in 3 parts. One part
is 2-J feet long, another 2| feet, and the other 3f feet.
How long is the rod?
26. f of the days in April are how many days?
RELATIONS RATIO. 227
27. From a piece of ribbon | ft. long a piece -f^ ft.
long was cut off. Show the length of the remainder.
28. A rectangle is i ft. long and i ft. wide. What is
the perimeter? How many square inches does it contain?
29. A box is li ft. long and f ft. wide. Find how
many square inches in the lid.
30. A lady bought 3i yd. of ribbon, and divided it
equally among 5 girls. What part of a yard did each girl
get? (3iyd. ^5 = -i/yd. - 5).
31. Draw an 8-inch square. In it draw a square i
as large. How many square inches between the two
perimeters?
Relations— Ratio.
332. 1. One line is 12 ft. long, another is 3 ft. long.
Compare their lengths.
(a) The 3-ft. line must be taken (repeated) times to make
up the 12-ft. line.
(6) The 12-ft. line is times as long as the 3-ft. line.
(c) The 12-ft. line is composed of 3-ft. lines.
{d) The 3-ft. line is one — — as long as the 12-ft. line.
By comparing or measuring we find the answers required. When
we know the answers to a and 6, we know the relation {ratio) of 12
ft. to 3 ft. The ratio is 4.
When we know the answers to c and d, we know the ratio of 3 ft.
to 12 ft. It is J.
2. One package weighs 2 lb., another 8 lb. Make four
statements similar to the four above, and find the ratio of
each weight to the other.
3. Measure your foot-rule with a 4-inch unit. Tell
what you can about the ratios.
4. Find the ratio of your foot-rule to a 6-inch unit.
A 2-inch unit. A 1-inch unit.
228 SCHOOL AKITHMETIO.
5. What is the ratio of the 6-iiich unit to the foot-rule?
Of the 2-iiich unit? The 1-inch unit?
6. Find two ratios by comparing a yardstick and a
foot-rule.
7. What two ratios can be found by comparing a
gallon and a quart?
8. Draw a 2-in. square and a
4-in. square. Divide them into
Btjuare inches, and find the ratio of
eacli to tlie other.
9. What is the ratio of a dollar
to a dime? Of a dime to a dollar?
10. Ten is how many times 2? Then what is the ratio
of 10 to 2? Of 2 to 10?
11. How many times must one be taken to make ten?
Then the ratio of 10 to 1 is , and the ratio of 1 to
10 is .
12. The ratio of 10^ to ^ is 2. The ratio of ^
to 10^ is i.
13. A man counting a roll of 5-dollar bills says, $5,
$10, $15, $20. How many equal parts make up his $20?
How many times must one of the parts be taken to equal
his $20? What is the ratio of $20 to $5? Of $5 to $20?
14. $50 is how many times $10? That is, what is the
ratio of $50 to $10?
15. Four feet is what part of 20 feet? That is, what
is the ratio of 4 ft. to 20 ft?
16. Five inches is one-half of what? That is, the ratio
of 5 in. to in. is -J.
17. Thirty dollars is five times what? That is, the
ratio of $30 to $ is 6.
RELATIONS RATIO. 229
. 18. What is the ratio of i (f) to | ? Of i to | ? Of
■|- to ^ ? Show by drawing.
19. Find the ratio of 24 to 8. Of 42 to 6.
20. By what process do you find the ratio of one num-
ber to another? (See Division.)
21. Select any number you please, and state its ratio
to one. To two.
333.
ARTICLE COST ARTICLE COST
1 apple 2 cents 2 apples 5 cents
. 5 apples 10 cents 8 apples 20 cents
Five apples are how many times 1 apple? Then they
will cost how many times as much? Point out two ratios
that are equal. Eight apples are how many times 2 apples?
How many times as much will they cost? Point out the
ratios.
1. At 3^ each, what will be the cost of a dozen oranges?
. 2. When lemons are selling at the rate of 3 for 5^,
what will a dozen cost?
3. If 11 lb. of sugar cost 50^, what will 22 lb. cost?
4. When you can buy 3 handkerchiefs for 25^, how
many can you buy for $1 ?
5. A lady paid 30^ for a dozen eggs. How much would
4 eggs cost at that rate?
6. A boy running takes 3 steps every 10 ft. How
many steps does he take in running 100 ft.?
7. A man earns $21 every two weeks. How much
does he earn in six weeks?
8. How much do I gain by buying 10 pigs at $2 each,
and selling them at $3 each?
(a) How much do I gain on 1 pig? On 10 ?
(b) How much do I pay for the 10 pigs? How much do I get
for them ? Then how much do I gain ?
230 SCHOOL AKITHMETIO.
9. If 5 apples cost 10 cents, what is the cost of 1 apple? .
10. If 4 sheep are worth $20, what are 3 sheep worth ?
11. A girl bought 3 pairs of shoes for $6. At the
same rate, what would 5 pairs cost?
12. Draw two lines showing the ratios 4 and i.
13. What is the ratio of a rectangle 4 in. by 5 in. to
one 2 in. by 5 in. ?
Review.
334. 1. Find the cost of a ton of hay, when f of a
ton costs $6.
2. 9 is f of what number?
3. 15 is y of what number?
4. 14 is ^ of what number?
5. 20 is t of what number?
6. 3i is f of what number?
7. If S of a yard of satin costs 80^, what is the cost
of one yard? Of 5 yards?
8. If f of a ton of coal occupies 24 cubic feet, how
many cubic feet will 1 ton occupy?
9. If f of a barrel of fish cost $10, what will 1 barrel
cost?
10. What is the price of a dozen, when f of a dozen
oranges sell for 20^?
11. 2 times f are how many fourths?
12. ^ of 18 is i of what number?
13. If f of a pound of rice costs 6 cents, what will 5
pounds cost?
14. What is the cost of 6^ gallons of molasses at $.40
a gallon?
15. A woman has 15 yards of muslin. How much will
she have after she uses 14f yards?
16. What is the cost of f of a pound of candy at 15^
a pound?
REVIEW. 231
17. What will 15^ dozen eggs cost at 20^ a dozen?
18. A boy after selling ^ and i of his marbles had 12
marbles left. How many had he at first?
19. A boy has i of a peck of nuts. If he gives away
I of them, what part of a peck will he have left?
20. If ^ of an ounce of tea costs 5^, what will 1 pound
cost?
21. Four fifths of 20 is y of what nimiber?
22. If I can buy 7 pencils for ^ir of a dollar, how many
can I buy for -^ oi a. dollar?
23. If ^ of a cord of wood is sold for $4, what will 5
cords bring?
24. If f of a barrel of sugar costs $12, what will f
of a barrel cost?
28. If yi^ of a lot of goods is worth $360, what is i
of the lot worth?
26. $40 is equal to i of my house rent for 1 year. How
much do I pay a month?
27. If ^ of a ton of coal lasts 2 days, how long will i
of a ton lafit?
28. What will ^ of a pound of tea cost at i of a dollar
a pound?
29. At i of a dollar a bushel, how many bushels of
apples can be bought for 10 dollars?
30. One third of a pole is blue, ^ of it is red, and the
rest is white. What part of the pole is white?
31. If 5i pounds of nuts are divided equally ainong
7 boys, what part of a pound will each boy receive?
32. When a furnace consumes coal at the rate of i of
a ton a day, how much will it consume in 4|^ weeks?
33. When f of a yard of ribbon is put into a loop, how
many loops can be made from 3 yards?
34. At f of a cent a square foot, what will it cost to
paint a blackboard 24 feet long and 4^ feet wide?
COMPOUND NUMBERS. 233
COMPOUND NUMBERS.
Liquid Measure.
335. Liquid Measure is used in measuring liquids, as
water, milk, etc.
n 1
Pint Quart Gallon
2 pints (pt.) = 1 quart (qt.).
4 quarts = 1 gallon (gal.).
1. How many pints are there in 3 qt.? In 5 qt.?
2. How many quarts are there in 3 ^al. ? In 10 gal. ?
3. How many pints in 5 gal. 3 qt. and 1 pt.?
5 gal. = 6 X 4 qt., or 20 qt. ; 20 qt. + 3 qt. = 23 qt.
23. qt. = 23 X 2 pt., or 46 pt.; 46 pt. -f 1 pt. = 47 pt.
4. How many pints in 4 gal. 2 qt. 1 pt.?
5. How many gallons are there in 24 qt. ? In 40 qt. ?
6. How many quarts are there in 12 pt.? In 16 pt.?
7. How many gallons are there in 110 pints?
1 pt. = J of a qt., and 110 pt. = 110 X J qt., or 55 qt.
1 qt. — I of a gal., and 65 qt. = 55 X t gal., or 13 gal. and 3 qt.
8. How many gallons in 129 pints?
9. How many pints in 1 gal. ? ^\ gal. ?
10. How many galloiis/in 40 quarts? In 75 qt.?
336. 1. How many quart jars will hold 2i gallons
of milk?
2. How many half -pint bottles can you fill with a
gallon of olive oil?
234 SCHOOL ARITHMETIC.
3. A milkman sold 18 gal. of milk at 6^ a quart. How
much did he get for it?
4. At 10^ a pint, how much syrup can be bought for
$3.60?
5. How many pint bottles will hold 2 gal. 1 qt. of oil?
6. If a gallon of molasses costs 80^, how much will 6
pints cost?
7. A man bought 2 cans of mineral water, each con-
taining a gallon and a half. The price was 20^ a gallon.
How much did he pay?
8. There are 231 cu. in. in a gallon. How many cubic
inches in a quart?
9. A lady sold 2 gal. 3 qt. 1 pt. of vinegar at 6^ a
quart. How much did she get for it?
10. A man paid 52^ for 1 gal. 2 qt. 1 pt. of milk. He
paid f^ a quart.
11. If a family pays 8^ a quart for milk and uses 3
pt. a day, what is the milk bill for the month of March?
12. If a barrel holds 31^ gallons, and a hogshead holds
twice as much, what does a hogshead hold?
Dry Measure.
337. D^y Measure is used in measuring^ dry articles,
as grain, seeds, fruit, vegetables.
lyi
Pint Quart Peck Bushel
2 pints (pt.) = 1 quart (qt.).
8 quarts = 1 peck (pk.).
4 pecks = 1 bushel (bu.).
COMPOUND NUMBERS. 236
1. How many pints in 3 qt.? In 5 qt.?
2. How many qt. in 4 pk.? In 5 pk.?
^ How many pk. in 3 bu.? In 7 bu.?
How many quarts in -5 bu. 3 pk. 4 qt. ?
How many pecks in 8 bu. 3 pk.?
How many pecks in 32 qt.? In 20 qt.?
-. How many bushels in 4096 pints?
8. How many pecks in ^ bu.? In i bu.?
9. In 32i pecks how many bushels?
iO. In 784 quarts how many bushels?
2.
3.
4.
8.
6.
7.
10.
338. 1. When potatoes are worth 80^ a bushel, what
is i peck worth?
2. If apples are selling at 10^ a quarter-peck, how
much will a bushel cost?
3. A boy sold i bu. of berries at 5^ a quart. He
received f^ for them.
4. Two bushels of cherries were divided equally among
4 persons. How many quarts did each receive?
5. A man bought 5 bu. 3 pk. of corn at 40f^ a bushel.
How much did it cost him?
6. How many peck baskets can you fill with 64 qt.
of onions?
7. A woman bought 2 bu. 1 pk. 3 qt. of strawberries
at 5^ a quart. She paid for them with a $5-bill, and got
$ in change.
8. How many pint packages can a seedsman make
from 2 bu. 2 pk. and 2 qt. of seeds?
9. A grocer bought 10|^ bu. of apples at 60^ a bushel,
and sold them at 10^ a half -peck. What was his profit
on them ?
236
SCHOOL ARITHMETIO.
Avoirdupois Weight.
339, Avoirdupois Weight is used in weighing all com-
mon articles.
16 ounces (oz.) = 1 pound (lb.).
2000 pounds = 1 ton (T.).
1. How many ounces in 4 lb.? In 2^ lb.?
2. In 2 lb. 8 oz. how many ounces?
3. What part of a pound are 4 oz.? 10 oz.?
4. How many poimds in 160 ounces? In 336 oz.?
5. What part of a ton is 500 lb.? 200 lb.?
6. A barrel of flour weighs 196 lb. What is the
weight of a sack of flour containing i of a barrel?
7. A bushel of wheat weighs 60 lb. What does a peck
weigh?
8. From a firkin of butter containing 42 lb. a grocer
sold 13 lb. 10 oz. How much was left?
We cannot take 10 oz. from
oz , so we take 1 lb. from the
42 lb. and change it to ounces.
Then 16 oz. — 10 oz. =6 oz.,
28 6 28 6 and 41 lb. — 13 lb. = 28 lb.
9. A butcher sold 24 lb. 12 oz. of lard from a can
containing 40 lb. How much was left?
10. One crock of butter weighed 8 lb. 10 oz., and
another 9 lb. 14 oz. How much did both weigh?
340. 1. Find the cost of 3i lb. of cheese at 12^ a
pound.
2. What will 3 lb. 8 oz. of butter cost at 20^ a pound?
lb.
oz.
lb.
oz.
42
=:
41
16
13
10
=:
13
10
COMPOUND NUMBERS. 237
3. How many ImadiiBd pounds make a ton?
4. If hay is worth $20 a ton, what is 100 lb. worth?
5. A bushel of wheat weighs 60 lb. How many bushels
in a bag weighing 120 lb.?
6. A bin contains 6^ bu. of wheat. What is the weight
of the wheat?
7. Three boys bought 2 lb. 4 oz. of candy. Each paid
16^. How many ounces should each one receive?
8. If a man eats 3 8-oimce loaves of bread in one day,
how many pounds will he eat in one week?
9. A bushel of oats weighs 32 lb. Find the weight of
2 bu. 2 pk.
10. A sack of oats weighs 96 lb. What is it worth
at 30^ a bushel?
11. At $4 a ton, how much coal can be bought for $25 ?
12. What is the value, at $2 a ton, of 7000 lb. of coal?
Time Measure.
341. Time Measure is used in measuring duration.
60 seconds (sec.) = 1 minute (min.).
60 miQutes = 1 hour (hr.).
24 hours = 1 day (da.).
7 days = 1 week (wk.). •
365 days = 1 year (yr.).
12 months (mo.) = 1 year.
238 SCHOOL ARITHMETIC.
1. How many seconds are *there in 5 min.? In
10 min.?
2. How many hours are there in 2 da.? In i da.?
3. How many days are there in 2 weeks? In 4 wk?
4. How many days are there in 4 wk. 3 da.?
5. How many hours in 240 min.? In 180 min.?
6. 100 years make 1 century. How many centuries
in 1900 yr.?
7. In 1^ hr. how many minutes?
8. What part of a day is 6 hours? 16 hours?
9. How many days in this month? How many wee'ks?
342. 1. How many days in 52 weeks? Then .a year
is how much longer than 52 weeks?
2. How long is it from Christmas to New Teax's Day?
3. How many months is it from one Christmas to
another?
4. How many years and months have you lived?
5. How many weeks and days in May?
6. How many times does the clock strike 12 every day?
7. When we have daylight 14 hours, how long is the
night?
8. How many centuries are there between 1300 and
1900?
9. If you go to bed at 9 o'clock at night and get up at
6 in the morning, how long are you in bed?
10. Eight hours is what part of a day? 16 hr.?
11. Cousin Fred came to our house on Monday and
stayed 2 weeks. On what day did he start home?
12. If a train runs 30 miles an hour, how far does it
run in 2 hours and a half?
13. How many times does the second hand of a watch
go around while the minute hand goes once around?
COMPOUND NUMBERS. 239
14. While the hour hand goes once around, the minute
hand goes around times.
15. How often does the hour hand go aroimd in a day?
The minute hand?
16. How many minutes in J of an hour?
17. Are the two hands of a clock together 12 times or
13 times in 12 hours?
18. If a boy saves 10^ a day, how much will he save
in a year?
19. If a man earns $30 a month, how much does he
earn in a year?
20. A girl walked i mile and back in 20 minutes.
How far would she walk in an hour at that rate?
21. How many days is it from October 24 to November
3? From Dec. 25 to Jan. 10?
22. If a man gets $2 for working 8 hours, how much
should he get for 44 hours?
23. If a horse can trot a mile in 3 minutes, how far
can he trot in an hour?
24. If a boy walks 3 miles an hour, how far does he
walk in 4 hr. 40 min.?
Long Measure.
343. Long Measure is used in measuring lines and
distances.
8
Id II 12
12 inches (iq.) = 1 foot (ft.).
3 feet = 1 yard (yd.).
H yards ) - 1 rod Trd ^
leifeet ] - iroa (^ra.).
320 rods = 1 mile (mi.).
240 SCHOOL ARITHMETIC.
How many feet are there in 5 yards? In ^ of a yard?
In 6i yards?
A distance of 5^ yards is called a rod. How many feet
in a rod?
A barn 4 rods long is how many yards in length? How
many feet?
How many rods long is your schoolroom? Find by
measuring.
Find the perimeter of a field 32 rods long and 25 rods
wide.
Name a place about a mile from your home. One about
2 miles. One about half a mile.
A distance of 320 rods is called a mile. How many rods
in i of a mile?
In i of a mile there are rods; in J of a mile there
are rods.
What part of a mile is 160 rods? 80 rods?
Complete:
1. 1 rd. 2 yd. = yd. 6. 1 mi. 40 rd. = rd.
2. 3 ft. 2 in. = in. 7. 6 yd. 2 ft. = ft.
3. 2 yd. 1 ft. = ft. 8. 1 rd. 8 ft. = ft.
4. 1 yd. 4 in. = in. 9. 1 mi. 80 rd. = mi.
6. 2 rd. 2 ft. = ft. 10. 1 yd. 1 ft. 1 in. = in.
344. If you walk 20 rd. a minute, how long will it
take you to walk a mile?
What is the perimeter of a field 80 rods square?
If a boy walks a mile to school in 20 minutes, he walks
at the rate of rods a minute or miles an hour.
COMPOUND NUMBERS. 241
What is the length of this line? If 1 inch represents 3
feet, what does the line represent? Then to what scale
is the line drawn?
A line 6 in. long is drawn to the scale of 1 inch to 3 feet.
What length does the line represent?
Draw a line 5^ in. long. Let each inch represent 3 feet.
What length does the whole line represent?
What would the line represent if the scale were 12 feet
to 1 inch?
Making each inch represent 10 feet, draw a line to
represent 30 feet. 40 feet. 25 feet.
A field is 48 rods long and 36 rods wide. Represent it
on a scale of 12 rods to the inch.
A township in some states is a mile square. Draw a
map of one on a scale of 1 inch to 80 rods.
345, 1. A room 18 ft. long is how many yards long?
2. A fence is 11 yards or feet or rods long.
3. The perimeter of a rectangle is 40 feet. If the
length is 12 feet, what is the width ?
4. Ten rods is how much greater length than 50 yards?
5. Find the distance around the schoolhouse in feet.
In yards. In rods.
6. Frank can walk 3 miles in an hour. In what time
can he walk 160 rods?
7. A room is 16i ft. square. What is the distance
around it?
8. What part of a yard is 1 ft. 6 in. ?
9. How many feet and inches in ^ of a rod?
*i6
11 J^l'. -^ :*^- > .r f.-fn A 'o 3 Trr-HL 3 "t> I . ^
c - . " /
14. T..^ !!-r^r./^ :/ m Z "o Z ^ -^-iijir parr xt Tii» iis-
li A r-^'*^ ir.-:.^ 'o in^e ±tjiil A, to •!. Wj«l ie:
^^^r-:/ %r.^ z-'^. r»o^ .na,xi^ "laaea ':rLl diey t>i r ?i fn owrimg;
17, A r'^iT^m :« 1 ^ f^. >>n^ and 1^ f:. ^ji&^ Tie <srpec
'« .sf..4 ^;n$rr.'r:s.#3j am<i la a yard wide. Eitw mair^ ^cji|m.
il^'rm mfvnj J»Tl«i in a*;, ".ke stripe?
!•. ff -i *- -^r;^ -- ^ 74ri xi.ie. and is .aid len^tiLw^e^
fc»>w nym/ r^H-* ^:,: ^.**^ -:.e :!..-/r .>t a r».*>ni 1± fc. w^fe
COMPOUND NUMBERS.
243
Square Measure.
346. Square Measure is iised in measuring surfaces.
, 3 ^
ISfft.
144 square inches (sq. in.) = 1 square foot (sq. ft.).
9 square feet = 1 square yard (sq.yd.).
30 J square yards = 1 square rod (sq. rd.).
160 square rods = 1 acre (A.).
We have learned what a square foot is. Draw one, and
divide it into square inches.
How many square inches in one row? In all rows?
Then how many square inches make 1 square foot?
How many square inches in 2 sq. ft. ? In i of a square
foot?
What part of a square foot is 72 sq. in.? 36 sq. in.?
How many square feet are there in 288 sq. in.?
Draw a square yard, divide it into square feet, and find
how many square feet make 1 square yard.
In 2 sq. yd. how many square feet? In 5 sq. yd.?
A square 1 rod long and 1 rod wide is called a square
rod.
How many square rods in a garden 5 rd. long and 3 rd.
wide? Make a map of the garden, letting 1 inch represent
a rod.
244
SCHOOL AKITHMETIC.
Areaa.
347. The Area of a surface is ^^
the number of square units of AI^H B
measure it contains.
If each side of one of the small
squares in the figure is one inch
long, then each part is 1 square
inch (square unit of measure).
The area of the strip AB is 4 X 1 sq. in., or 4 sq. in.,
and the total area is 3 X 4 sq. in., or 12 sq. in.
The area of a rectangle is expressed hy the product of
the numbers that represent its length and width.
348, 1. How many square feet in a strip of carpet a
yard wide and 10 yards long?
2. A table is 6 ft. long and 3 ft. wide. It contains
sq. ft., or sq. yd. '
3. How many square feet of oilcloth will cover a floor
15 ft. square? How many square yards?
4. Find how many square yards would be needed to
cover your kitchen at home. What would it cost at 30f^
a square yard?
5. A lot is 16 rd. long and 5 rd. wide. How many
square rods in it? What part of an acre?
6. What part of an acre is 40 sq. rd.? 120 sq. rd.?
7. In 2 acres how many square rods? In 5 A.? In
10 A.?
8. An acre and 40 sq. rd. = A.
9. A field is 16 rd. by 20 rd. How many acres in it?
10. A rug is 9 feet square. How many square feet in it?
11. The area of a rectangle 8 ft. long is 40 sq. ft.
What is the width?
COMPOUND NUMBERS.
245
12. The perimeter of a square is 12 yards. What is
the area in square feet?
13. A rectangular lot is 50 ft. hj 75 ft. The house on
the lot is 25 ft. by 50 ft. How many square feet are there
in the yard?
14. How many square inches are there in the surface
of a common brick, which is 8 inches long, 4 inches wide,
and 2 inches thick?
15. A farmer wishes to make a grain bin 8 ft. long, 5
ft. wide, and 4 ft. deep. How many square feet of boards
will he have in the bottom? In one end? In one side?
A
B
C
D
This figure is drawn to a scale of 12 ft. to 1 inch.
349. To find the area of the entire figure we divide it
into four rectangles and find the area of each separately.
1. What is the length of A? The width? The area
in square feet? In square yards?
2. Find the area of B in square feet. In square yards.
3. What is fhe area of C? The area of D?
4. Find the area of the entire figure in square yards.
5. How does the area of A compare with that of C?
6. A is what part of D? D is what part of B?
7. What part of the entire figure is B ? What part is 1) ?
8. Copy the figure, omitting the dotted lines. Make
other dotted lines dividing the figure into 3 rectangles.
Find the area of each rectangle.
246
SCHOOL ARITHMETIC.
350. Draw a rectangle 4 in. long and 3 in. wide, and
divide it into square inches. How many sq. in. have you?
Draw another rectangle 6 in. long and 2 in. wide. Is its
area equal to that of the first rectangle? Has it the same
dimensions (length and width) ?
Draw a third rectangle 12 in. long and wide enough
to have the same area. What is its width?
Draw a rectangle 6 in. by 8 in. Draw another twice as
long, but only half as wide. Are their areas equal?
Draw another twice as wide as the first, but only half
as long. Compare the areas.
What may be the dimensions of a rectangle containing
24sq. ftJ 36 sq.ft.? 64 sq.ft.?
Complete:
A rectangle 6 in. by 3 in. equals another 3 in. by in.
A rectangle 20 ft. by 2 ft. equals another 10 ft. by ft.
A rectangle 5 in. by 4 in. equals another 2i in. by in.
A rectangle 4 in. by 7 in. is how many times one that is
2 in. by 7 in.?
A rectangle that is 6 in. by 5 in. is what part of one that
is 9 in. by 5 in. ?
How many rectangles each 2 in. by 3 in. are equal to one
that is 6 in. by 3 in.? To one 10 in. by 3 in.?
1. Poiiu. out the bti^e of the shaded triangle. The
COMPOUND NUMBERS.
247
What part of the rectangle is the triangle?
What is the area of the rectangle? What, then, must be
the area of the triangle?
The area of the rectangle is 3 X 4 sq. units.
The area of the triangle is -J of 3 X 4 sq. units.
The area of a triangle is expressed hy one-half of the pro-
duct of the nurribers that represent its base and altitude.
1. If the base of a triangle is 6 inches and the altitude
3 inches, what is its area?
} of ( 3 X 6 ) sq. in. =^ 9 sq. in.
Find the area of the following triangles:
2. Altitude 8 inches, base 6 inches.
3. Altitude 10 inches, base 8 inches.
4. Altitude 12 inches, base 12 inches.
5. Altitude 9 inches, base 16 inches.
6. Altitude 5 inches, base 3 inches.
lOubic Measure.
352. Cubic Measure is used in measuring solids.
1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).
27 cubic feet = 1 cubic yard (cu. yd.).
Figure 1 represents a cubic
inch. Each face is an inch
square. Is each face a rectangle?
Suppose Fig. 1 is drawn to
a scale of 1 foot to 1 inch. Then
OD represents what length?
What is the area of each
face? Does the figure repre-
sent a cubic foot?
A solid that is 1 foot lon^, 1 foot wide, and 1 foot thick
is called a cubic foot.
Fig. 1.
248
SCHOOL ARITHMETIC.
Find a block of wood, a stone, or a box that is about as
large as a cubic foot.
Suppose Fig. 1 is drawn to a scale of 1 inch to 3 feet,
or 1 yard. Then OD represents what length?
What is the area of each face? Does the figure represent
a cubic yard?
A solid that is 1 yard long, 1 yard wide, and 1 yard
thick is called a cubic yard.
353. Figure 2 represents
a cubic yard. If we cut it
into cubes as indicated, what
will be the size of each cube ?
Each cube is a cuibic foot.
How many of tliem are
there in one layer? In the 3
layers? Then how many
cubic feet in a cubic yard?
^
^^^^j
^--
y^
^.' ^1 1
1
1
>
M
1
■4
1
1
i
1j 1 J
1
ipr
Pw. 2.
Fig. 3.
354, Fig. 3 represents a
rut lie foot. If we cut off a
pii f!e an inch thick and divide
it into inch cubes, how many
uf them shall we have?
How many such pieces can
i 1' cut from a cubic foot? Then
l\*yw many cubic inches in a
nildc foot?
A cubic yard is 3 ft. long, 3
ft. wide, and 3 ft. thick. Find
the value of 3 X 3 X 3. Is
the product the number of cubic feet in a cubic yard?
COMPOUND NUMBERS.
249
What are the dimensions of a cubic foot? Find the
value of 12 X 12 X 12, and compare it with the number
of cubic inches in a cubic foot.
Find how many cubic inches in a cube that measures 4
inches on each side. Build the cube with blocks (inch
cubes).
Volumes.
355. How many faces has a cube? Are they all equal?
Is each face a rectangle?
Fig. 4
Figure 4 represents a solid 6 inches long, 4 inches wide,
and 3 inches thick.
How many faces has the solid? Is each face a rectangle?
A solid bounded by 6 rectangles is called a rectangular
solid.
In Figure 4 each little cube represents 1 cubic inch.
Find how many cubic inches there are.
There are three layers, each containing 4 rows of the little cubes,
as ABCD. Each row contains 6 little cubes, or cubic inches, hence
the 4 rows contain 24 cubic inches.
Since there are 24 cu. in. in each layer, in the 3 layers there are
3 X 24 cu. in., or 72 cu. in., which is the volume.
Find the value of 6 X 4 X 3. Does the product equal
the number of cubic inches in Fig. 4? (6 X 3 X 4) X
1 cu. in. = cu. in.
The volume of a rectangular solid is expressed by the
250 SCHOOL ARITH3fETIC.
product of the numbers that represent its lengthy breadth,
and thickness.
The number of cubic units (cu. in., cu. ft., cu. yd., etc.) in a solid
is called its volume.
1. How many cubic inches in a brick 8 in. long, 4 in.
wide, and 2 in. thick?
2. How many cubic feet in a wall 16 ft. long, 4 ft.
high, and 2 ft. thick?
3. A hole is 3 ft. long, 2 ft. wide, and 6 ft. deep. How
many cubic feet of earth have been removed?
4. A cistern is 6 ft. square and 9 ft. deep. How many
cubic feet of water wiU it hold? How many cubic yards?
5. How many cubic feet in a cord?
A pile of wood 8 ft. long, 4 ft. wide, and 4 ft. high is called a cord.
6. How many cords are there in a pile of wood 16 ft.
long, 4 ft. wide, and 4 ft. high?
7. A cubic foot of water weighs 1000 oz. What is the
weight of a cubic yard of water?
8. Find the dimensions of a box that will hold 24 cu.
in. of water.
9. What are the width and depth of a cistern 6 ft. long
that will hold 144 cu. ft. of water?
10. An ice box holds 20 cu. ft. of ice. It is 4 ft. long
and 2 ft. deep. How wide is it ?
DECIMAL FRACTIONS.
251
Decimal Fractions.
A B
356. What part of A is dark? Into how many parts is
each strip divided in B?
What part of each strip is the shaded square? What part
of the large square?
Then -^ of one-tenth of B is one of B.
When anything is divided into ten equal parts, what is
each part called?
When each of these ten parts is divided into ten parts,
how many parts are there?
When each of these hundred parts is divided into ten
parts, how many parts are there?
When anything is divided into tenthSy hundredths j thousandthSj etc.,
the parts are called decimal parts ; that is, tenth-parts.
357. You have already learned that 10 hundredths
make 1 tenth, and that 10 tenths make 1 one, just as 10
ones make 1 ten, 10 tens 1 hundred, and so on. You have
also learned that tenths and hundredths may be written
with the decimal point and without denominators. Frac-
tions so written are called Decimals or Decimal Fractions.
358. Tenths must stand next to ones, because 10 of
them make 1 one; hundredths next to tenths, because 10
262
SCHOOL ARITHMETIC.
of them make 1 tenth, Kext to hundredths we must write
thoicsandths, because 10 of them make 1 hundredth, etc.
359. In decimals, as in integers (whole numbers), the
position of the figures indicates their value. Thus, in 3.15
we know that the 1 is one-tenth, because tenths are written
only in the first place to the right of ones; and that the 5
is five hundredths, because it is in the second place.
360, One-tenth of a cent is called a mill; then how
many mills make 1 cent?
How many mills in 10 cents? In 100 cents, or $1?
Then 1 mill is what part of a dollar?
What part of a cent are 5 mills, or 5 thousandths of a
dollar?
In $.125, how many dimes, cents, and mills? Which
figure is in tenths' place? In hundredths'? In thousandths'?
How many mills make 1 cent, or 1 hundredth of a dollar?
How many mills in 1 dime? In 2 cents? Then may
$.125 be read as 125 mills, or as 125 thousandths of a
dollar?
00
^ i
QQ
QQ
1
Who
J
•73 a +?
"5 g o rt
HteHH
12345. 6789
Integers, Decimals.
361. Examine this table. Ten of any order make one
of the next higher order. With reference to ones^ where
DECIMAL FRACTIONS. 253
are tens and tenths written? Hundreds and hundredths?
In what place is the 8? What does it express?
In the decamal .125, there are 1 tenth, 2 hundredths, and
5 thousandths, or 125 thousandths. When there are no
tenths or hundredths, we write thousandths in the third
place, and put ciphers in the first two places.
Thus, 5 thousandths is written .005.
What decimal place is occupied by tenths? By thou-
sandths? By hundredths?
What occupies the second decimal place? The fourth?
The third?
Extend the table, and tell what occupies the fifth place.
The sixth place.
362. In reading integers we omit the name, which is
oneSy the name of the lowest integral order. Decimals are
read just as integers are, except that the name of the lowest
decimal order is given.
In reading an integer and decimal, use the word and
between the integral and decimal parts of the number, but
nowhere else.
325.46 is read 325 and 46 hundredths.
73.05 is read 73 and 5 hundredths.
.08 is read 8 hundredths.
517.325 is read 517 and 325 thousandths.
82.073 is read 82 and 73 thousandths.
716.0034 is read 716 and 34 ten-thousandths.
254
SCHOOL ARITHMETIC.
363. Read the following:
X.
.7
10.
.225
19.
278.35
2.
.15
11.
.600
20.
51.07
3.
.38
12.
.012
21.
39.50
4.
.03
13.
.708
22.
624.054
5.
.44
14.
.1325
23.
516.0027
6.
.044
15.
.4016
24.
88.0008
7.
.444
16.
.7203
25.
200.0200
8.
.707
17.
.0518
26.
765.4004
9.
.005
18.
.0024
27.
394.3275
364. Write 7 thousandths as a dechnal.
Thousandths occupy the third place, hence we write the 7 and put
ciphers in the first two places, thus : .007.
Express 25 thousandths as a decimal.
25 thousandths = 2 hundredths and 5 thousaudths. There are no
tenths, hence we put a cipher in the first place, thus : .025.
Write as decimal fractions:
5 tenths
7 hundredths
42 hundredths
8 thousandths
216 thousandths
103 thousandths
68 hundredths
50 hundredths
75 thousandths
40 thousandths
90 hundredths
6 thousandths
36 thousandths 9 thousandths 82 thousandths
5 and 37 hundredths
24 and 5 hundredths
17 and 9 tenths
32 and 8 hundredths
40 and 40 hundredths
46 and 7 thousandths
75 and 14 thousandths
8 and 125 thousandths
92 and 8 thousandths
72 and 72 thousandths
DECIMAL FBACJTIONS. 255
Addition and Subtraction.
365. 1. Add .7, .42, .05, 2.7, and 15.48.
.7
• 4:2 Are the tenths all written in the same column ? Where
.05 are the hundredths written? How are the decimal
2 . 7 points arranged ?
15.48 Are decimals added just as integers are added ?
19.35
2. Subtract .17 from .56, and .24 from .8.
.66 .8
.17 .24
.39 .66
Are tenths written in one column? C
take 4 hundredths from no hundredths?
must you do? Do we subtract as in who
bers?
Add:
3
42.3
4
13.256
5
7.0296
6
.032
16.07
6.09
5.724
.85
5.45
54.307
38.602
.027
.08
8.9
3.08
.645
24.06
36.005
6.7043
.930
Subtract:
7
8
9 10
11
37.42
51.63
7.15 .672
.0072
12.51
28.35
6.47 .348
14 15
.0036
12
13
16
2.57
5.02
16.3 .207
.87
.39
2.76
2.14 .0525
.254
What
256 SCHOOL ASTTHMETIC.
Find the value of:
17. 72.5 + .324 + 5.07 23. 6.08 + .027 — 4.44
18. 61.3 + 2.79 + .008 24. 8.72 + .803 — .75
19. 26.7 + 41.3 + .802 25. 3.60 + 34.2 — .016
20. 5.34 + .534 + 53.4 26. .542 + 7.61 — 3.25
21. .016 + 0.16 + .024 27. 9.27 — 3.45 — .005
22. 7.03 + .300 + 5.04 28. .172 + 61.5 — 2.64
Multiplication and Division.
366. How many tenths are 5X6 tenths? 30 tenths
are equal to how many ones? 3.0 = 30 tenths.
How many tenths are 8X5 tenths? 40 tenths =
ones.
5 X .6 = 30 tenths, or 3. 8X5 tenths = 40 tenths, or 4.
In 25 tenths, how many ones and tenths?
1. Multiply 4.2 by 6.
^2 6X2 tenths = 12 tenths, or 1.2. Where do we write
'/* the 2? What is done with thel? Do we multiply as
in whole nambers ? How many decimal places in the
25.2 factors ? How many in the product ?
There must he as many decimal places in the prodicct 05
there are in both factors.
Find the products:
2.
5X3.7
7.
2X.24
12.
4 X 1.36
3.
7X2.3
8.
5X.13
13.
7 X 3.35
4.
4X5.6
9.
4 X .23
14.
3 X 8.72
5.
6X1.7
10.
7 X .14
15.
.12 X .48
6.
8X4.2
11.
8X.06
16.
2.4 X 1.2
DECIMAL FRACTIONS. 257
17. Multiply .14 by .7.
7 X 14 = 98, only two places. What must we do
• 7 to make three places ? How do we know there should
~~0Q« ^ three decimal places ?
Find the products:
18. .5 X .5
23.
12.5 X
.5 28.
.48 X .4
19. .8 X A
24.
16.3 X
.2 29.
.25 X .5
20. .6 X .6
25.
24.6 X
.3 . 30.
.32 X .3
21. .9 X .3
26.
33.2 X
.4 31.
.17 X .5.
22. .7 X .8
27.
53.2 X
.5 32.
.55 X. 3
33. Multiply 142 by .06.
142
Qg How many decimal places in tlie factors?
many must we point off in tlie product?
8.52
Then how
Multiply:
34. 125
by .03
39. 376 by
.05
35. 234
by .06
40. 428 by
.03
36. 145
by .05
41. 706 by
.06
37. 421
by .04
42. 250 by
.07
38. 845
by .06
43. 625 by
.05
367. What is
i of 8
tenths?
i of .8 =
What is
4 of 9 tenths?
I of .9 =
What is
i of 24 hundredths? i of .24=^=
What is
I of 18 tenths
? i of 1.8 =
=
What is
I of 36 tenths
? i of 3.6 =
=
(^py and find
:
1. I of .6 4.
I of 2.4 7,
. i of 36 tenths, or 3.6
2.- iof .8 5.
I of 3.9 8,
. iof 52 tenths, or 5.2
3. iof .6 6.
i of 8.4 9,
. i of 42 tenths, or 4.2
*I7
258 SCHOOL ARITHMETIC.
Copy- a
10.
nd complet(
3)126
3:
3) 12.6
3) 13.5
3) 13.8
11.
4)168
4)16.8
4) 17.2
4) 17.6
12.
6)126
6) 12.6
6) 13.2
6) 14.4
13.
8)168
8) 16.8
8) 17.6
8) 18.4
14.
7)217
7) 21.7
7) 22.4
7) 23.1
15.
4)568
4) 56.8
4) 57.2
4) 59.6
16. Divide 75 by
) 7.5.00 7 tens ■+
4.
4 = 1 ten,
and 3 tens remaining.
18.
67 -r- 4
22.
19.
53^4
23.
20.
66^5
24.
25.
121-
■^8
26.
130-
■^8
27.
146-
-H4
28.
255-
-=-6
^^* * ^ 3 ones and tenths = 30 tenths. 30 tenths -^ 4 =
7 tenths, and 2 tenths remaining. 2 tenths and
hundredths = 20 hundredths. 20 hundredths h- 4 = 6 hundredths.
Find the quotients:
17. 49-^4 21. 71-^5
79-^4
35^2
87-^2
368. How many tenths in 1? In 2? In i? In 2^?
IIow many hundredths in 1? In i? In i?
Write as decimals: ^, i, f, i i f , iVi A-
How many thousandths in 1? In i? In i?
Write as decimals: i, f, f, |, ^.
Change to common fractions: .5, .25, .75, .2, .075.
The following exercises will show you that —
(a) Moving the decimal point one place to the right
multiplies a number by 10.
(b) Moving the decimal point one place to the left
divides a number by 10.
DECIMAL FRACTIONS. 259
1. 10X2.5 = 25. 6. 25.0-^10 = 2.5
2. 10X1.25 = 12.5 7. 12.5 -MO = 1.25
3. 10 X. 25 = 2.5^ 8. 2.5 ^10 = .25
4. 10 X .5 = 5.0 ' 9. 5.0 ^ 10 = .5
5. 10 X .05 = .5 10. .5 ^ 10 = .05
Find the products and quotients by moving the decimal
point:
11. 10X2.7 17. 27^10 ' 23. 10X4.265
12. 10 X 2.45 18. 24.5 -^ 10 24. 10 X 30.74
13. 10X.36 19. 3.6 H- 10 25. 10X261.7
14. 10 X .8 20. 8. -f- 10 26. 375 X 10
15. 10X.07 21. .7^10 27. 625.4X10
16. 10 X 1.03 22. 10.3 H- 10 28. 71.68 X 10
Complete the following and show that —
(c) Moving the decimal point two places to the right
multiplies a number by 100.
(d) Moving the decimal point two places to the left
divides a number by 100.
29. 100 X 25.0 = 39. 2500 -f- 100 =
30. 100 X 1.25 = 40. 125 H- 100 =
31. 100 X 12.5 = 41. 1250 -v- 100 =
32. 100 X .125 = 42. 12.5 H- 100 =
33. 100 X .042 = 43. 4.2 -^ 100 =
34. 100 X .005 = 44. .5 -J- 100 =
35. 100 X 3.07 = 45. 307 -^ 100 =
36. 100 X. 5= 46. 50^100 =
37. 100 X .25 = 47. 25 -^ 100 =
38. 100 X. 05= 48. 5^100 =
260 SCHOOL ASITHlf£nC.
369. 1. Divide .098 by .7.
.09^ -1. .7 = .14 Is.098the/wv)rftirtof .7 (the divisor) and
.14 (the qaotient)? Does it contain as
many decimal places as both the factors.
The dividend contains 3 decimal places, the divisor 1. How many
moflt the qnotient contain ?
There must be as many decimal places in the quotient
<is the number of such places in the dividend exceeds the
number in the divisor.
Find the products:
1,
.6 X .7
2.
.3 X .15
3.
.5 X 4,3
4.
3.6 X .9
6.
.7 X .05
6.
.9 X .017
7.
310 X .05
Find the quotients:
8.
.42 -^
.6
9.
.45 -^
.3
10.
2.15 H
- .5
11.
3.24 -;
- .9
12.
.035 ^
- .7
13.
.0153
-^ .9
14.
15.50
H- .05
370. Another name for hundredths is jjer cent Instead
of saying 5 hundredths of $250, we may say 5 per cent of
$250.
To find 1 hundredth of a number we divide it by 100.
Hence, to find 1 per cent of a number we divide the num-
ber by 100.
What is the easiest way to divide by 100?
1. Find 1 per cent of $125.
$125 ^100 = $1.25.
2. Find 1 per cent of $275. Of $325. Of $152.50.
3. Wliat is 1 per cent of $200? What is 2 per cent
of $200?
4. Find 2 per cent of $300. Of $500. Of $250.
PERCENTAGE.
261
5. What is 3 per cent of $217.50? Of $187.50?
6. When you know what 1 per cent of a number is,
liow do you find 4 per cent of the number?
7. Find 4 per cent of $732.50. Of $364.25.
8. What is 6 per cent of $75? Of $87.25?
9. Find 5 per cent of 200. Of 800. Of 24.5.
10. What per cent of a number equals 100 hundredths
of the number?
11. Multiply $125 by .05, and compare the product
with 5 per cent of $125.
12. Find 6 per cent of $240; multiply $240 by .06.
Are the results equal?
13. Compare .04 X $325 with 4 per cent of $325. Are
they equal?
14. In how many ways can you find a per cent of a
number?
15. If you borrow money, do you have to pay anything
for its use?
16. Find out at home all you can about what is paid for
the use of money.
Percentage.
371. This square is di-
vided into equal parts.
Each part is 1 of the
square.
What part of the square
is A + B?
How many hundredths of
tlie square in each horizon-
tal strip? Each strip is what
part of the square?
A
B
C
D
E
...J
;...^
■■1
. . i 1
.■
...^J_ :^
262 SCHOOL ARITHMETIC.
Instead of hundredths we may use the term per cent,
because per cent means hundredths.
Then what per cent of the square is A? A + B?
How many per cent are there in the square? In any-
thing?
One hundred per cent of a number is the number itself.
What per cent of the square is above the line RD?
What part of anything is 50 per cent of it?
What part of the square is shaded ? What per cent of it
is shaded?
How many small squares in 10 per cent of the large
square? In 20 per cent?
The sign % stands for the term per cent, and means
either per cent or hundredths. Thus, 5% of the square
means 5 per cent, or 5 hundredths of it.
What per cent of the square isA + B + C + D + E?
What part of the square is 10^ of it? 20^? 40^?
50^? 60^? 6^?
Cover 25% of the square. What % is not covered?
372. What % of $100 is $5? $10? $25?
Draw a rectangle and divide so as to show 50% of it.
25%. 12i%.
Divide a square so as to show that 50% =i, and that
25% =i
' Draw a line an inch long, and another line 50% as long.
This line is an inch long. . Draw
another line 100% as long.
How many times a number is 200% of it? 300%?
Yij- of a number is what % of it?
How do you find 1 hundredth, or 1%, of a number?
PERCENTAGE. 263
What is the effect of moving the decimal point two places
to the left?
When you have found 1% of a number, how do you find
3% of it? 5%?
Find 1% of 200. Of 500. Of 250. Of 12.5.
Find 5% of 200. Of 125. Of 315. Of 41.2.
State the simplest way of finding 10%, or ^, of a num-
ber. What is the effect of moving the decimal point one
place to the left?
Find 10% of 50. Of 12.5. Of 345. Of 624.
What is the ratio of 200% to 100%? 100% to 50%?
25% to 100%?
What is 100% of 5^? Of $10? Of 25 gal.?
373. 1. Find 2i% of $400.
Ifo of $400 = 14.00.
2i% of $400 = 2J X $4.00, or $10.
Find:
2. li % of $1200. 6. 334 % of 900 ft.
3. 12^ % of $600. 7. 2i % of $1500.
4. 161 % of 120 bu. 8. i % of $1000.
5. 17 % of $320. 9. i% of $2000.
374, Be sure you understand the following:
100 % of a number = all of it.
200 % of a number = twice the number.
24 % of a number = ^ of it.
12i% of a number = i of it.
37^% of a number = f of it.
33i% of a number = 4 of it.
1. Find 200% of $5. Of 3 ft. Of i gal.
2. What is 25% of 24 in.? Of 16 ft.? Of 8^?
264 SCHOOL ABITHMETIC.
3. Find 50% of $20. Of $.40. Of a dime. Of a gallon.
4. Find 12^% of 40^. Of 8 yd. Of 4 bu. Of 72 ft.
5. Wbat is 33i% of a yard? Of 12 qt? Of $300?
6. A man who had $10 spent 50% of it. How much
had he left?
7. Mr. Lee has 40 acres of land. If he plants 25%
of it in corn, how many acres does he plant?
8. How many days in 33i% of the month of June?
9. n $6 is 50% of my cash, how much have I?
10. 6 is i of what number? 6 is 20% of what number?
11. A farmer had 80 chickens, but a hawk caught 25%
of them. How many did the farmer have left?
12. What is the difference in hours between 16§%
and 12^% of one day?
13. Eva's age is 75% of the age of Ethel, who is 16
years old. How old is Eva?
14. Pencils bought at 48 f^ a dozen were sold at a gain
of 25%. Find the selling price of each pencil.
15. A girl spelled correctly 99% of 200 words. How
many did she miss?
16. Some boys bought a pie, and each ate 25% of it.
If the whole pie was consumed, how many boys were there ?
17. What is the distance between two towns if 5 miles
is 33i% of the distance?
18. I had $20, but spent $10 of it for a dress. What
per cent of my money did I spend?
19. A farmer who had 8 cows sold 2 of them. What
per cent of them did he sell?
20. I bought a stove for $12 and sold it so as to gain
$3. What per cent of the cost did I gain?
Gain or loss is always some per cent of the cost
PERCENTAGE. 265
21. A boy bought a watch for $12 and sold it for $9.
How much did he lose? What per cent of the cost?
22. Robert paid $15 for an overcoat and sold it for
$20. What per cent did he gain?
23. If I pay $2 for an article and sell it for $1, what
per cent do I lose?
24. If a sheep is bought for $4 and sold at a gain of
25%, for how much is it sold?
25. A man paid 50^ for a knife and sold it at a loss of
10%. What did he get for it?
26. If a grocer buys sugar at 4<^ a pound and sells it at
5^ a pound, what per cent does he gain?
27. At what price must coffee which cost 15f^ a pound
\^e sold to make a profit of 20% ?
28. How much must be paid for a book marked $2, if
25% is taken off the marked price?
29. If $12 is 37i% of my money, how much have I?
30. An organ which was marked $70 I bought for
10% less. Tell me what I paid for it.
31. Of a regiment of 1000 soldiers 5% were made
prisoners. How many escaped ?
32. How much must be paid for a bicycle, if the marked
price is $75, and the discount, or the simi taken off, is 40% ?
33. What per cent of the day has passed at 6 o'clock
A. M.?
34. Oranges were bought at the rate of 2 for 5^, and
sold at 3f^ apiece. What per cent was gained?
35. A man who earned $60 a month had his salary
increased 25%. He then earned $ a month.
36. If you get 6 cents niter est for every 100 cents you
loan for a year, what per cent are you getting?
266 SCHOOL AKITHMETIC.
Interest.
375, If a man borrows a horse, he does not pay for its
use; if he hires the horse, he must pay the owner whatever
is agreed upon.
When a man borrows money, he is usually required to
pay something for its use. Money paid for the use of
money is called Interest.
1. If you borrow $100 from me and agree to pay me
6% a year for its use, at the end of the year you must
give me back the $100 and pay me the interest, which is
(>% of $100, or $ .
2. If you borrow $100 at 4% a year, how much interest
will you owe at the end of one year?
3. What is the interest of $100 for 1 year at 5%?
4. At 6%, what is the interest of $200 for 1 year?
Of $500? Of $300?
6. At 4%, what is the interest of $300 for 1 year?
For 2 years?
6. At 3%, what is the interest of $400 for 1 year?
For 2 years?
7. Find the interest of $300 for 1 year at 5%. For
2 years.
8. At 6%, what is the interest of $200 for 6 months?
9. At 5%, what is the interest of $600 for 4 months
(lyr.)?
10. At 6%, what is the interest of $200 for 1 year
and 6 months (1^ yr.)?
INTEREST. 267
376. Find the interest of $200 for—
1. 2 yr. @ 6% 7. 2 yr. @ 8%
2. 5 yr. @ 6% • 8. 6 yr. @ 8%
3. 6 mo. @ 6% 9. 3 yr. @ 3%
4. 3 mo. @ 6% 10. 4 mo. @ 3%
5. 2 mo. @ 6% 11. 6 mo. @ 4%
6. 9 mo. @ 6% 12. 9 mo. @ 4%
13. Find the interest of $150 at 4% for 2 yr. 3 mo.
11.50 — interest for 1 yr. at 1%.
4
16.00 = interest for 1 yr. at 4^.
2
112.00 =: interest for 2 yr. at 4%.
1.50 = interest for 3 mo. ( J yr. ) at 4%.
$13.50 = interest for 2 yr. 3 mo. at 4%.
Find the interest of $150 for —
14. 3 yr. 4 mo. @ 4% 16. 2 yr. 9 mo. @ 4%
15. 4 yr. 6 mo. @ 4% 17. 5 yr. 2 mo. @ 4%
Find the interest of $240 for —
18. 1 yr. 3 mo. @ 5% 25. 5 yr. 2 mo. @ 2%
19. 3 yr. 6 mo. @ 6% 26. 7 yr. 4 mo. @ 8%
20. 2 yr. 4 mo. @ 4% 27. 1 yr. 1 mo. @ 4%
21. 4 yr. 8 mo. @ 4% 28. 3 yr. 9 mo. @ 6%
22. 1 yr. 9 mo. @ 6% 29. 4 yr. 2 mo. @ 5%
23. 6 yr. G mo. @ 3% 30. 10 yr. 4 mo. @ 7%
24. 8 yr. 4 mo. @ 5% 31. 16 yr. 8 mo. @ 6%
268 SCHOOL ARITHMETIC.
GENERAL REVIEW.
Oral Work.
377. 1. A nmn bought a book for 56^ and gave a
silver dollar in payment. Count up the change.
2. How many handkerchiefs at 25^ each can be bought
for $3?
3. Find the perimeter of a rectangle 8 ft. long and 50%
as wide.
4. If 6 men can build a stable in 8 days, how long
would it take one man?
5. If one man can build a wall in 32 days, how long
would it take 4 men?
6. If 5 cows are worth 25 sheep, 8 cows are worth*
sheep. "^
7. How many pounds of butter at 12^ a pound must be
given for 3 lb. of coffee at 16^ a pound?
8. At the rate of 3 for 5^, how many oranges can be
bought for $1?
9. James bought 3 bushels of pears at $2 a bushel.
Henry bought twice as many at the same price. How
much did both pay?
10. Lemons were bought at the rate of 2 for 5f^, and
sold at 3^ apiece. Find the gain on a dozen.
11. A grocer paid 75^ a bushel for potatoes and sold
them at 25ff a peck. How much did he gain on 10 bushels?
12. What is the ratio of a gallon to a pint?
13. A farmer had 40 sheep. Dogs killed one out of
every 8. How many were not killed?
14. If 10 men weigh a ton, what is the average weight
of each man ?
GENERAL REVIEW. 269
15. How many square inches in a rectangle 8 in. long
and 25% as wide?
16. A rectangle 6 ft. long contains 18 sq. ft. What is
its width ? Draw the figure.
17. What is the perimeter of a square garden contain-
ing 25 square rods?
18. A man bought a hat for $2.65. What 4 pieces of
money would exactly pay for it?
19. How many 2-inch squares are equal to a 6-inch
square?
20. A lady having $20 gave 50% of it to her son and
50% of the remainder to her daughter. How much had
she left?
21. If a horse trots 10 miles in an hour, how far does
he trot in 6 minutes?
22. A man sold a cow for J of her cost. What per
cent did he lose?
23. If $50 is S of my cash, how much have I?
24. Helen's age is 25% of her father's. If Helen's
age is 8 years, what is her father's age?
25. Mr. Jones pays $300 a year for rent, which is 10%
of the value of the house. In how many years will his
rent amount to the value of the house?
Written Work.
378. 1. Find the cost of 25 bushels of wheat at $1.1 5
a bushel.
2. A sheep cost $4, a cow 6 times as much, and a horse
8 times as much as the cow. They all cost $ .
3. A grocer bought a barrel of vinegar containing 42
gallons at 15^ a gallon. He sold it at 6ff a quart. How
much did he gain?
270 SCHOOL ARITHMETIC.
4. The distance from Pittsburg to Philadelphia is 354
miles. At 2^ a mile, what is the fare for a round trip?
5. How long is the side of a square whose area is 12i%
of that of a rectangle 8 ft. by 16 ft.?
6. A lady bought 8 yd. of silk @ $1.25 a yard, 3 pairs
of shoes @ $2.50, 6 lb. of butter @ 15^, and li pk. of
apples @ 20^ a half peck. Make out the bill.
7. A field is 40 rods long and 16 rods wide. How many
square rods does it contain? How many acres?
8. A 2-foot cube of marble was polished at a cost of
25^ a square foot. How much was paid for polishing?
9. How many square yards of oilcloth will cover a room
18 ft. long and 16 ft. wide?
10. At 12^^ a yard, what will be the cost of 36 yards
of cloth?
11. What number divided by 12 will give the quotient
144?
12. How many boards, each 12 ft. long, will be required
for a fence 600 ft. long, and 5 boards high?
13. From a cheese which weighed 75 lb. a grocer cut
42 lb. 8 oz. How much remained?
14. There are 16.5 ft. in a rod. How many feet are
there in 320 rods, or 1 mile?
15. How many rails, each 30 ft. long, mil be required
for a mile of railroad?
16. A fence is 120 ft. long and the posts are 8 ft. apart.
Find how many posts there are. Make a drawing.
17. If 2 bushels of oats cost 64^, what is the cost of 2
pecks?
18. At 12i^ a quart, how many quarts of molasses will
$2 buy?
GENERAL REVIEW. 271
19. How many eggs, at 10^ a dozen, can be bought for
$2.50?
20. Find two numbers whose product is 105. Two
other numbers.
21. In an orchard ^ of the trees are apple, i peach,
and the remainder pear. There' are 10 pear trees. How
many peach trees?
22. On Friday a man started on a trip. He was gone
24 days. On what day of the week did he return?
23. A man feeds his horse 6 qt. of oats 3 times a day.
How long will 9 bushels of oats last?
24. Does your pulse beat 76 times in a minute? If it
does, how many times does it beat in a day?
25. How many pint bottles will it take to hold 0^
gal. of ink?
26. How many cubic feet of water can be put into a
trough 6 ft. long, 2 ft. wide, and 1 ft. deep?
27. At $2.40 a square yard, what will it cost to lay a
pavement 90 ft. long and 6 ft. wide?
28. Find the interest of $50 for 4 mo. at 6%.
29. I lost $5 by selling a wagon for $35. What per
cent did I lose?
30. Wliat is tlie length and widtli of your schoolroom 'i
Find the cost of painting the ceiling at 5^ a square yard.
fQ 17355
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