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O
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Inductiue Series,
FIRST LESSONS
AEITHMETIC
INDUCTIVE PLAN,
INCLUDING
ORAL AND WRITTEN EXERCISES.
BY
WILLIAM J^MILNE, A.M.
PRINCIPAL OF TiJJ(e(^^£~NORS^£^SieftpOI., GENESEO, N. Y.
JONES BROTHERS & COMPANY:
CINCINNATI, PHILADELPHIA,
CHICAGO, MEMPHIS.
1878.
COPYKIGHT, 1878, BY JOHN T. JONES.
ELECTROTYPED AT
FRANKLIN TYl'E KOUNDRY,
CINCINNATI.
This book is designed to teach the principles of Arithmetical
Science as far as they are involved in the elementary processes, and
to secure a reasonable degree of accuracy and rapidity in express-
ing numbers and computing results.
The pupils for whose use this book is intended can not be ex-
pected, at the outset, to explain processes, give definitions, or assign
reasons, though their notions of all of them may be quite correct;
much less should they be expected to grasp the principles of a
science by committing to memory statements which are the deduc-
tions and generalizations of persons entirely familiar with the sub-
jects treated. And, therefore, this work has been prepared upon the
inductive and objective methods, so that the pupil may obtain his
knowledge of arithmetic from actual work with numbers, rather
than from the stereotyped statements of the book.
The true method of awakening in the child a clear idea of num-
bers is through a perception of objects, or by pictures or other repre-
sentations of them. After he has become familiar with things and
their names, the name will signify to him all that he needs to know
about the objects so far as number is concerned; and it is no longer
necessary that the objects should be present before him. The ne-
cessity, too, of associating the same numbers with such a variety
of things, causes him at length to cease to regard them in connec-
tion with any particular thing, or as any thing more than abstrac-
tions.
(iii)
IV P K E F A C E .
In harmony with these laws of the development and growth of
mind, this work presents at first the idea of number connected with
visual representations of objects; afterward, when the pupils become
familiar with the objects, concrete examples are given without illus-
tration, and these are immediately followed by exercises upon ab-
stract numbers, so that the pupil may become familiar with the
various combinations that may be formed.*
The first lessons are devoted to instruction in counting, reading,
and writing numbers up to twenty. Immediately following these,
are lessons upon Addition, in which abundant practice is given in
combining numbers. The fundamental processes of Subtraction,
Multiplication and Division, are treated upon a plan similar to
that exemplified in Addition, including besides, numerous ex-
amples combining two or more of the previous processes.
The lessons on Fractions are so simple and yet so thorough, that
the pupil is enabled to read, write, add, subtract, multiply, and
divide fractions when the processes are not very complex.
The work on Written Arithmetic, which follows, is believed to be
simple, thorough, and practical; and the brief and practical treat-
ment of the various classes of denominate numbers in common use,
makes the work quite comprehensive within its scope.
With the hope that the features of this book will commend it to
all intelligent persons, and that instruction in the rudiments of
arithmetic may be rendered more interesting and efiective through
its agency, it is confidently offered to the public.
W. J. M.
State Normal School,
Geneseo, N. Y., Januciry, 1878.
i
CONTENTSI
^1
7^\
I. Objects and numbers from 1 to 10 .
II. Counting numbers from 1 to 20
III. Oral and slate exercises in Addition
IV. Special review of Addition
V. Oral and slate exercises in Subtraction
VI. Special review of Subtraction and Addition
VII. Heading and writing numbers to 100 .
VIII. Oral and slate exercises in Multiplication
IX. Special review of Multiplication, Subtraction
Addition
X. Oral and slate exercises in Division
XI. Special review of Division, Multiplication
tion, and Addition ....
XII. Heading and writing Fractions
XIII. Addition of Simple Fractions
XIV. Subtraction of Simple Fractions .
XV. Multiplication of Simple Fractions
XVI. Division of Simple Fractions
XVII. Notation and Numeration of Numbers .
XVIII. Written exercises in Addition
XIX. Written exercises in Subtraction .
XX. Written exercises in Multiplication
XXI. Written exercises in Division
XXII. Exercises in Denominate Numbers
XXIII. Table of Boman Notation
Subtrac-
and
16
30
32
48
50
53
70
72
91
93
96
99
103
104
107
113
118
122
128
134
144
(V)
Jhe Inductive ^£rie^
OF
MATHEMATICAL TEXT-BOOKS.
I. FIRST LESSONS IN ARITHMETIC.
II. PRACTICAL ARITHMETIC.
III. KET TO PRACTICAL ARITHMETIC.
IV. ELEMENTS OF ALGEBRA. {In preparation.-)
V. ELEMENTS OF GEOMETRY. {In preparation.)
(vi)
«* >
FIRST LESSOtI£BflVBB.»IT
ilPOT^
t^i
Jv -A" 7<- yi> ^
1
NUMBERS FRmi^ TO 10
■t-
Dog
One
Two Trees 2
Three Horses 3
Four Sheep 4
Five Houses 5
I.
II.
III.
IV.
V.
Sloe Ships 6 VI.
Seven Birds 7 A^II.
J5J/r//if Books 8 VIII,
Nine Cherries 9 IX.
Ten Stars 10 X.
,. -(vii)
8
FIRST LESSONS
liESSOlS^ I.
1. Of what is this a picture?
2. How many tables are there in the picture?
3. How many balls are there?
4. Make as many marks on your slates as there
are lamps in the picture.
5. The figure 1 represents one table, one ball, one
lamp, or one object of any kind.
6. Make the figure one on your slates. /.
7. How many kittens are playing with the ball?
8. How many kittens are playing with the cat?
9. How many kittens are 1 kitten and 1 kitten?
10. How many chairs do you see in the picture?
11. Name two objects on the table.
12. Make two marks on your slates.
13. The figure 2 represents two chairs, two books,
or two objects of any kind.
14. Make the figure two on your slates. ^.
15. Make the figures one and two.
IN ARITHMETIC.
LESSON II.
1. How many boats do you see in the picture?
2. How many fishes has one of the boys caught?
3. How many fishes has the other boy caught?
4. Two fishes and one fish are how many fishes?
5. How many fishing-rods do you see?
6. Make as many marks as there are fishing-rods.
7. The figure 3 represents three objects.
8. Make the figure three on your slates. */.
9. Make the figures one, two and three.
10. How many boys in the picture are fishing?
11. How many boys are digging for bait?
12. How many boys are three boys and one boy?
13. How many oars has each boat in the picture?
14. Make as many marks on your slates as there
are boys in the picture.
15. The figure 4 represents four objects.
16. Make the figure four on your slates. ^.
17. Make the figures one, two, three and four.
10
FIRST LESSONS
LESSOI^ III.
1. How many roses do you see on the bush?
2. How many birds are flying near the bush?
3. How many birds are there on the bush ?
4. How many birds are four birds and one bird?
5. How many eggs are there in the nest?
6. Make a mark for every egg in the nest.
7. The figure 5 represents five things.
8. Make the figure five on your slates. <^,
9. Make the figures one, two, three, four and five.
10. How many rose-buds are there near each other?
11. How many do you find growing alone?
12. How many rose-buds are five rose-buds and one
rose-bud ?
13. Make six marks on your slates.
14. The figure 6 represents six things.
15. Make the figure six on your slates. ^
16. Make the figures one, two, three, four, five, six.
/ J J J ^ ^
IN ARITHMETIC,
11
I^ESSON^ IV.
1. How many lambs are at the left in the picture?
2. How many trees are in a row in the picture?
3. How many trees are standing alone?
4. How many trees are six trees and one tree?
5. How many lambs are there in the picture?
6. Make seven marks on your slates.
7. The figure 7 represents seven things.
8. Make the figure seven on your slates. /^
9. How many sheep are feeding in the field?
10. How many sheep are with the lambs?
11. Seven sheep and one sheep are how many sheep?
12. How many posts do you see in the picture?
13. Make as many marks as there are posts.
14. The figure 8 represents eight things.
15. Make the figure eight on your slates. <f.
16. Make the figures one, two, three, four, five, six,
seven, eight.
12
FIKST LESSONS
liESSON V.
1. How many trees are there in a row in the
picture ?
2. On how many trees are there ladders?
3. How many trees are eight trees and one tree?
4. How many rounds has the ladder?
5. Make nine marks on your slates.
6. The figure 9 represents nine objects of any
kind.
7. Make the figure nine on your slates. ^'
8. How many loads of grain are there?
9. How many horses do you see?
10. How many rakes are there in the picture?
11. How many rails are there in each section of
fence in the picture?
12. How many men do you see in the picture?
13. How many shocks of grain are there?
14. How many sections of fence are there?
15. How many posts has the fence?
16. Make the nine figures on your slates.
/ J J J ^ ^ / .
/
IN ARITHMETIC,
13
liESSOI^ TI.
How many
1. How many cherries are there on the larger
twig in the picture?
2. How many cherries
are on the other twig?
3. How many cherries
are nine cherries and one
cherry? Ten cherries.
4. Make nine marks and one mark,
marks are nine marks and one mark ?
5. How many pens are nine pens and one pen ?
6. How many boys are nine boys and one boy?
7. How many pears are there represented in the
following picture?
8. How many groups
of ten pears are there?
9. Make ten straight
marks on your slates.
10. The number ten is
expressed thus: 10,
11. The figure 1 at the left shows that there is one
ten. The figure at the right shows that there are
no ones,
12. Express ten. What does the figure 1 denote?
What does the figure denote?
13. How many fingers have you on both hands?
14. Make as many marks as you have fingers.
15. Express the number ten by figures.
16. Name ten things that you see.
#^
14
FIRST LESSONS
LESSON Til.
1. How many ducks are swimming in the pond?
2. How many ducks are there on the bank?
3. Ten ducks
and one duck
are how many?
Eleven ducks.
4. How many
groups of ten
ducks are there?
5. How many
ducks are there besides the group of ten ducks?
6. Make ten marks and one mark. (//////////] /
7. Eleven is expressed thus : 11*
8. Express eleven on your slates.
When tivo figures are written side by side, the one on
the right denotes ones, the one next to it denotes tens.
9. Express ten. Express eleven. What does 10
represent? What does 11 represent?
10. Make ten marks in a group and two besides
on your slates. (//////////) //
11. How many marks are ten marks and two
marks? Twelve marks.
12. Express one ten and two ones, or twelve. 12,
13. Express with figures, ten, eleven and twelve.
14. Make ten marks and three marks. (//////////J ///
15. Ten and three, or thirteen, is expressed thus : 13,
16. Write all the numbers from one to thirteen.
i:n arithmetic. 15
liESSON VIII.
1. Make ten marks and four marks, or fourteen
marks, on your slates. [llllllllll] I III
2. Fourteen is expressed thus : 14=.
3. How many books are ten books and four books?
4. Represent ten books and five books, or fifteen
books, by marks. [llllllllll ] lllll
5. Express one ten and five ones, or fifteen. 15»
6. How many are one ten and six ones?
7. Express one ten and six ones, or sixteen. 10.
8. Express one ten and seven ones, or seventeen. 17*
9. Express eighteen. 18. Express nineteen, 10.
10. Make ten marks and ten marks in separate
groups on your slates. [llllllllll) [llllllllll)
11. How many tens are one ten and one ten?
12. Express two tens, or tioenty. 20,
13. What does denote? What does 2 denote?
14. Express by figures all the numbers from one
to twenty.
15. How many tens are there in fifteen?
16. How many ones are there in fifteen?
17. How many tens are there in twenty-four?
18. How many ones are there in twenty-four?
19. What shows that there are no ones in a number?
Slate Exercises.
Copy and read the following :
12 11 10 19 ^y^^^
16 13 14 17 ^^5oe T'lR
16
FIRST LESSONS
liESSON IX.
1. How many balls are 1 ball and 2 balls? Ex-
press the answer on your slates, thus: 1 ball and 2
balls are 3 balls; or, 1
and 2 are 3.
2. How many balls
are 2 balls and 2 balls?
Express the answer thus :
2 balls and 2 balls are 4
balls; or, 2 and 2 are 4.
3. How many balls
are 3 balls and 2 balls?
Express the answer thus :
3 balls and 2 balls are 5
3 + 2 = 5.
It
balls; or, 3 and 2 are 5.
The sign + takes the place of the word and
is read jplus.
The sign = takes the place of the word are. It
is read equal. Then 1 and 2 are 3, is written 1 + 2
= 3, and read, 1 plus 2 equal 3.
4. Express 2 and 2 are 4, and 3 and 2 are 5, on
your slates, using the signs.
5. How many balls are 4 balls and 2 balls?
4+2=? 5+2=? 6+2=? 7+2=? 8+2=?
6. How many are 9 balls and 2 balls? 10 + 2 = ?
Counting numbers together is called Addition*
7. Form the addition table of twos.
IN ARITHMETIC,
TABLE.
17
1 + 2 = 3
4+2 = 6
7 + 2= 9
2 + 2 = 4
5 + 2 = 7
8+2 = 10
3 + 2 = 5
6 + 2 = 8
9 + 2 = 11
Slate Exeecises.
Copy and add the following :
242728623
629252242
:>J<Kc
1. How many birds are 1 bird and 3 birds?
2. How many acorns are 2 acorns and 3 acorns?
3. Harry bought 3
oranges one day, and 3 i^iTw^J^ A
the next. How many ^s ^?^*^^
oranges did he buy?
4. How many figs
are 4 figs and 3 figs?
5. How many boys
are 5 boys and 3 boys?
6. Helen gave a beggar 6 cents, and Mary gave
him 3 cents. How many cents did both give him?
7. A man bought 7 loads of hay one week, and
3 the next. How many loads of hay did he buy?
2
18
FIEST LESSONS
8. How many are 8 and 3? How many are 9
and 3?
9. How many tops are 10 tops and 3 tops?
10. How many bees are 1 bee and 4 bees?
11. How many butterflies are 2 butterflies and 4
butterflies ?
12. Mary had 3 cents, and her brother gave her
4 more. How many cents had she then?
13. A' boy bought 4 pencils one day, and 4 the
next. How many pencils did he buy in both days?
14. How many books are 5 books and 4 books?
15. How many are 6 and 4? 7 and 4?
16. If there are 7 boys on one seat and 4 on
another, how many boys are there on both seats?
17. 8 + 4 = ? 9 + 4 = ? 10 + 4 = ?
18. Form the tables of threes and fours.
TABLES.
1+3=4 6+3= 9
1+4 = 5 6 + 4 = 10
2 + 3 = 5 7 + 3 = 10
2 + 4 = 6 7 + 4 = 11
3 + 3 = 6 8 + 3=11
3 + 4=7 8 + 4 = 12
4 + 3 = 7 9 + 3 = 12
4 + 4 = 8 9 + 4=13
5 + 3 = 8 10 + 3 = 13
5 + 4=9 10 + 4 = 14
Slate Exercises.
Copy and add the following:
3473434526
52495822 73
IN ARITHMETIC. 19
I.ES80N XI.
1. James had 3 oranges, and bought 4 more.
How many had he then ? 3 -f 4 = ?
2. Mary had 4 pencils, and her aunt gave her 2
more. How many had she then?
3. If there are 9 cows in one field and 3 in
another, how many are there in both fields?
4. John had 4 pennies, and earned 7 pennies.
How many had he then?
5. Helen picked 3 roses from one bush and 7 from
another. How many roses did she pick from both?
6. One hen's nest had 3 eggs in it, and another
had 5. How many eggs were there in both nests?
7. 3 + 4 = ? 4 + 7==? 4 + 6 = ?
8. There are 6 lambs in one field and 2 in another.
How many lambs in both fields? 6 + 2 = ?
9. 4 + 2 = ? 7 + 3 = ? 3 + 5 = ?
10. A man paid 10 dollars for a coat and 4 dol-
lars for a hat. What did he pay for both?
11. 9 + 3 = ? 3 + 8 = ? 8 + 4 = ?
12. How many are 10 and 2? 2 and 10?
13. How many are 9 and 2? 2 and 9?
14. How many robins are 5 robins and 3 robins?
Slate Exercises.
Copy and add the following:
3865897621
7434224318
20
FIEST LESSONS
liESSOlS^ XII.
1. There is 1 pigeon on one lirab and there are 5
pigeons on another. How many are there on both
limbs? 1 + 5 = ?
^'^ 2. A man put 2
bushels of wheat in
one bin and 5 in
another. How many
bushels did he put in
both bins? 2 + 5 = ?
3. Richard gave 3
cents for a lemon and 5 cents for an orange. How
much did he give for both ? 3 + 5 = ?
4. How many girls are 4 girls and 5 girls?
5. How many canes are 5 canes and 5 canes?
6. 6 + 5 = ? 7 + 5 = ? 8 + 5 = ? 9 + 5 = ?
7. How many sheep are 10 sheep and 5 sheep?
8. A girl gave 1 cent for a needle and 6 cents
for a spool of thread. How much did she pay for
both? 1 + 6 = ?
9. A boy gave 2 cents for marbles and 6 cents
for a top. How much did he pay for both?
10. How many lamps are 3 lamps and 6 lamps?
11. How many are 4 and 6? How many are 5
and 6?
12. A man bought 6 bushels of potatoes at one
time, and 6 more at another time. How many did
he buy at both purchases ? 6 -{- Q^^'}
13. How many lambs are 7 lambs and 6 lambs?
IN ARITHMETIC.
21
14. How many are 8 and 6? How many are 9
and 6?
15. How many pinks are 10 pinks and 6 pinks?
16. Form addition tables of fives and sixes.
TABLES.
1 + 5-= 6 6 + 5-=ll
1 + 6= 7 6 + 6 = 12
2 + 5= 7 7 + 5 = 12
2 + 6= 8 7 + 6 = 13
3 + 5= 8 8 + 5 = 13
3 + 6= 9 8 + 6 = 14
4 + 5= 9 9 + 5 = 14
4 + 6 = 10 9 + 6 = 15
5 + 5 = 10 10 + 5 = 15
5 + 6 = 11 10 + 6 = 16
y>^c
liESSOX XIII.
1. How many apples are 1 apple, 2 apples and 3
apples? 2 apples, 4 apples and 1 apple?
2. If you put 2 dol-
lars, 3 dollars and 4 dol-
lars into an empty purse,
how many dollars will
there be in the purse?
2+3+4=?
3. How many are 9 and 6 ?
4. How many are 8 and 5?
5. Walter caught 2 fishes, Harry caught 5, and
Webster caught 3. How many fishes did they all
catch?
6 and 9?
5 and 8?
22 FIRST LESSONS
6. Arthur had 7 chickens, and his father gave
him 6 more. How many had he then?
7. 3 + 3 + 7=-? 4 + 1 + 6 = ? 3 + 2 + 8 = ?
8. How many are 3 books, 5 books and 6 books?
9. How many are 3 slates, 4 slates and 5 slates?
10. There are 5 birds in one nest and 4 in another.
How many birds are there in both nests?
11. How many are 10 and 3? 3 + 10 = ?
12. How many are 10 and 4? 4 and 10?
13.2 + 3 + 5 = ? 2 + 2 + 2 = ? 1 + 5 + 6 = ?
14. What is addition ? What is the sign of ad-
dition?
15. What is the sign of addition called?
16. Make the signs used in addition.
17. In one nest there were 5 little birds, in an-*
other 4, and in another 4. How many birds were
there in these nests?
18. In a school 5 pupils were tardy on Monday,
2 on Tuesday, 3 on Wednesday, 3 on Thursday, and
on Friday. How many pupils were tardy during
the week?
Slate Exercises.
Copy and add the following:
2 3 4 4 6 7 1
4 2 12 2 3 5
8 5 6 5 3 3 6
Copy and read the following:
20 18 15 17 13 12 11 19
IN ARITHMETIC. 23
LT]SSO]S^ XIV.
1. If a darning-needle costs 1 cent, and a skein
of silk 7 cents, what will both cost?
2. How many skeins are 2 skeins and 7 skeins?
3. If there are 3
spools in one group —
and 7 in another, how
many spools are there
in both groups?
4. ^ A woman who
had 4 quarts of cherries,
bought 7 quarts. How many did she then have?
4+7 = ?
5. There are 5 boys in one group and 7 in an-
other. How many boys are there in both groups?
6. There are 6 cows in one field and 7 in an-
other. How many cows are there in both fields?
7. How many are 7 and 7? How many are 8
and 7?
8. How many are 9 and 7? How many are 10
and 7?
9. If I have 1 dollar, and my brother gives me
8 dollars, how many dollars will I then have?
10. How many chairs are 2 chairs and 8 chairs?
11. How many are 3 and 8? How many are 4
and 8?
12. George walked a distance of 5 miles one day,,
and 8 miles the next day. How far did he walk
in both days? 5 + 8 = ?
24
FIRST LESSONS
13. 6 + 8 = ? 7 + 8 = ? 8 + 8 = ? 9 + 8=?
14. There are 10 girls in one class and 8 in an-
other. How many girls are there in both classes?
15. Form the addition tables of sevens and eights.
TABLES.
1 + 7= 8 6 + 7 = 13
1 + 8= 9 6 + 8 = 14
2 + 7= 9 7 + 7 = 14
2 + 8 = 10 7 + 8 = 15
3 + 7 = 10 8 + 7 = 15
3 + 8 = 11 8 + 8 = 16
4 + 7 = 11 9 + 7 = 16
4 + 8 = 12 9 + 8 = 17
5 + 7 = 12 10 + 7 = 17
5 + 8 = 13 10 + 8 = 18
:>U^c
I^ESSO]^ XV.
1. How many peaches are 7 peaches, 2 peaches
and 5 peaches? 7 + 2 + 5=?
2. A man gave 4 dollars for corn and 8 dollars
for a ton of hay. How much did he pay for both ?
3. A man has 2 cows in one pasture, 4 in an-
other, and 7 in another. How many cows has he
in the three pastures?
4. A woman sold 5 dozen eggs at one time, 4
dozen at another time, and 8 dozen at another. How
many dozen did she sell?
5. A woman sold 7 pounds of butter at one
time, 3 at another time, and 5 at another. How
many pounds did she sell?
IN ARITHMETIC. 25
6. 6 + 3 + 2-=? 4 + 5 + 7 = ? 3 + 2 + 5 = ?
7. How many are 9 and 4? 4 and 9?
8. How many are 10 and 7? 7 and 10?
9. 8 + 5 + 7 = ? 3 + 7 + 5 = ? 8 + 6 + 3 = ?
10. A farmer paid 5 dollars for sugar, 2 dollars
for coffee, and 10 dollars for flour. What was the
cost of the whole?
11. How many are 8 boys, 2 boys and 5 boys?
12. 8 + 3 + 2 = ? 3 + 2 + 6 = ? 5 + 2 + 4 = ?
Slate Exercises.
Copy and add the following :
673835648
256145221
223256343
3>a^c
i.esso:n^ XVI.
1. There is 1 man on the steps and there are 9
men in the store. How many men are there in both
places ?
2. Henry sold 2 books on Tuesday and 9 books
on Wednesday. How many books did he sell in both
days?
3. How many shells are 3 shells and 9 shells?
4. How many boats are 4 boats and 9 boats?
5. If Jennie is 5 years old, and her sister is 9
years older, how old is her sister?
3
26
FIRST LESSONS
6. How many are 6 and 9? 7 and 9?
7. There are 8 trees in one row and 9 in an-
other. How many trees are there in both rows?
8. How many plants are 9 plants and 9 plants?
9. How many books are 10 books and 9 books?
10. A beggar had 1 cent, and a boy gave him 10
cents. How many cents did he have then?
11. If there are 2 straw-
berries on one stem and 10
on another, how many are
there on both stems?
12. How many are 3 or-
anges and 10 oranges?
13. 4 + 10 = ? 5 + 10 = ?
6 + 10 = ?
14. A boy paid 7 shil-
lings for oil and 10 shillings for a lamp. What
was the cost of both ? 7 + 10 = ?
15. How many are 8 pigeons and 10 pigeons?
16. How many are 9 and 10? 10 and 10?
17. Form the addition tables of nines and tens.
TABLES.
1+9=10
6+9=15
1+10=11 6+10=16
2+9=11
7+9=16
2+10=12 7+10=17
3+9=12
8+9=17
3+10=13 8+10=18
4+9=13
9+9=18
44-10=14 9+10=19
5+9=14
10+9=19
5+10=15 10+10=20
-^
IN ARITHMETIc/'g^JY^v27
liESSON XVII,
'k
■rm.tl
1. Ruth picked 4 pinks from one stem, 3 from
another, and 2 from another. How many pinks did
she pick?
2. If there are 6 boys in one
class, 7 boys in another, and 5 boys
in another, how many boys are
there in the three classes ? 6 + 7
3. 2 + 2 + 2 = ? 3 + 3 + 3 = ?
5+5+5=? 6+6+6=?
4. Begin with 2 and count to 8
by 2's ; thus : Two, four, six, eight.
5. Begin with 3 and count to 15 by 3's.
6. Begin with 1 and count to 19 by 3's.
7. How many bells are 5 bells, 2 bells, 6 bells
and 4 bells? 5 + 2 + 6 + 4 = ?
8.10+5 + 3 + 4 = ? 6 + 8 + 4 + 2 = ?
9. 2 + 3 + 6 + 1 = ? 3 + 2 + 4 + 7 = ?
10. Count to 20 by 5's. To 18 by 6's.
11. A merchant sold 5 yards of calico to one girl,
3 yards to another, and 6 to another. How many
yards did he sell?
12. Begin with 2 and count to 17 by 3's.
13. How many are 7 barrels, 6 barrels and 4
barrels?
14. How many are 8 and 7 and 3?
15. Lucy had 8 pins, and found 10 more. How
many had she then?
28 fikst lessons
Slate Exekcises.
Copy and add the following:
941268513
125510286
432423625
203331-544
3»<00-
LESSON XTIII.
1. Jennie gave the teacher 6 hyacinths, Mary
gave her 4, and Minnie gave her 3. How many
hyacinths did they all give her? 6 + 4 + 3 = ?
2. In the park 3 boys are flying kites, 6 are play-
ing ball, and 3 are rolling hoops. How many boys
are there in the park? 3 + 3 + 6 = ?
3. There are 4 soldiers in one squad, 5 in an-
other, and 6 in another. How many soldiers are
there in the three squads?
4. How many are 4 guns, 5 guns and 6 guns?
5. There are 5 flags on one building, 2 on an-
other, and 4 on another. How many flags are there
on the three buildings? 5 + 2 + 4 == ?
6. There are 6 birds in one cage, 2 in another,
and 7 in another. How many birds are there in
the three cages? 6 + 2 + 7 = ?
7. 1 + 2 + 6 + 9==? 8 + 1 + 5 + 3 = ?
8. 7 + 1 + 8 + 2 = ? 3 + 3 + 3 + 3 = ?
IN ARITHMETIC. 29
9. Jennie is 8 years old, and her brother is 5
years older. What is the age of her brother?
10. Delia has 1 doll, Mina has 2 dolls, Carrie has
3 dolls, and Ruth has 2 dolls. How many dolls have
these girls?
11. How many are 6 and 3 and 5? 6 + 3 + 5 = ?
12. How many are 4 and 7 and 8? 4 + 7 + 8 = ?
13. There are 8 goblets on the shelf, 6 on the
table, and 4 on the stand. How many goblets are
there in all?
14. A wealthy gentleman had 3 draft-horses, 5
riding-horses, and 6 carriage-horses. How many
horses did he have?
15. A gentleman spent 4 months of every year in
Florida, 2 months in the White Mountains, 3 months
in Europe, and the rest of the year at home. How
many months was he away from home?
16. James wrote 6 lines in his writing-book on
Monday, 3 lines on Tuesday, 7 lines on Wednesday,
and 4 lines on Thursday. How many lines did he
write in those four days?
17. 8 + 2 + 3 + 5 = ? 7 + 3 + 4 + 4 = ?
Slate Exercises.
Copy and add the following:
211648564
253152344
247321254
264235424
30 FIRSTLESSONS
t
REVIEW EXERCISES.
Find the value of each of the following :
5 + 4 6^8 6 + 3 9 + 4 8 + 1
6 + 4 5 + 9 ^5 + 7 5 + 3 7 + 9
7 + 6 2 + 8 8 + 3 6 + 4 8 + 8
5 + 6 4 + 7 7 + 9 3 + 9 7 + 5
3 + 9 3 + 5 9 + 3 4 + 4 6 + 3
8 + 3 5 + 6 8 + 7 4 + 8 7 + 8
Q + 6 5 + 5 6 + 9 6 + 5 4 + 9
8 + 4 4 + 9 5 + 8 7 + 6 5 + 7
Add the following without using slate :
2 + 3 + 4 3 + 4 + 5 6 + 1 + 5
7 + 2 + 5 6 + 5+3 2 + 9 + 2
4 + 7 + 5 6 + 3 + 4 5 + 2 + 7
6 + 5 + 8 4+9 + 6 5 + 6 + 8
3 + 5 + 6 3 + 9 + 2 4 + 6 + 2
3 + 5 + 6 7 + 5 + 4 7 + 3 + 5
4 + 1 + 9 5 + 9 + 2 7 + 6 + 2
6 + 8 + 3 5 + 3 + 4 4 + 7 + 5
3 + 8 + 4 3+9 + 6 5 + 9 + 4
2+5 + 4 2 + 7 + 3 6+1 + 5
6 + 5 + 4 7 + 9 + 2 5 + 7 + 8
3 + 1 + 6 5 + 2 + 7 6 + 3 + 4
7 + 2 + 7 5 + 5 + 6 6 + 5 + 6
3 + 7 + 2 3+2 + 5 5 + 7 + 6
2 + 5 + 7 3 + 6 + 8 5 + 2+7
7 + 3 + 5 4 + 6 + 5 6+5 + 4
IN ARITHMETIC. - 31
REVIEW EXERCISES.
Copy and add the following :
875356 5 67
4 6 9 8 4 4 12 2
352682246
42423783 5
3
6
5
5
4
6
3
2
4
4
2
3
9
7
4
2
1
2
5
3
8
4
3
1
5
6
7
4
5
1
1
8
4
4
6
2
2
3
2
5
1
2
5
1
Copy and add the following:
3 -f 4+2 + 6 2 + 4+2 + 3 2 + 6 + 8 + 4
3+2+1+6 4+8+2+4 2+6+1+7
4+2+3+9 8+1+7+4 8+4+2+5
4+7+4+3 6+4+2+7 5+2+7+6
7+2+9+1 5+6+4+3 9+2+6+3
4+2+6+5 4+9+2+4 5+2+7+6
5+2+4+3 7+4+6+1 9+1+4+2
8+2+6+3 9+1+4+5 4+2+6+7
5+2+7+4 5+9+2+3 8+7+2+2
4+3+5+8 4+7+6+2' 6+2+3+5
5+4+9+2 9+2+3+6 4+7+2+6
5+1+4+9 6+3+1+8 4+7+5+4
7+3+3+7 6+4+4+6 8+2+2+7
9+1+6+3 8+5+2+4 7+7+2+3
32
FIRST LESSONS
T.ESSON XIX.
1. Make two marks on your slates. Erase one.
How many marks are there left?
2. 1 mark from 2 marks leaves how many marks?
3. If there were 3 pencils on the table, and
Helen took 1 away, how many were left?
4. How many are 3 pencils less 1 pencil ?
5. If 4 apples were put in a box, and afterward
1 was taken out, how many remained?
6. How many are 4 apples less 1 apple?
7. Hold up 5 fingers. Put one down. How
many fingers are you holding up?
8. How many are 5 fingers less 1 finger?
9. Make 6 dots on your slates. Erase one. How
many are there left?
10. How many are 6 dots less 1 dot?
11. How many steamships are represented in the
picture ?
12. If 1 sails away, how many are left?
13. How many vessels are 7 vessels less 1 vessel?
14. How many boats do you see in the picture?
IN ARITHMETIC
33
15. How many are being rowed away ? How many
are left?
16. How many boats are 8 boats less 1 boat?
17. If there are 9 trees, and a man cuts 1 down,
how many will be left?
18. How many trees are 9 trees less 1 tree?
3j*iC
I^ESSON XX.
1. A rose-bush had 3 roses on it, but 1 dropped
off. How many roses were there left on the bush?
2. How many are 3 less 2?
3. Make 4 marks. Erase 2.
How many are left?
4. How many marks are 4
marks less 2 marks?
5. Helen had 5 pennies, and
gave 2 to a beggar. How many
had she left ?
6. How many are 5 less 2?
The sign — takes the place of the word less. It
is read minus. Thus, 4 less 2 equals 2, is written
4 — 2 = 2, and is read 4 minus 2 equals 2 ?
7. If you take 2 apples from a group of 6 apples,
how many apples will be left?
8. How many apples are 6 apples less 2 apples?
9. Express 6 less 2 equals 4. 6 — 2 = 4.
34
FIRST LESSONS
10. William had 7 pennies, and gave 2 for a pen-
cil. How many had he left? 7 — 2 = ?
11. How many slates are 8 slates less 2 slates?
12. How many are 9 less 2? How many are 10
less 2? How many are 11 less 2?
13. How many are 12 dollars less 2 dollars?
Taking one number from another is called Sub-
traction,
14. Form the subtraction tables of ones and twos.
TABLES.
1 — 1=0
6-1
L = 5
2 — 2 = 7 — 2 = 5
2 — 1 = 1
7 — ]
L = 6
3 — 2 = 1 8 — 2 = 6
3 — 1 = 2
8-1
L = 7
4 — 2 = 2 9 — 2 = 7
4 — 1=3
9-1
[ = 8
5 — 2 = 3 10 — 2 = 8
5 — 1 = 4
10—]
L = 9
6 — 2 = 4 11 — 2 = 9
3>»<C
i:.esso:n^ xxi.
1. Helen had 3 cents, and gave them for a pen-
cil. How many cents had she left? 3 — 3 = ?
2. A man had 4 horses, and sold 3 of them.
How many had he left? 4 — 3=?
3. How many cows are 5 cows less 3 cows?
4. A boy had 6 marbles, and gave away 3. How
many marbles had he left? 6 — 3 = ?
IN ARITHMETIC. 85
5. How rnany dollars are 7 dollars less 3 dollars?
How many are 8 less 3?
6. A woman had 9 dollars, and gave 3 for a hat.
How many dollars had she left?
7. How many horses are 10 horses less 3 horses?
How many are 11 minus 3?
8. If there were 12 pigeons on a limb, and 3
flew away, how many remained? 12 — 3 = ?
9. If James had 4 apples, and gave away 4, how
many had he left? 4 — 4 = ?
10. If Emily had 5 cents, and gave 4 cents for
paper, how many cents had she left?
11. How many are 6 less 4? 7 minus 4 are how
many?
12. How many are 8 less 4? 9 minus 4 are how
many ?
13. How many are 10 books less 4 books? 11 hats
less 4 hats?
14. How many are 12 minus 4? 13 less 4 are how
many ?
15. Form the subtraction tables of threes and fours.
TABLES.
3 — 3 = 8 — 3-5
4 — 4 = 9 — 4 = 5
4—3 = 1 9 — 3 = 6
5 — 4=1 10 — 4 = 6
5 — 3 = 2 10 — 3 = 7
6 — 4 = 2 11—4 = 7
6 — 3 = 3 11 — 3 = 8
7 — 4 = 3 12 — 4 = 8
7 — 3 = 4 12 — 3 = 9
8—4 = 4 13 — 4 = 9
36
FIRST LESSONS
LESSON XXII.
1. There were 7 cents in a box, and William
took out 3. How many cents were left in the box^^
2. A merchant bought 12 lamps, and sold 4 of
them. How many had he left?
3. John has 10 marbles, and Henry has 3. How
many more has John than Henry ?
4. A woman who had 9 yards of calico, used 4
yards. How many yards had she left?
5. 8 — 2--? 9 — 2 = ? 10 — 3 = ?
6. 6 — 3 = ? 13 — 4 = ? 11 — 4 = ?
7. A man bought 9 barrels of flour, and sold all
but 3 of them. How many barrels did he sell?
9 — 3 = ?
8. A man bought a boat for 11 dollars, and sold
it for 4 dollars. How much did he lose?
9. 3 from 12 leave how many? 12 — 3 = ?
10. William had 10 cents. He spent 1 cent for
a pencil and 3 cents for paper. How many cents
had he left?
11. Carrie had 12 apples, but she gave 2 to her
sister and 1 to her brother. How many apples had
she left?
12. How many are 6 less 2? 9 less 1 are how
many ?
13. There were 11 passengers in a stage-coach, 5
of whom got out. How many remained ?
14. 8 — 3 = ? 7 — 1=? 12 — 4 = ?
15. How many are 8 less 2? 8 — 2 = ?
in arithmetic. 37
Slate Exercises.
Copy, subtract, and add the following :
48 7 9 8 6 5 7
24232132
3^^C
IjESSON XXIII.
1. A woman had 5 quarts of berries, and sold 5
quarts. How many had she left? 5 — 5 = ?
2. If 6 gallons of water run into a cistern in one
hour, and 5 run out in the same time, how many gal-
lons remain ? 6 — 5 = ?
3. 5 books from 7 books leave how many books ?
4. A merchant bought 8 penknives, and sold 5 of
them. How many had he left?
5. Henry had 9 fish-hooks, and gave 5 of them to
Martin. How many had he left?
6. How many are 10 less 5? 11 less 5?
7. 5 pencils from 12 pencils leave how many
pencils ?
8. 5 from 13 leave how many? 5 from 14?
9. In a class there are 7 girls and 6 boys. How
many more girls are there than boys?
10. From a bunch of 8 keys, 6 keys were lost.
How many keys were not lost?
11. A boy having 9 pennies, lost 6. How many
had he left? 9 — 6 = ?
38
FIEST LESSONS
12. 6 from 10 leave how many? 6 from 11 = ?
13. How many are 12 less 6 ? 13 minus 6 are how
many ?
14. A farmer who had 14 bushels of potatoes, sold
6 bushels. How many bushels had he left?
15. How many are 15 boys less 6 boys? 15 — 6
= 2
16. Form the subtraction tables of fives and sixes.
TABLES.
5 — 5 = 10 — 5-=5
6 — 6 = 11 — 6 = 5
6 — 5 = 1 11 — 5 = 6
7 — 6 = 1 12 — 6 = 6
7 — 5 = 2 12 — 5 = 7
8 — 6 = 2 13 — 6 = 7
8 — 5 = 3 13 — 5 = 8
9 — 6 = 3 14—6 = 8
9 — 5 = 4 14 — 5 = 9
10 — 6 = 4 15 — 6 = 9
Dj^C
liESSON^ XXIV.
1. A man who earned 7 dollars a week, saved only
2 dollars. How much did he spend? 7 — 2 = ?
2. A woman bought 9 yards of calico, and used 5
yards of it. How many yards had she left?
3. Henry had 11 rabbits, and James had 8. How
many had Henry more than James?
4. Rush is 14 miles from Geneseo, and Avon is 9
mile^ from Geneseo, on the same road. How much
farther from Geneseo is Rush than Avon?
IN ARITHMETIC.
39
, 6. James had 8 marbles, but lost 2 of them.
How many marbles had he left? 8 — 2 = ?
6. A boy caught 9 pig-
eons, and gave 4 of them to
a poor woman. How many
had he left? ^ — 4 = ?
7. If 6 gallons of water
run into a cistern in one
minute, and 5 gallons run
out, how much is the cis-
tern filled?
8. Ned had 6 chickens,
but the cat killed 3 of them. How many were left?
9. 7 — 1=? 9 — 6 = ? 8 — 5 = ?
10. 13 — 5 = ? 15 — 4 = ? 13 — 2 = ?
11. How many sheep are 9 sheep less 3 sheep?
12. A carriage-maker had 15 carriages, and sold 9
of them. How many had he left?
- 13. A clothier sold 8 coats, 6 of which were for
boys and the rest for men. How many of the coats
were for men?
14. Martha is 12 years old, and Mary is 4. How
many years older than Mary is Martha.
15. 6 + 8 — 1=? 4 + 5 — 3 = ? 3 + 7 — 2 = ?
16. 7 + 1 — 3 = ? 5 + 3 — 6 = ? 7 + 4 — 1 = ?
17. How many are 7 and 3 less 2?
-18. In a basket containing 12 oranges, 4 were de-
cayed. How many were sound?
'19. Amasa picked 16 quarts of berries, and sold 6
quarts of them. How many quarts had he unsold ?
40 fiest lessons
Slate Exercises.
Copy, subtract, and add the following:
97897847
4 2 5 6 6 3 12
aj^c
LESSON XXV.
1. Eichard saw 8 ducks in a pond, 7 of which
swam away. How many remained?
2. In a class of 9 children 7 are boys. How
many are girls ? 9 — 7 = ?
3. A cooper made 10 firkins, and sold 7 of them.
How many had he left? 10—7 = ?
4. William is 11 years old, and Thomas is 7.
How much older is William than Thomas?
5. A house has 12 windows, 7 of which are in
the first story, and the rest in the second story.
How many are there in the second story?
6. How many are 13 less 7? 14 less 7?
7. A farmer who had 15 turkeys, sold 7 of them.
How many had he left? 15 — 7==?
8. There were 16 bottles on a shelf, 7 of which
were filled with pickles, and the remainder with
fruit. How many were filled with fruit?
9. There were 9 passenger-cars on a railroad track,
8 of which were filled with passengers. How many
were empty?
IN ARITHMETIC.
41
10. How many are 10 less 8? 11 less 8? 12
less 8?
11. A merchant had 13 barrels of salt, and sold
8 of them. How many barrels remained unsold?
12. 14—8-=? 15 — 8 = ? 16 — 8 = ?
13. How many are 17 trunks less 8 trunks?
14. Form the subtraction tables of sevens and
eights.
TABLES.
7 — 7=0 12 — 7 = 5
8 — 8 = 13 — 8 = 5
8 — 7=1 13 — 7 = 6
9 — 8 = 1 14 — 8 = 6
9 — 7=2 14—7 = 7
10—8 = 2 15 — 8 = 7
10—7=3 15 — 7 = 8
11 — 8 = 3 16 — 8 = 8
11 — 7=4 16 — 7 = 9
12 — 8 = 4 17 — 8 = 9
Dj^C
IiESSO:N^ XXVI.
1. There were 12 musk-rats in traps, but 2 es-
caped. How many were there left in the traps?
2. Helen had 6 violets, and Jennie had 16. How
many more had Jennie than Helen?
3. What number added to 6 makes 16 ?
4. 5 + 8 + 2 — 5 = ? 7 + 3 + 4 — 7 = ?
5. Henry gave his sister 12 figs. She gave 3 to
Sarah and 5 to Flora. How many had she left?
12 — (3 + 5)=?
6. 12 are how many more than 5?
4
42 FIRST LESSONS
7. 16 are how many more than 9?
8. What number added to 8 makes 16?
9. What number added to 5 makes 13?
10. Edgar having 14 phims, exchanged 5 of them
for an orange. How many had he left?
11. How many are 14 less 8? 13 less 7?
12. Henry caught 7 pigeons at one time, 3 at
another, and then sold 4 of them. How many had
he left? 7 + 3 — 4=-:?
13. Frank earned 13 dollars and George earned 6.
How many dollars more did Frank earn than George ?
14. There were 11 trunks on a baggage-wagon, 7
of which the baggage-man left at the depot. How
many were left in the wagon?
15. Out of 15 vases which were in a basket 6
were broken. How many were uninjured?
16. Mr. Jones planted 17 shade-trees, but 5 of
them died. How many lived?
17. In a class of 19 all but 6 were promoted.
How many were promoted?
18. There were 14 persons on board a ship that
was wrecked, of whom 8 were saved. How many
were lost?
19. 16 + ?=-18. 18 — ?=-12. 13 + ? = 19.
Slate Exercises.
Copy, subtract, and add the following:
97867587
33424231
IN ARITHMETIC.
43
LESSOIST XXVII.
1. Eobert's father gave him 10 doves, but 9 of
them died because they were not properly cared for.
How many of them lived?
2. Eva solved 11 exam-
ples, 9 of which were correct.
How many were wrong?
3. A painter bought 12
gallons of oil, and used 9
gallons. How many gallons
had he left?
4. A grocer bought 13 casks of vinegar, and sold
9 casks. How many casks had he left?
5. How many are 14 less 9? How many are 15
less 9? 15 — 9=-? 15 — ? = 9.
6. From a group of 16 boys 9 ran away. How
many were left? 16 — 9 = ? 16 — ? = 9.
7. 9 from 17 leave how many? 17 — 9==?
8. How many are 18 less 9? 18 — 9 = ?
9. A merchant bought 11 chests of tea, and sold
all but 1 of them. How many did he sell? 11 —
10 = ? 11_?:=10.
10. A boy had 12 steel-pens, and gave away 10
of them. How many had he left?
11. A man bought 13 tons of hay, and, after feed-
ing 10 tons to his horses, sold the rest. How many
tons did he sell? 13 — 10 = ? 14 — 10 = ?
12.15 — 10 = ? 16 — 10 = ? 17 — lj[V=^f'
13. 18 — 10 = ? 18 — ? = 10. lO-l-Z^-lS.
li-
44
FIRST LESSONS
14. A merchant bought 18 whips, and sold all but
How many did he sell? 18 — 8 = ?
15. How many are 19 stoves less 10 stoves?
16. Form the subtraction tables of nines and tens.
TABLES.
9_9--0 14 — 9 = 5
10—9 = 1 15 — 9 = 6
11 — 9 = 2 16 — 9 = 7
12 — 9 = 3 17 — 9 = 8
13_9 = 4 18 — 9 = 9
10 — 10 = 15—10 = 5
11 — 10 = 1 16 — 10 = 6
12 — 10 = 2 17 — 10 = 7
13 — 10 = 3 18 — 10 = 8
14 — 10 = 4 19 — 10 = 9
5>»iC
liESSO?^ XXTIII.
1. Begin with 1 and count to 11 by 2's.
2. Begin at 11 and count back to 1 by 2's.
3. Count 15 by 3^s. Count 16 by 4's.
4. Count back from 15 to by 3's.
5. Count back from 20 to by 5's.
6. Henry had fifteen dollars. He gave 2 dollars
for a hat, 3 dollars for a vest, and 6 dollars for a
coat. How much had he left?
7. What number added to 3 makes 10?
8. What number added to 9 makes 17?
9. A harness-maker having 19 harnesses, sold all
but 9. How many did he sell? 19 — ? = 9.
IN ARITHMETIC. 45
10. How many are 2 + 2? 2 + 12? 3 + 2? 3
+ 12? 4 + 2? 4 + 12? 5 + 2? 5 + 12?
11. How many are 3 + 3? 3 + 13? 4 + 5? 4
+ 15? 5 + 6? 5 + 16? 7 + 6? 7 + 16?
12. How many are 3 + 6? 3 + 16? 4 + 6? 4
+ 16? 5 + 8? 5 + 18? 5 + 9? 5 + 19?
13. How many are 3 + 5? 3+15? 4 + 5? 4
+ 15? 8 + 6? 8 + 16? 8 + 7? 8 + 17?
14. In the barn were 12 horses, but 5 of them
were taken out. How many remained?
15. 10 chestnuts from 16 chestnuts leave how many
chestnuts? 16 — 10 = ?
16. A grocer bought 19 brooms. He sold 3 at one
time, 5 at another, and 4 at another. How many
had he left? 19 — 3 + 5 + 4=-?
17. A lady purchased 4 dollars' worth of silk, 3
dollars' worth of velvet, 7 dollars' worth of lace, and
1 dollar's worth of linen. She gave in payment 20
dollars. How much should be returned to her?
Slate Exercises.
Copy and add the following:
4 5 3 2 6 1
4 5 3 2 6 1
4 5 3 2 6 1
Copy and subtract the following:
896789775
652523413
46
FIRST LESSONS
LESSOINr XXIX.
A man having 18 butter-tubs, sold 3 at one
5 at another, and 6 at another. How many
tubs had he left?
2. In a room there are 14 flower-
pots. There are 4 in one window, 5 in
another, and the rest are in the third
^r window. How many are there in the
<^li/,J^ third window?
3. On the first vine there are 12
bunches of grapes, on another there are
3 bunches, and on another 4 bunches.
How many bunches more are there on
the first vine than on the other two?
12 — (3-1-4)=?
4. How many are 7 and 5 less 3?
5. There are 13 boys playing ball,
and 5 playing marbles. How many
more are there playing ball than there
are playing marbles? 13 — 5 = ?
6. What is meant by the term addi-
)n? What is meant by the term subtraction?
7. Julia is 9 years old, and her sister is 5 years
der. What is the age of her sister?
8. Charles is 6 years old, and James is 17 years
d. How much older than Charles is James?
9. What number added to 7 will make 15?
10. What number added to 5 will make 12?
IN ARITHMETIC. 47
11. Begin with 2 and count to 17 by 3's.
12. Count from 19 back to 1 by 3's.
13. What number subtracted from 18 will leave
10? 18 — ?=10. 18 — 10 = ?
14. What number subtracted from 16 will leave
9? 16 — ? = 9. 16 — 9=?
15. In a school of 18 pupils all but 3 study ge-
ography. How many study geography?
16. James attended school 17 weeks, but Henry at-
tended only 8 weeks? How many weeks did James
attend more than Henry? 17 — 8 = ?
17. Julius had written all but 5 lines on a page
of his writing-book. If the book had 19 lines on
a page, how many had he written?
18. How many are 3 + 3 + 2 + 2 — 4+5 — 2 + 7?
19. How many are 5 + 7 + 1 — 3 — 2 + 5 — 9 + 8?
20. How many are 6 + 4 + 5 — 3 — 6 — 2 + 8 + 9?
21. How many are 8 — 3 + 2 — 3 + 6 + 2—6 + 2?
22. How many are 6 + 8 — 7 — 2 + 5 + 6 + 1—4?
Slate Exercises.
Copy and add the following:
56456532
4 2 2 12 9 4 3
35184657
Copy and subtract the following:
69864987
55712342
48 FIRST LESSONS
REVIEW EXERCISES.
Find the value of each of the following :
8-2
9-3 8-
-4
9-6
6-2
7 — 5
8 — 3 7-
-5
6-3
8 — 7
4 — 1
9 — 4 7-
-2
9-2
8-3
6 — 6
6 — 1 8-
-2
6-4
7 — 3
7 — 2
5 — 2 6-
-4
8 — 3
9-7
8 — 5
9 — 4 8-
-1
6 — 5
7-3
12-4
15 — 6 13-
-6
14—9
16-6
15-6
17 - 9 12 -
-8
11 — 4
15-7
13 — 4
10-5 14-
-9
13-9
11 — 8
18 — 9 :
17—8 10-
-8
11-8
16-9
15 — 6
13 _ 7 15-
-6
12-7
14-5
ind the vaL
Lie of the following, without using slat
3 + 2-4
4 + 6 — 5
6 + 3-2
5 + 6-8
4 — 3 + 6
9 — 4 + 2
6 + 5-8
5 + 6-9
5 + 8 — 7
6 + 9 — 5
9-
-5 + 2
6 + 7 — 6
4+7 — 3
5 + 6-9
8 + 7 — 9
6 — 3 + 4
8 + 5-3
9-6-2
9-
-8 + 6
8-3-4
9 — 6 + 5
9 + 5-6
8 + 2-6
9-3+2
7 — 2 + 5
8 — 3 + 4
6 + 3 — 8
7 + 5 — 9
8 — 4 + 3
6 — 4 + 2
7-
-5 + 6
9 — 7 + 2
9 + 2-8
8 + 6 — 9
7 + 3-4
9 — 4+2
8 + 3 — 9
8 — 6 + 2
9-
-7 + 3
8-6-2
8 — 2-4
9-3 — 6
8-
-6 + 2
8 + 6 — 9
9 — 3 + 6
9 + 2-8
9-
-6 + 4
8-3 + 7
6 — 4 + 2
6-4-2
8 + 3 — 9
8 — 3 — 4
IN ARITHMETIC. 49
REVIEW EXERCISES.
Copy and find the value of the following:
6 + 3 — 4 + 2—6 7 — 3 + 8 — 6 + 2
5 — 3 + 7 — 2 — 6 8 — 3 + 6 — 5 — 4
5 + 9 — 8 — 3 + 2 7 — 5 + 4 + 2 — 8
9__3 + 2 — 6 + 4 9 — 3 — 4 + 6 + 2
5 + 6 + 3 — 3 — 9 9 — 3 + 6-3-8
8 + 3 — 7 — 4 + 2 5 + 2 — 3 + 6 — 4
9 — 3 + 6 — 4 + 8 8 — 3 + 7 + 2 — 6
9 — 4 + 3 + 2 — 6 9 — 4 + 3 + 2 — 8
5+2 — 3 + 4 — 8 2 + 6 — 3 + 7 — 5
9—3+4—3+2 6—3+4—6+2
4+2 — 3 + 6 — 4 7 — 3 + 2 — 6 + 4
When an example has several numbers inclosed in a parenthesis,
find the value of those within the parenthesis first, and then of this
result, and the rest of the numbers.
Thus,4 + 6 — (3 + 2 — 4)=4 + 6 — 1; for (3 + 2 — 4) = 1.
Copy and find the value of the following:
5 + 8— (3 + 6 — 2) 6 + 8 — (7 — 2 + 6)
6 + 3 + (4 — 3 + 2) 7 + 3 — (5 + 2 — 6)
5 + 4 — (6 + 2 — 5) 9 — 2 + (6 — 4 + 2)
5 — 4 — (8 + 2 — 9) 8 + 6--(2 + 3 — 1)
6 + 8 — (3 + 4 — 2) 8 — 4+ (8 — 6 + 4)
9 — 3 + (2 + 6 — 4) 9 + 8 — (8 — 3 + 2)
9 + 6 — (3 — 2 + 7) 9 — 7— (8 — 6— 2)
8 — 3 + (2 + 6 — 3) 9 + 2 — (7 — 4 — 2)
6 + 5— (6 — [8— 3]) 2 + 6 — (3 — [4 — 3])
50 FIRST LESSONS
LESSON- XXX.
1. How many quails are there in each group?
2. Express ten on your slates.
3. How many quails are there in two of the
groups ?
4. How many are 1 ten and 1 ten?
5. Express 2 tens, or twenty : 20. What does
the 2 represent? What does the show?
6. Express 2 tens and 1, or twenty-one : 21.
7. Express 2 tens and 2 ones, or twenty-two.
8. Express twenty-three, twenty-four, twenty-five,
twenty-six, twenty-seven, twenty-eight, twenty-nine.
9. Read the numbers you have written.
10. How many quails are there in the 3 groups?
11. Express 3 tens, or thirty: 30. What does the
figure 3 represent? What does the show?
12. Express 3 tens and 1, or thirty-one. 3 tens
and 2 ones, or thirty-two.
13. Express all the numbers from thirty-two to
thirty-nine.
14. Express 4 tens, or forty. Express 4 tens and
1, or forty-one.
IN ARITHMETIC. 51
15. Express the numbers from forty-one to forty-
nine.
16. When two figures are written side by side,
what does the figure at the right represent?
17. What does the figure at the left represent?
18. Write all the numbers from one to forty-nine.
19. Express in words: 24, 32, 38, 47, 18, 29, 10,
31, 49, 30.
liESSON XXXI.
1. Express 5 tens, or fifty: 50.
2. How many figures are required to represent
the number fifty?
3. What is the figure at the right?
4. What is the figure at the left?
5. How many tens are there in fifty?
6. Express 5 tens and 1, or fifty-one.
7. Write the numbers from fifty-one to fifty-nine.
8. Express 6 tens, or sixty : 60.
9. Write the numbers from sixty to sixty-ninco
10. Express the number seventy.
11. How many tens are there in seventy?
12. How many ones are there in seventy? How
is this shown?
13. Write the numbers from seventy to seventy-
nine. Read them.
14. Write the numbers from eighty to eighty-
nine. Read them.
52 FIRST LESSONS
15. How many tens and ones are there in eighty-
seven? In eighty-five? In eighty-eight?
16. Express in figures the numbers from eighty
to eighty-eight.
17. Write 8 tens and 9 ones, or eighty-nine.
18. Express 9 tens, or ninety : 90.
19. Write the numbers from ninety to ninety-nine.
20. Ninety-nine and one more, make how many?
One hundred.
21. How many tens are 9 tens and 1 ten?
22. How many tens are there in one hundred?
23. One hundred is expressed thus : 100,
The figure at the right shows that there are no
ones, the next to it shows that there are no tens,
and the figure 1 shows that there is one hundred.
When three figures are written side by side, the fig-
ure in the first place at the right represents ones, the
one next to it tens, and the one at the left hundreds.
Slate Exercises.
Express in figures the following :
Thirty-two Eighty Forty-nine
Ninety-six Eighteen Sixty-seven
Eighty-four Seventy-one Thirty-three
Forty-seven Twenty-nine Thirty-eight
Copy and express in words the following:
36 52 28 77 78
84 81 39 29 55
IN ARITHMETIC. 53
liESSOlS^ XXXII.
* 1. If you pay 1 cent for a pear, how many cents
will you pay for 2 pears?
2. How many cents are 1 cent and 1 cent?
3. If you pay 1 cent for a slate-pencil, how many
cents will you pay for 3 pencils?
4. How does the price of 3 pencils compare with
the price of 1 pencil?
5. If a fig costs one cent, how many times 1 cent
will 4 figs cost?
6. How many chairs are 5 times 1 chair?
This sign X takes the place of the word times.
Thus, 2 times 1 are 2, is written 2X1 = 2, and is
read 2 times 1 equals 2.
7. If 1 marble costs 1 cent, what will 6 marbles
cost? 6X1=^6.
8. Seven boys each own a sled. How many sleds
do they all own ? 7 X 1 = ?
9. Each of 8 boys has a pair of skates. How
many pairs do they all own ? 8 X 1 = ?
10. Nine men each own an acre of land. How
many acres do they all own ? 9 X 1 = ?
11. How many are 10 times 1? 10 X 1=?
12. How many are 3 times 1 ? 3 X 1 =?
13. If you pay 1 cent for an apple, how many
cents will you pay for 7 apples?
14. If each pupil, in a class of 9 pupils, answers
1 question, how many questions will they all answer?
54 FIRST LESSONS
liESSON^ XXXIII.
1. A horse has 2 eyes. How many eyes have 2
horses? How many eyes are 2 times. 2 eyes?
2. A horse has 2 ears.
How many ears have 3
horses? 3X2==?
~ 3. If 1 rocking-horse
costs 2 dollars, what will
4 rocking-horses cost? 4
X2 = ?
4. If a boy goes to
school only 2. days each week, how many days will
he attend in 5 weeks?
5. A boy read 2 pages of his book each day for
6 days. How many pages did he read in that time?
6. If a boy earn 2 dollars a week, how many
dollars will he earn in 7 weeks ? 7X2 = ?
7. What will 8 sheets of blotting-paper cost at
2 cents a sheet? 8X2=?
8. What will 9 pairs of shoes cost at 2 dollars
a pair? 9X2 = ?
9. How many cents are there in 10 two-cent
pieces ?
10. If it requires 2 yards of cloth to make a child's
cloak, how many yards will it require to make ^
such cloaks?
A short process of adding equal numbers is called
Multiplication,
IN ARITHMETIC
55
11. Form the multiplication tables of ones and
twos.
TABLES.
1X1-1 6X1- 6
1X2— 2 6X2 — 12
2X1 — 2 7X1— 7
2X2— 4 7X2 — 14
3X1—3 8X1— 8
3X2— 6 8X2 — 16
4X1=4 9X1— 9
4X2— 8 9X2 — 18
5X1 — 5 10X1 — 10
5X2 — 10 10X2 — 20
3>>iC
IjESSOX XXXIV.
1. If a boy walks 3 miles in 1 hour, how many
miles will he walk in 2 hours ? 2X3 — ?
2. What will 3 engravings cost at 3 dollars each ?
- 3. Martha put 3 tulip bulbs in each of 4 pots.
How many bulbs did she plant ? 4X3 — ?
4. Each of 5 boys threw 3 stones into the water.
How many stones did they all throw ? 5X3 — ?
5. If the pupils learn 3 songs in a month, how
many songs will they learn in 6 months?
6. If there are 3 cherries in 1 bunch, how many
cherries are there in 7 such bunches?
7. If there are 8 boats, and 3 boys in each boat,
how many boys are there in the boats?
8. If there are 3 globes on 1 chandelier, how
many globes are there on 9 such chandeliers?
56
FIRST LESSONS
9. If a boy gives 4 cents for 1 orange, how many
cents will he give for 2 oranges ? 2X4 = ?
10. A lumberman put 4
logs in the river each day
for 3 days. How many
logs did he put in the
river? How many are 3
times 4? 3X4 = ?
11. If there are 4 crows
sitting on each of 4 limbs
of a tree, how many crows
are there on the tree ? 4X4 = ? How many are 4
times 4?
12. What will 6 tons of hay cost at 4 dollars a
ton ? 5X4 = ?
13.6X4 = ? 7X4 = ? 8X4 = ? 9X4 = ?
14. How many girls are there in 10 groups of 4
girls each ? 10X4 = ?
15. If a man can walk 4 miles in an hour, how
far can he walk in 6 hours? 6X4 = ?
16. Form the multiplication tables of threes and
fours.
TABLES.
1X3= 3
6X3 = 18
1X4= 4
6X4 = 24
2X3= 6
7X3 = 21
2X4= 8
7X4 = 28
3X3= 9
8X3 = 24
3X4 = 12
8X4 = 32
4X3 = 12
9X3 = 27
4X4 = 16
9X4 = 36
5X3 = 15
10X3 = 30
5X4 = 20
10X4 = 43
IN ARITHMETIC. 57
liESSOlSr XXXY.
1. If 1 man builds 2 rods of fence in one day,
how many rods can 5 men build in the same time?
2. If a shoe-maker makes 4 pairs of shoes in 1
day, how many pairs will he make in 6 days?
6X4-=?
3. If a turner can turn 3 rolling-pins in 1 min-
ute, how many can he turn in 8 minutes? 8X3 = ?
4. If a woman sells 4 quarts of milk a day, how
many quarts does she sell in 9 days ? 9X4 = ?
5. In 1 pint there are 4 gills. How many gills
are there in 5 pints ? 5X4 = ?
6. A boy bought 4 pints of chestnuts at 3 cents
a pint, and sold them for 20 cents. How much did
he gain ? 4X3 = ?
7. (5X3)-f(3X4) = ? (4X2) + (6X3)=?
8. If a boy husks 3 bushels of corn in 1 hour, how
many bushels will he husk in 7 hours ? 7X3 = ?
9. If 2 yards of lace will make 1 curtain, how
many yards are required to make 4 curtains?
10. In 1 bushel there are 4 pecks. How many
pecks are there in 7 bushels ? 7X4 = ?
11. How many are 9 times 2? 7X2? 5X2?
12. If there are 4 blades in 1 pocket-knife, how
many blades are there in 10 such knives? 10 X 4 = ?
13. What will be the cost of 9 historical charts
at 3 dollars each? 9X3 = ?
14. If in 1 field there are 4 acres, how many
acres are there in 4 such fields ? 4X4 = ?
58
FIRST LESSONS
Slate Exercises.
Copy and multiply the following :
3 2 4 3 2 4
5 4 8 7 9 6
>>©4c
IiESSO:N^ XXXTI.
1. John gave 5 cents apiece to each of 2 beggars.
How much did he give to both ? 2X5 = ?
2. If a boat sails 5
miles in 1 hour, how
far will she sail in 3
hours? 3X5 = ?
3. In each of 4
nests there are 5 eggs.
How many eggs are
there in the 4 nests?
How many are 4 times 5 ? 4X5 = ?
4. What will 5 barrels of flour cost at 5 dollars
a barrel ? 5X5 = ?
5. A cartman can draw 5 barrels of salt at 1 load,
How many barrels can he draw in 6 loads? How
many are 6 times 5?
6. What will 7 bunches of matches cost at 5 cents
a bunch ? 7X5 = ?
7. How many are 8 times 5? How many are 9
times 5 ?
IN ARITHMETIC. 59
8. How many cents are there in 10 five-cent
pieces? 10X5 = ?
9.4X5 = ? 3X5 = ? 7X5 = ? 8X5 = ?
10. There are 6 lamps on each of 2 shelves. How
many lamps are there on both shelves ? 2X6=?
11. If 6 bushels of wheat can be ground in 1 hour,
how many bushels can be ground in 3 hours? How
many are 3 times 6?
12. If a boy writes 6 lines in his writing-book
ach day for 4 days, how many lines will he write?
How many are 4 times 6?
13. If a man pays 6 dollars at 5 different times,
how many dollars will he pay? 5X6 = ?
14. How many are 6 times 6? How many are 7
times 6?
15. In 1 package there are 6 drawing-pencils.
How many pencils are there in 8 such packages?
8X6 = ?
16. How many are 9 times 6? 10 times 6 are
how many ?
17. Form the multiplication tables of fives and
sixes.
TABLES.
1X5= 5 6X5 = 30
1X6= 6 6X6 = 36
2X5 = 10 7X5 = 35
2X6 = 12 7X6 = 42
3X5 = 15 8X5 = 40
3X6 = 18 8X6 = 48
4X5 = 20 9X5 = 45
4X6 = 24 9X6 = 54
5X5 = 25 10X5 = 50
5X6 = 30 10X6 = 60
60 FIRST LESSONS
I.ESSON XXXTII.
1. If a croquet-player drives a ball through 2
arches at each stroke, through how many arches
will he drive it by 3 strokes ? 3X2 = ?
2. How many are 9 sleds, 2 sleds, and 8 sleds?
3. A boy who shot 18 prairie-chickens, gave 2 to
George, 3 to Henry, and 7 to Caspar. How many
had he left? 18 — (2 + 3 + 7) = ?
4. A man bought 6 bushels of wheat at 2 dol-
lars a bushel, and 8 bushels of barley at 1 dollar a
bushel. What did he pay for both?
5. How many soldiers are there in 4 squads of
5 soldiers each?
6. (6X2) + (8X1)=? (3X5) + (4X1)=?
7. (4X2) + (3X3) = ? (2X5) + (2X3)=?
8. How many feet have 4 dogs? 7 dogs?
9. How many eyes have 6 horses? 9 horses?
10. How many legs have 6 rabbits? 8 rabbits?
11. How many wings have 10 birds? 7 birds?
12. From a bin containing 16 bushels of potatoes
4 bushels were taken at one time, and 6 at another.
How many bushels remained in the bin?
13. A woman had a jar of butter, containing 20
pounds. She used 5 pounds one week, 6 pounds
the next week, and the remainder the third week.
How much did she use the third week?
14. There are 3 feet in 1 yard. How many feet
are there in 7 yards?
15. 10 + 6 — (4X2)=? 12 — 3 + (5X6) = ?
IN ARITHMETIC. 61
16. A drover had 6 cows in one field, 8 cows in
another, and 12 in another. How many cows had
he in the three fields?
17. If a girl can pick 3 quarts of berries in 1
hour, how many quarts can she pick in 3 hours?
Slate Exercises
Copy and multiply the following :
6543273643
5798947987
>»-o<v-
r.ESSOK XXXTIII.
1. In 1 week there are 7 days. How many days
are there in 2 weeks? 2X7==?
2. How many rods of ditch were dug, if 7 rods
were dug each day for 3 days ? 3X7 = ?
3. If there are 7 pickets in 1 gate, how many
pickets are there in 4 such gates ? 4X7 = ?
4. How many tomatoes are there, if there are 7
tomatoes on each of 5 plants ? 5X7 = ?
5. If there are 7 flags displayed at each of 6
windows, how many flags are displayed ? 6X7 = ?
6. What will a man receive for setting 7 panes
of glass at 7 cents a pane ? 7X7 = ?
7. If you can make 7 marks in 1 second, how
many marks can you make in 8 seconds ? 8 X 7 =: ?
62 FIEST LESSONS
8. If it takes 9 men 7 days to do a piece of work,
how long will it take 1 man to do it ? 9X7 — ?
9. How much will Henry earn in 10 weeks, if
he earns 7 dollars a week? 10X7=?
10. If a woman packs 8 pounds of butter in 1
week, how much will she pack in 2 weeks ? 2X8==?
11. What will 3 pounds of raisins cost at 8 cents
a pound ? 3X8 = ?
12. How many are 4 times 8? How many are
5 times 8?
13. If a man draws 8 loads of grain in 1 day,
how many loads will he draw in 6 days ? 6X8 = ?
14. If there are 8 candles in 1 pound, how many
candles are there in 7 pounds ? 7X8 = ?
15. What will 8 quarts of cherries cost at 8 cents
a quart? 8X8 = ?
16. If a cooper sells 8 barrels each day for 9 days,
how many barrels will he sell ? 9X8 = ?
17. If 8 pupils can sit on 1 seat, how many pupils
can sit on 10 such seats? 10X8 = ?
18. Form the multiplication tables of sevens and
eights.
TABLES.
1X7= 7 6X7=42
1X8= 8 6X8=48
2X7=14 7X7=49
2X8=16 7X8=56
3X7=21 8X7=56
3X8=24 8X8=64
4X7=28 9X7=63
4X8=32 9X8=72
5X7=35 10X7=70
5X8=40 10X8=80
INARITHMETIC. 63
liESSOlS^ XXXIX.
1. A boy having 24 cents, bought 2 oranges at 6
cents apiece. How many cents had he left? 24 —
(2X6)=?
2. John sold 3 bananas at 8 cents apiece, and 2
cups of peanuts at 5 cents a cup. What did he re-
ceive for the whole? '
3. Henry solved 7 examples on Monday, 5 on
Tuesday, and 9 on Wednesday. How many exam-
ples did he solve in the three days?
4. If he solved 16 examples the next week, how
many examples more did he solve the first week than
the second?
5. Count to 50 by lO's. Count to 30 by 5's.
6. How many are 2 and 4? 2 and 14? 2 and
24? 2 and 34?
7. How many are 4 and 5? 4 and 15? 4 and
25? 4 and 35?
8. How many are 5 and 6? 15 and 6? 25 and
6 ? 35 and 6 ?
9. If a horse eats 3 bushels of oats in one week,
how many bushels will he eat in 8 weeks?
10. AVhat is the cost of 7 cakes of soap at 10 cents
a cake?
11. A boy Avorked 7 weeks for 8 dollars a week,
and spent 20 dollars for clothes. How much money
had he left? (7X8) — 20 = ?
12. If a wheel has only 7 spokes, how many spokes
will 7 such wheels have?
64 FIRST LESSONS
13. A man earns 16 dollars a week, and his son
earns 10 dollars. How much do they both earn?
14. How much more does the father earn than
the son?
15. If a mechanic earns 5 dollars a day for 2 days,
and 6 dollars a day for 3 days, how much money
will he earn in that time? (2 X 5) + (3 X 6) = ?
16. A boy sold 2 chickens for 3 dimes each, and
2 dozens of eggs at 2 dimes a dozen. How many
dimes did he receive?
17. What will be the cost of 2 pairs of pantaloons
at 6 dollars a pair, and 3 vests at 3 dollars each?
18. What will be the cost of 8 ounces of candy at
5 cents an ounce, and 2 packages of envelopes at 15
cents a package?
19. How many days are there in 7 weeks? How
many are 7 times 7?
20. If a family burns 8 tons of coal worth 6 dol-
lars a ton, and 5 cords of wood worth 5 dollars a
cord, how much will the fuel cost?
21. If 4 chairs are bought at 5 dollars apiece, and
3 tables at 6 dollars each, how much will they all
cost?
• 22. 4+5 + (3X8)=? (2X6) + 5 — 3-?
Slate Exercises.
Copy and multiply the following:
876945768 5
568476863 5
I
IN AKITHMETIC.
65
1. A man bought 2 loaves of bread at 9 cents a
loaf. How much did they cost him ? 2 times 9 = ?
2. If there are 9
rose-buds in one bou-
quet, how many rose-
buds are there in o
such bouquets?
3. If it require 9 !^'
tons of coal to run a
train of cars one trip,
how many tons will it
require to run 4 such trips ? How many are 4X9?
4. In one square yard there are 9 square feet.
How many square feet are there in 5 square yards?
5. At 9 dollars a barrel, what will 6 barrels of
flour cost?
6. In an orchard there are 9 trees in a row, and
7 rows. How many trees are there in the orchard?
7. What will 8 pounds of nails cost at 9 cents a
pound?
8. When sugar is selling at 9 cents a pound, how
much will 9 pounds cost? 9X9 = ?
9. How many cents must be paid for 10 yards of
muslin at 9 cents a yard? 10 X 9 = ?
10. Mary is 10 years old, and her sister is twice
as old. How old is her sister? 2 X 10 = ?
11. There are 10 cents in a dime. How many
cents are there in 3 dimes? 3X10^=?
6
eQ
Fill ST LESSONS
12. If one shelf will hold 10 books, how many
books will 4 such shelves hold ? 4 X 10 = ?
13. In one dollar there are 10 dimes. How many
dimes are there in 5 dollars ? 5X10 = ?
14. Henry received 10 credit marks per day for
6 days. How many did he receive? 6X10 = ?
15. If 10 marbles can be bought for 1 cent, how
many can be bought for 7 cents? 7 X 10 = ?
16. If there are 10 weeks in one term of school,
how many weeks are there in 8 terms? 8X10 = ?
17. A farmer sold 9 hogs at 10 dollars apiece.
How many dollars did he get for them? 9 X 10 = ?
18. If sewing needles cost 10 cents a paper, what
will 10 papers cost? 10X10 = ?
19. Form the multiplication tables of nines and
tens.
TABLES.
1X9= 9 6X9=54
1X10=10 6X10= 60
2X9=18 7X9=63
2X10=20 7X10= 70
3X9=27 8X9=72
3X10=30 8X10= 80
4X9=36 9X9=81
4X10=40 9X10= 90
5X9=45 10X9=90
5X10=50 10X10=100
Slate Exercises.
Copy and multiply the following :
5 3 6 5 4 5 4
4 2 3 7 3 8 7
7
10
INAEITHMETIC. 67
liESSON^ Xlil.
1. If thera are 8 goslings in the water and 6 on
the land, how many goslings are there altogether?
2. How many more gos-
lings are there in the water
than there are on the land? K"^-ri^r<, ^z :^
3. Henry has 7 sheep, and ^>^ ^{^
his father has 9 times as many. -. t2el„,, ''4'^^
How many sheep has his fa-
ther?
4. How many sheep have
Henry and his father? How many are 63 and 7?
5. An Indian sold 8 baskets at 10 cents apiece.
How much did he receive for them? 8X 10 = ?
6. A boy having 6 rabbits, bought 8 more, and
then sold 9. How many had he left?
7. Count to 48 by 6's. Count to 63 by 7's.
8. Count back from 45 to by 9's.
9. From a crock of butter weighing 25 pounds
7 pounds were taken at one time, 3 at another, and
6 at another. How many pounds remained?
10. A laundress bought at one time 3 flat-irons,
each weighing 6 pounds; at another time 2 flat-
irons, each weighing 8 pounds. What was the en-
tire weight of the irons?
11. At 8 dollars a term each, how much will a
music-teacher receive for 6 pupils ? 6X S = 2
12. There are 7 days in one week. How many
days are there in 9 weeks? 7x9 = ? 9X7 = ?
68 FIRST LESSONS
13. If a horse trot 9 miles in one hour, how far
will he travel in 10 hours? lOX 9 = ? 9 X 10 = ?
14. If one passenger-car has 8 wheels, how many
such wheels will 5 cars have ? 5X8=^? 8X5 = ?
Slate Exercises.
Copy and multiply the following :
789689787
543595632
3^^C
IjE8So:n^ xlii.
1. A cutler sold 6 sets of knives one day, 5 sets
the next day, and 8 sets the next. How many sets
did he sell?
2. What is addition ? What is the sign of addi-
tion?
3. A painter having 13 pounds of paint, used 6
pounds one day and 3 the next. How many pounds
had he left? 13 — (6 + 3)=? 13 — 6 — 3 = ?
4. What is subtraction ? What is the sign of sub-
traction ?
5. A farmer sold 3 sheep at 4 dollars apiece, and
6 calves at 5 dollars a head. What did he receive
for the whole? (3 X 4) + (6 X 5) =?
6. What is multiplication? What is the sign of
multiplication ?
IN ARITHMETIC. 69
7.8 + 5 + 6 = ? 24 — 3 — 6 = ? 8X2 = ?
8. In one yard there are 3 feet. How many feet
are there in 4 yards? How many feet are there in
5 yards?
9. If a squirrel eats 8 nuts in one day, how many
nuts will he eat in 9 days? 9X8 = ? 8X9 = ?
10. What will be the cost of 6 pears at 6 cents
each ? 6X6 = ?
11. In one peck there are 8 quarts. How many
quarts are there in 5 pecks ? 5 X 8 ^^ ?
12. How many are 9 times 5? How many are 7
times 6?
13. There are 4 classes in a school, each class con-
taining 10 pupils. How many pupils are there in
the school? 4X 10 = ?
14. In an orchard there are 7 rows of trees, and
9 trees in each row. How many trees are there in
the orchard? 7X9 = ? 9X7 = ?
15. A man having 16 cords of wood, used all but
5 cords. How many cords did he use? 16 — 5 = ?
16. Helen gave 7 yards of cloth to a poor woman,
and had 9 yards left. How many yards had she at
first?
17. 17 + 3 — 8 = ? 21 — 6 = ? 21 — (6 + 5)=?
Slate Exercises.
Copy, add, subtract, and multiply the following :
5 8 9 8 ^5 6 9 - 8
37423244
70 FIRST LESSONS
REVIEW EXERCISES.
Find the value of the following :
7X9 3X4 3X8 8X6 6X6
6X5 8X5 5X4 7X3 3X9
5X8 6X7 6XS 4X9 7X5
4X7 3X9 2X9 3X5 8X9
6XQ 4X8 8X8 8X7 5X4
4X3 5X5 7X4 6X2 6X8
8X2 6X9 6X9 8X4 7X4
7X7 3X3 5X3 7x7 5X9
8X4 5X9 8X9 5X9 5X6
3X5 4X4 5X6 3X4 6X7
QXQ 3X6 3X8 8X7 4X9
5X8 6X2 7X2 9X4 8X9
Find the value of the following :
(7 + 2)X9 8X(9~3) 4X(6 + 2)
(3 + 4)X6 5X(8+1) 5X(7 + 3)
(5 + 3)X8 4X(7-4) 3X(8-2)
(9 + l)X7 9X(9-3) 7X(9 + 1)
(8-3)X6 6X(8 + 2) 6X(6-4)
- (8 + 2)X7 5X(9-6) 8X(7 + 2)
(4 + 3)X5 4X(9-2) 4X(8 + 1)
(5 + 5) X 5 8X(5 + 2) 5X(9-6)
(4 + 3)X8 9X(3 + 7) 6X(9-2)
(9-2)X3 7X(3 + 2) 7X(8 + 2)
(8-4)X9 4X(9-4) 9X(7 + 2)
(9-5)X8 6X(8-3) 4X(5H-4)
J
IN ARITHMETIC
REVIEW EXERCISES.
■^ Off T.
Copy and fiiK
1 the vahie of the J
following :
2X3X4
7 + 3X(6 + 2)
4 + (3X9)-5
5X2X5
4 + 5X(9-3)
8+(7x2)-6
3X2X9
8 + 6X(4 — 2)
7 + (6X4) + 2
2X4X7
9 + 4X(9-3)
6 + (8X3)+5
4X2X8
5 + 5X(8-5)
6— (3X2) + 6
3X3X6
4+3X(6 + 4)
9 — (2X4) + 5
5X2X7
5 + 3X(8 + 4)
16 — (4X3) + 5
4X2X5
6 + 5X(9 + l)
20 + (2X6)-8
3X3X3
7 + 4X(8 — 3)
17 — (3X3) + 6
3X3X9
4 + 6 X ( 7— 2 )
25-(7x3)-4
3X2X8
9 + 4X(5 + 2)
40 — (6X3)-8
2X5X9
2 + 3X (6-3)
29-(4X6)-5
2X4X 8
8 + 6 X (8-6.)
30 + (2X3) -9
3X2X6
6 + 4X(9-2)
50- (3X8) + 6
Copy and find tlie value of the i
following :
6X8==40+? 3X9 = 20 +
? 3X?=20 + 1
7X5==30 + ? 5X8 = 33 +
? 5x? = 30 + 5
6X4 = 18 + ? 7X6 = 36 +
? 7X? = 37 + 5
9X3 = 22 + ? 5X9 = 40 +
? 6X? = 29 + 7
6X8 = 39 + ? 6X6 = 30 +
? 4X? = 22 + 6
5X7 = 30 + ? 7X7 = 50 —
? 9X? = 59 + 4
6X6 = 40-
_? 8X4 = 36-
? 3X?=18 + 6
7X9=70-
_? 7X5 = 40-
? 8X?=-59 + 5
8X8=60 + ? 9X6 = 60-
? 7X?-=41 + 8
5X9 = 51-
-? 7X3 = 20 +
? 6X? = 49 + 6
' \ )/t I 'i'/i/4" ' ' "-^y^^ ////'//.
72 FIRST LESSONS
IjESSON XIjIII.
1. If Dick had 4 rabbits, how many times could
he give away 2 rabbits to his companions?
2. Richard sold 6
apples, selling 2 at
a time. How many
times did he sell 2
apples ?
3, If William had
8 cents, and spent it
2 cents at a time for
candy, how many times did he purchase candy?
How many 2's are there in 8?
4. How many times is 2 contained in 8?
5. If you pay 2 cents for a slate-pencil, how
many can you buy for 10 cents? How many 2^s
are there in 10?
6. How many times is 2 contained in 10?
7. 10 is how many times 2?
Finding how many times one number is contained
in another is called Division.
The sign -^ is used to indicate division. It is
read divided by. Thus the expression 8^4=2, is
read 8 divided by 4 is equal to 2.
8. Read the following: 6-^2 = S; 8-i-2-=4;
10-^-2 = 5; 12-^3 = 4. .
9. At 2 cents apiece, how many lemons can be
bought for 12 cents? 12-^2=?
IN ARITHMETIC
73
10. If a boy earns 2 cents an hour, how long will
it take him to earn 14 cents?
11. How many 2's are there in 16? In 18?
12. If I have 20 cents in two-cent pieces, how
many pieces have I?
13. Form the division tables of ones and twos.
TABLES.
l-f-l = l 6^1= 6
2-^2 = 1 12^2-= 6
2^1 = 2 7^1= 7
4-1-2 = 2 14-^2= 7
3--lr=3 8-^1== 8
6-^2 = S 16-^2= 8
4^1=^4 9-^1-= 9
8-f-2 = 4 18-^2= 9
5-1 = 5 10-^1 = 10
10^2 = 5 20-^-2 = 10
3j«<C
liESSON XI.IV.
1. If a man walks 3 miles in one hour, in how
many hours will he walk 6 miles ? 6-^3 = ?
2. If a boy commits to memory 3 pages of his-
tory in one day, in how many days will he com-
mit to memory 9 pages ? 9-^3 = ?
3. At 3 cents apiece, how many lemons can be
bought for 12 cents? 12-^3 = ?
4. A w^oman exchanged 15 pounds of butter for
cloth, giving 3 pounds of butter for a yard of cloth.
How many yards did she receive? 15-^3 = ?
74 FIRST LESSONS
5. A woman sells 3 quarts of milk each day. In
how many days will she sell 18 quarts? 18-^3 = ?
6. In one yard there are 3 feet. How many
yards are there in 21 feet? 21h-3 = ?
7. At 3 dollars a cord, how many cords of Avood
can be bought for 24 dollars? 24-^-3 = ?
8. If a boy walks 3 miles in one hour, in how
many hours will he walk 27 miles ? 27-^3 = ?
9. How many times is 3 contained in 30?
10. At 4 dollars a cord, how many cords of wood
can be bought for 8 dollars?
11. A man sold 12 sheep, selling 4 at a time.
How many sales of sheep did he make? 12h-4 = ?
12. 16^4? 20^4=-? 24-^4 = ? 28-^4==?
13. In one pint there are 4 gills. How many
pints are there in 32 gills? 32-^4 = ?
14. In one bushel there are 4 pecks. How many
bushels are there in 36 pecks ? 36 -^- 4 = ?
15. In how many days will an engineer earn 40
dollars, if he earns 4 dollars a day ? 40 -f- 4 = ?
16. Form the division tables of threes and fours.
TABLES.
3-^3 = 1 18^3= 6
4^4 = 1 24-^4= 6
6-^3=^2 21-^3-= 7
8-^4 = 2 28-^4= 7
9-^-3=-3 24-^3-= 8
12-^4 = 3 32-^4= 8
12-^3 = 4 27h-3= 9
16^4 = 4 36-^4= 9
15-v-3 = 5 30^3 = 10
20-^4 = 5 40^4 = 10
I
IN ARITHMETIC
75
LESSON XLT,
1. If there are 6 chickens in groups containing
3 each, how many groups of chickens are there?
.2. If a man earns 3 dol-
lars a day, in how many
days can he earn 12 dol-
lars?
3. How many seats will
be required to seat 21 pu-
pils, sitting 3 on a seat?
21-^3 = ?
4. If a traveling agent
can earn 4 dollars a day,
in how many days can he earn 24 dollars at that rate ?
5. 32 is how many times 4? 32-^4 = ?
6. 30 is how many times 3? 30-^3 = ?
7. A boy sold 5 pencils at 4 cents apiece, and
took his pay in apples at 2 cents apiece? How
many apples did he receive ? (5X4)-^2^?
8. A boy had 25 cents. He bought 2 apples at
5 cents apiece, and 2 oranges at 6 cents apiece.
How many cents had he left? (2 X 5) -f (2 X 6) =?
9. How many times 4 is 16? How many are 2
times 18?
10. A man sold 6 barrels of apples at 3 dollars a
barrel, and took in exchange some cloth at 2 dollars
a yard. How many yards did he receive?
11. How many times 2 acres are 6 acres?
12. How many times 4 gills are 40 gills?
76 first lessons
Slate Exercises.
Copy and read the following:
55 89 76 54 35 72 98
79 95 84 63 55 49 100
Copy and multiply the following :
58696576 5 3
7452358989
Division is also expressed by a curved line placed
between numbers.
Copy and divide the following:
4)8 3)9 4)12 3)18 4)24 2)16
3>»^C
1. If a boy rides one mile on the cars for 5 cents,
how many miles can he ride for 10 cents? 10-i-5 = ?
2. If a boat sails 5 miles in one hour, in how
many hours will it sail 15 miles? 15-^5 = ?
3. At 5 dimes apiece, how many tickets can be
bought for 20 dimes? 20-^5 = ?
4. In how many hours will a horse travel 25
miles, if he travels 5 miles an hour? 25-^5 = ?
5. 30-^5=:? 35-^5==? 40-^5 = ?
6. Fannie attends school 5 days in a week. How
many weeks will she attend if she is present 45 days?
IN ARITHMETIC. 77
7. How many tons of coal at 5 dollars a ton, can
be bought for 50 dollars? 50^5 = ?
8. A boy sold brackets at 2 dimes apiece, and got
12 dimes. How many did he sell? 12-v-2 = ?
9. When biscuits are 6 cents a pound, how many
pounds can be bought for 18 cents? 18-^6 = ?
10. If it requires 6 yards of cloth for one cloak,
how many cloaks can be made from 24 yards of
cloth ? 24 -^ 6 =: ?
11. How long will it take a boy to read 30 pages,
if he reads 6 pages every day ? 30 -^ 6 == ?
12. At 6 cents a quart, how many quarts of cher-
ries can be bought for 36 cents? 36-^-6 = ?
13. How many fields of 6 acres each can be formed
out of 42 acres ? 42 ^ 6 = ?
14. If there are 6 tea-spoons in one set, how many
sets will 48 tea-spoons make ? 48 -^ 6 = ?
15. If there are 6 pairs of kid gloves in one pack-
age, how many packages are there in 54 pairs? How
many packages are there in 60 pairs?
16. Form the division tables of fives and sixes.
TABLES.
5^5 = 1 30-^5= 6
6-^6 = 1 36-i-6= 6
10-^5 = 2 35^5= 7
12-^6=-2 42^6= 7
15-^-5 = 3 40-^5=- 8
18-^6 = 3 48^6= 8
20^5=-4 45^5= 9
24-^6 = 4 54--6=- 9
25^5 = 5 50-^5 = 10
30-^6 = 5 60-^6 = 10
78 FIBST LESSONS
liESSON XI.VII
1. If a man earns 5 dollars in one week, in how
many weeks will he earn 50 dollars? 50-4-5 = ?
2. How many times can you take 6 cents out of
a purse that contains 48 cents? 48-^6 = ?
3. How many times 3 apples are 12 apples? 12
^3 = ?
4. How many calves at 3 dollars each, can be
bought for 18 dollars? For 21 dollars? For 24
dollars? 18h-3 = ? 21-^3 = ? 24-^3 = ?
5. There are 4 pecks in 1 bushel. How many
pecks are there in 7 bushels? In 4 bushels?
6. In 32 pecks how many bushels are there?
7. A man gave to each of 4 boys 8 quails. How
many quails did he give them ? 4X8 = ?
8. A clothier bought 10 coats at 5 dollars apiece,
and sold them for 6 dollars apiece. How much did
he gain? (10 X 6) - (10 X 5) =? 10X(6-5) = ?
9. How many bushels of potatoes at 1 dollar a
bushel, must be given for 6 yards of cloth at 2 dol-
lars a yard?
10. At 5 dollars a barrel, how many barrels of
flour can be bought for 30 dollars? 30^5 = ?
11. How many balls at 6 dimes apiece, can be
bought for 54 dimes ? For 30 dimes ? 54 -^ 6 = ?
12. If a cutler uses 18 blades, putting 3 blades in
each knife, how many knives does he make?
13. A carman can draw 4 hogsheads of sugar at one
load. How many loads will 16 hogsheads make?
in arithmetic. 79
Slate Exercises.
Copy and multiply the following :
5634875321
5387564689
Copy and divide the following :
6)42 5)35 3)21 2)18 3)27 4)36
>i:«>iC
liESSON XI.TIII.
• 1. In one week there are 7 days. How many
weeks are there in 14 days? 14^-7 = ?
• 2. In how many hours can Carrie solve 21 prob-
lems, if she can solve 7 per hour ? 21 -^- 7 = ?
3. Helen sold her doll for 28 cents, and spent the
money for drawing-pencils, paying 7 cents for each.
How many pencils did she buy ? 28 -i- 7 = ?
4. At 7 dollars a picture, how many pictures can
be bought for 35 dollars ? 35 ^ 7 = ?
5. If a fish weighs 7 pounds, how many such fish
will be needed to weigh 42 pounds ? 42 -f- 7 = ?
6. If a man earns 7 dollars in one week, in how
many weeks will he earn 49 dollars ?
7. If it requires 7 yards of cloth to make one
cloak, how many cloaks can be made from 56 yards?
- 8. If one box holds 7 quarts of nuts, how many
boxes are required to hold 63 quarts ? 63 -^ 7 = ?
80
FIRST LESSONS
9. When flour is 7 dollars a barrel, how many
barrels can be bought for 70 dollars ? 70 -r- 7 = ?
10. If a railroad coacjh
has 8 wheels, how many
such coaches will have 16
wheels? 16-^8 = ?
11. At 8 cents a yard, how many yards of calico
can be bought for 24 cents ? 24 ^ 8 = ?
12. If a window requires 8 panes of glass, how
many windows will 32 panes make ? 32 -^ 8 = ?
13. If there are 8 trees in a row, how many rows
of trees are there in an orchard containing 40 trees?
40-^8-=?
14. How many gallons are there in 48 pints, since
there are 8 pints in one gallon ? 48 -^ 8 = ?
15. 56 divided by 8 = ? 64 divided by 8 =- ?
16. How many bins will be required to hold 72
bushels, if one bin holds 8 bushels? 72-^8==?
17. In one pile of money there are 8 cents. How
many such piles are there in 80 cents ? 80 h- 8 = ?
18. Form the division tables of sevens and eights.
TABLES.
7h-7=-1 42^7== 6
8-
-8=:1 48-
-8= 6.
14-^7 = 2 49-f-7= 7
16-
-8.-2 56-
-8= 7
21-^7 = 3 56-^7= 8
24-
-8-3 64-
-8== 8
28-^7 = 4 63-^7= 9
32-
-8 = 4 72-
-8-: 9
35^7 = 5 70^7 = 10
40-
-8=:5 80-
-8-=10
IN ARITHMETIC. 81
liESSOK XlilX.
1. If 8 bushels of potatoes are needed to plant
one acre of ground, how many acres will be planted
if 40 bushels are used ? 40 -^ 8 ::= ?
2. If a blacksmith makes 6 horseshoes in one day,
in how many days can he make 60 horseshoes?
3. If a man paid 5 dollars for taking one trip on
the cars, how many such trips could he take for 30
dollars? 30^5 = ?
4. In a school of 56 pupils there are 7 pupils in
each class. How many classes are there ? 56 -^ 7 =^ ?
5. In one pint there are 4 gills. How many pints
are there in 36 gills ? 36 -^ 4 == ?
6. In one yard there are 3 feet. How many yards
are there in 21 feet? In 30 feet? In 12 feet?
7. If one ball costs 2 dimes, how many balls can
be bought for 6 dimes? For 12 dimes? For 18
dimes ?
8. How many oranges at 5 cents apiece must be
given for 3 dozen of eggs at 10 cents a dozen ?
9. How many sleds at 3 dollars apiece can be
bought for 27 dollars ? 27-^3 = ?
10. How many yards of calico at 8 cents a yard
must be given for 10 pounds of maple sugar at 8
cents a pound? (10 X 8)^8 = ?
11. If there are 4 pecks in one bushel, how many
bushels are there in 40 pecks ?
12. How many 7's are there in 63? In 49?
13. How many 6's are there in 54? In 48?
82 first lessons
Slate Exercises.
Copy and multiply the following:
687846875
423525369
Copy and divide the following :
7)70 8)64 5)50 4)32 5)40 7)28
5^8^c
1. If one dress can be made from 9 yards of
cloth, how many dresses can be made from 18 yards?
18-^9 = ?
^2. If a painter can paint 9 boards of fence in
one hour, in how many hours can he paint 27 boards?
27-^-9 = ?
3. There are 9 square feet in 1 square yard. How
many square yards are there in 36 square feet? In
45 square feet? 36-^9-=? 45-^9 = ?
4. If there are 9 candles in one pound, how many
pounds are there in 54 candles? 54-^-9=?
- 5. A man gave 63 bushels of corn to poor fam-
ilies, giving 9 bushels to each family. How many
families were relieved ? 63 -^ 9 = ?
6. If you travel 9 miles in one hour, in how
many hours will you travel 72 miles? 81 miles?
-7. 90 is how many times 9 ? 90 ^ 9 == ?
IN ARITHMETIC. 83
- 8. If it requires 10 pickets to make one gate,
how many such gates can be made using 20 pickets?
20^10=-?
9. How many ten-cent pieces are there in 30
cents? 30-^-10 = ?
10. There are 10 cents in one dime. How many
dimes are there in 40 cents? 40-^10 = ?
11. If a man can drill 10 feet per day, how many
days will it take him to drill 50 feet ? 50 ^ 10 == ?
12. James bought a Christmas gift for 60 cents,
paying for it with ten-cent pieces. How many ten-
cent pieces did he give for it ? 60 -^ 10 = ?
13. How many hours will it take a steamboat to
make a trip of 70 miles, if it travels 10 miles in
one hour? 70-^10 = ?
14. How many pupils, at 10 dollars a term, must
a teacher instruct to receive 80 dollars ? 80 -f- 10 = ?
15. At 10 cents a pound, how many pounds of
starch can be bought for 90 cents? 90-^10 = ?
16. How many tens are there in 100?
17. Form the division tables of nines and tens.
TABLES.
9^9=1
54^9= 6
10-^10--1 60-^10= 6
18^9=2
63^9= 7
20-^-10=2 70-^10= 7
27^9=3
72^9= 8
30^10=3 80^10=- 8
36^9=4
81-^9= 9
40^10=4 90^10- 9 1
45^9=5
90-^9=10
50-^10=5 100-^10=10 1
84
FIRST LESSON
L^g^^^-S
LESSOlSr LI.
1. If there are 5 monkeys on one branch of a
tree, 4 on another, and 3 on another, how many
monkeys are there on the tree ? 5 + 4 + 3^?
2. How many more than 5 monkeys are 7 monk-
eys ? 7 — 5=-?
3. How many more than 4 monkeys are 8 monk-
eys? 8 — 4==?
4. How many more than 3 monkeys are 9 monk-
eys? 9 — 3=-?
5. If you have 5 apples, how many more must
you get to have 12 apples? 5 + ?= 12.
6. Mary is 6 years old, and her brother is' 15.
In how many years will Mary be as old as her
brother is now? 6-\-? = 16.
7. In one week there are 7 days. How many
days are there in 4 weeks ? 4X7 = ?
8. Into how many groups of 5 oranges each can
you divide 15 oranges ? 15-^5 = ?
INARITHMETIC. 85
9. How many are 2 times 8? 4 times 8? 6
times 8?
10. How many times is 8 contained in 24? In
40? In 64?
11. If a cow gives 9 quarts of milk in the morn-
ing, and 10 quarts at night, how many quarts does
she give in one day?
12. George having 20 cents, paid 6 cents for candy
and 8 cents for peanuts. How many cents had he
left?
13. If one lily has three petals, how many petals
have 9 lilies?
14.4-1-8 + 2 = ? 9 + 7-1-3 = ? 28 — 3 — 6 = ?
19_4=:? 7-1-8 — 6=?
15.7X7 = ? 9X8 = ? 45-^5 = ? 90-^10 = ?
16. In one dime there are 10 cents. How many
cents are there in 4 dimes? 4 X 10=?
17. Mary bought 4 pencils at 5 cents apiece, and
a drawing-book for 25 cents. What was the total
cost of her purchases?
18. How many are 6 and 8 ? 16 and 8 ? 26 and
8? 36 and 8? 46 and 8 ? 56 and 8?
19. How many are 4 and 9? 14 and 9? 24 and
9 ? 34 and 9 ? 44 and 9? 54 and 9 ?
20. Count to 32 by 4's. Count to 54 by 6's.
21. Count to 90 by 9's. Count to 72 by 8's.
22. Count to 40 by 5's. Count to 63 by 7's.
23. How many 8's are there in 80 ? 80 -^ 8 = ?
24. How many 7's are there in 49 ? 49 ^ 7 = ?
25. How many 6^s are there in 54 ? 54 -r- 6 = ?
86 FIRST LESSONS
IjESSON Hill.
1. Henry takes 9 steps in crossing the room
once. How many times will he cross the room in
taking 54 steps ? 54-^9 = ?
2. If a man works 10 hours in one day, how
many hours will he work in 8 days? 8 X 10 = ?
- 3. If a man works 10 hours in one day, in how
many days will he work 100 hours? 100-^-10 = ?
4. Count to 27 by 3's. Count to 48 by 4's.
5. How many times is 5 contained in 30? In
45?
6. How many five-dollar bills will be required to
pay for 5 tons of coal at 4 dollars a ton ?
7. A boy having 50 cents, paid 30 cents for a
ball and 15 cents for a bat. How many cents had
he left? 50-30—15=-?
> 8. When clover seed is 8 dollars a bushel, how
many bushels can be bought for 48 dollars? For
56 dollars? 48^8=? 56-^8=?
9. In one square yard there are 9 square feet.
How many square feet are there in 6 square yards ?
10. 36 is how many times 4? How many times
6 ? How many times 9 ?
11. 24 is how many times 8? How many times
6 ? How many times 4 ?
1?. In an orchard there are 56 trees and 7 trees
in a row. How many rows are there ? 56 + 7 — ?
13. In one yard there are 3 feet. How many
feet are there in 8 yards? In 6 yards? In 9 yards?
I N ARITHMETIC.
87
14. A house has 10 windows, and 8 panes of glass
in each window. How many panes of glass are there
in the house? 10X8 = ?
15. How many are 6 + 4 + 5? 8 + 3 + 7?
16. How many are 12 and 5? 22 and 5? 32 and
5? 42 and 5? 52 and 5? 62 and 5?
17. How many are 8 less 5? 18 less 5? 28 less
5? 38 less 5? 48 less 5? 58 less 5?
18. Two men start from the same place and travel
in opposite directions, one at the rate of 6 miles an
hour, and the other at the rate of 4 miles an hour.
How far apart are they in 5 hours?
3^^C
liESSON lilll.
1. If a blacksmith uses 8 nails in setting one
horseshoe, how many nails will he uae in setting
8 horseshoes? 8X8=:=?
2. If one horse re-
quires 4 horseshoes, how
many horseshoes will be
needed for 5 horses? For
6 horses? 5X4 = ?
3. How many times is
7 contained in 21 ? In
49? In 56?
4. How much can a wagoner earn in 9 days, if
he earns 4 dollars per day? 9 times 4 = ?
88 FIRST TjESSONS
5. How many are 4 times 7 ? 5 times 7 ? 9
times 7?
6. How many crows are 5 crows, 3 crows, 6
crows, and 2 crows?
7. How many more than 10 crows are 18 crows?
8. How many more than 6 pens are 18 pens?
9. How many ten-dollar bills must be given for
8 boxes of handkerchiefs at 5 dollars a box?
10.6 + 7 — 4 = ? 8 + 5 — 7 — ? 9 + 3 — 6 = ?
11. (7X4)^2==? (8X6)H-4 = ? (6X6)-^9=-?
12. A farmer having 18 bushels of corn sold 5
bushels to one man and 3 to another. How many
bushels had he left? 18 — (5 + 3) = ?
13. A woman put 20 quarts of strawberries into
cans, putting two quarts into each can. How many
cans did she use? 20h-2 = ?
14. In one pint there are 4 gills. How many gills
are there in 7 pints ? 7X4 = ?
- 15. In one gallon there are 4 quarts. How many
gallons are there in 16 quarts? 16-i-4 = ?
16. In a school-room there are 48 desks arranged
in rows containing 8 desks each. How many rows
of desks are there in the room ? 48 -^ 8 = ?
17. A farmer sold some grain for 40 dollars, and
took his pay in sheep at 5 dollars a head. How
many sheep did he receive ? 40 ^ 5 = ?
18. How many dozens of eggs at 10 cents a dozen
will pay for 6 yards of calico at 5 cents a yard?
19. If there are 6 forks in one set, how many
forks are there in 9 sets? 9X6 = ? 6X9 = ?
INARITHMETIC. 89
liESSOlS^ lilV.
- 1. If a basket-maker can make 7 dinner-baskets
in one day, in how many days can he make 42 such
baskets ?
2. If one dining-table has 4 legs, how many legs
have 9 such dining-tables ? 9X4 = ?
3. What will be the cost of 2 tops at 10 cents
apiece, and 6 oranges at 5 cents each?
4. In one dime there are 10 cents. How many
dimes are there in 90 cents? In 70 cents? In 40
cents ?
5. How many cents are there in 5 dimes? In
8 dimes? In 9 dimes?
6. What is the diiference in the cost of 6 peaches
at 3 cents apiece, and 6 apples at 2 cents apiece?
7. 8 + 2 + 5 = ? 17— (8 + 4)=? 25— (5 + 2)=?
8. (3X2) + (7X3) = ? 27^(3X3) = ?
9. At 5 dollars apiece, how many hats can be
bought for 25 dollars?
10. In one gallon there are 4 quarts. How many
quarts are there in 4 gallons?
-11. If one fish weighs 9 pounds, how many such
fish will weigh 81 pounds? 81 ^9=?
12. If there are 3 joiners' planes on one bench, 8
on another, and 5 on another, how many planes are
there on the 3 benches?
-- 13. In a class, 36 questions were answered, each
pupil answering 4 questions. How many pupils were
there in the class? 36^4 = ?
90 FIRST LESSONS
14. There are 9 pins in the pin-cushion, 12 on the
paper, and 5 in the box. How many pins are there
in all? 9 + 12 + 5 = ?
15. A tailor earned 12 dollars one week, and 15
dollars the next, and after paying his expenses had
8 dollars left. How much money did he expend?
(12 + 15) — 8-=?
16. How many more than 5 times 4, is 30?
17. How many more than 6 times 3, is 24?
18. How many are 7 + 3 + 5 divided by 3? Di-
vided by 5?
19. How many are 7 + 9 + 2 divided by 6? Di-
vided by 3 ?
Slate Exercises.
Copy and add the following :
32235537 5
435287626
7445645 17
679442442
Copy and multiply the following :
867987698
595388749
Copy and divide the following :
6 )36 8 )48 8 )72 9)81 7 )70
24-^6 36-^4 27-4-9 35^5
42^6 50-^5 56^8 60-^6
IN AKITHMETIC
91
REVIEW EXERCISES
Find the value of the following :
81^9
45^5
36^6
72^8
40^5
27^3
18-^6
24^4
20-^2
32^8
63^7
60-4-6
28^4
18-^9
25-^5
15^3
18^2
36^4
28-^7
30 -f- 6
64^8
81-^9
20-^2
56^8
30-^3
16-^-2
45^5
24^8
36^9
32^4
35^5
48^6
35 -f- 7
40^8
32^4
12^2
35^5
16^4
27-^9
24^3
18^2
64^8
54^6
45^5
63^9
35^7
28-^4
27^3
Find the value of the following
(25 —
(36 +
(41 +
(51 +
(67 +
(18 +
(28 +
(29 +
(13 +
(60-
(47-
(33 +
5)
6)
7)
3)
5)
3)
4)
7)
3)
4)
2)
3)
(37-2)
(49-7)
(33 + 3)
( 80 — 8 )
( 60 — 6 )
(33 + 7)
(18 + 3)
(22 + 5)
( 43 + 6 )
(21+3)
(31 + 5)
(32 + 3)
^5
21^
^7
36^
f-4
48^
^-9
32^
^6
35 4
i-8
28^
f-3
27-4
f-9
63^
f-7
45 4
^6
56^
^-4
49^
f-5
72-^
28 H- 4
21^7
40 H- 5
54 H- 9
56^8
16^2
36^6
46^9
30^5
36^4
48-4-8
24 H- 6
(5 + 2)
(7 + 2)
(2 + 4)
(3 + 5)
(9-2)
(8-4)
(6-3)
(7 + 2)
(2 + 3)
(3 + 4)
(2 + 5)
(6 + 3)
92
FIRST LESSONS
REVIEW EXERCISES,
Copy and find the value of the following
(48^8)^2
(6+15)-^
-(6-3)
4+ (16^4)— 6
(81-^-9)-i-3
(84-24)^
-(9-1)
7+(35-^-5)— 4
(56^7)-^4
(7+18)-.
-(7-2)
8-(36-f-9) + 2
(70-^7)^5
(8+28)-
-(5+4)
9+(81-^9)-6
(36-h6)^3
(9+36)-
-(3+2)
7+(32^4)-3
(20^5)-^2
(8+40)-
-(7-1)
3+(49-i-7)— 5
(48-f-6)^4
(6+30)-
-(8-4)
6+(64-^8)-4
(54-^6)-^3
(3+27)-
^(7+3)
5-(45-^5)+4
(36^9) -^2
(8+24)-
K3+5)
9— (42^6)— 2
(70-^7)-^2
(7+43)-
^(2+3)
8+(16^4)— 6
(54-^9)-^3
(9+40)-
-(5+3)
9+(21-^7)-6
(64-v-8)^4
(6+54)-
K5+1)
3+(64^8)-7
(56-i-7)^2
(8+72)-
^(7+3)
3+(63-^-9)— 9
(72-^-8) -3
(9+47)^(2+5)
8+(60-^6)-5
Copy and find the value of the following
45-^5=-6+ ?
27-^ 3==6+ ?
45-
-?=6+3
32-f-4==5+ ?
54-^ 6-^5+?
36-
-?=4+2
81-^9-=3+?
80-f- 8=7+ ?
72-
- ?=6+3
72h-9-:6+ ?
63-^ 9=3+?
70-
-?=6+4
60-^6=8+ ?
21 : 3—4+?
42-
- ?=3+4
49^7=4+ ?
14-f- 2=6-F?
40-
-?=l+3
36-^4=3+?
64-^ 8=5+?
54-.
-?=4+2
27 : 3—4+ ?
35^ 5=5+?
48-
-?=5+3
164-2-=6+?
42^ 7=3+?
35-
-?=6+l
24-^6-=3+ ?
48^
6=2+?
70-
- ?=8+2
IN ARITH METIC
93
P^^^^^^
1. Into how many parts has one of the apples in
the picture been divided?
2. How do these two
parts compare in size?
3. What is one of these
two equal parts called?
One-half.
4. How many halves of the apple make the whole
apple ?
5. Into what number
of parts is one of the pears
divided ?
6. How do these three
parts compare in size? ~ ~
7. What is one of these three equal parts called?
One-third.
8. What are two of these three equal parts called ?
9. How many thirds are
there in the whole pear?
10. Into how many parts
has one of the oranges in
the picture been divided?
11. How do these four parts compare in size?
94 FIEST LESSONS
12. What is one of these four equal parts called ?
One-fourth,
13. What are two of the parts called? What are
three of the parts called?
14. How many fourths are there in the whole
orange ?
One or more of the equal parts of any thing is
called a Fraction,
Two numbers written one above the other, with
a line between them, are used to express a fraction.
The number below the line shows the number of
equal parts into which the thing is divided.
It is called the Denominator,
The number above the line shows how many parts
form the fraction.
It is called the Numerator,
One-half is therefore expressed thus : \.
One-third is therefore expressed thus: \.
One-fourth is therefore expressed thus: \.
Two-fourths is therefore expressed thus : J.
Three-fourths is therefore expressed thus: J.
Slate Exeecises.
Copy and read the following :
i * i I I
Express in figures the following :
One-half Two-thirds One-fourth
One-third Three-fourths Two-fourths
IN ARITHMETIC. 95
U?f.. I i- I i IT I i I feli- 111 i-l il i I
1. Draw a line and divide it into 5 equal parts.
2. What is one of these parts called ? One-fifth.
3. What are two of the parts called? What are
four of the parts called ?
4. How many fifths make the whole line?
5. Draw a line and divide it into 6 equal parts.
6. What is one of these parts called ? One-sixth.
7. What are three of the parts called ? What are
five of the parts called ?
8. How many sixths make the whole line?
9. If a pie is divided into seven equal pieces, what
part of the pie is one piece ? Three pieces ? Four
pieces ? How many sevenths make the whole pie ?
10. If a pound of candy is equally divided among
eight boys, what part of the pound will one boy
receive ?
11. How many eighths of it will four boys receive ?
Three boys ? Six boys ?
12. A miller divided a barrel of flour equally among
nine poor families. What part of the barrel of flour
did he give to each family?
13. How many parts did he give to five families?
To eight families?
14. If a dollar is divided into ten equal parts,
what is one of the parts called ? What are foi+r oF=-^
the parts called? W^hat are ten of the pac/^ called?
(us
96
FIRST LESSONS
Slate Exercises,
Copy and read the following :
1
f
lift
i
i
i ^ i i
All
Express in figures the following:
3 fifths 4 fifths 3 eighths
3 sixths 2 thirds 5 eia^hths
5 tenths 8 tenths 6 eighths
2 ninths 7 ninths 5 sevenths
3j#4C
1. Mary had 1 half of a dollar, and her mother
gave her 1 half of a dollar more. How much money
had she then?
2. How many thirds are 1 third and 2 thirds?
3. If John gave ^ of an orange to his sister, and
I to his cousin, how many fourths did he give both ?
4. Henry earned ^ of a dollar in one day, and f
of a dollar the next day. How much money did he
earn in both days? How many fifths are \ and f ?
5. Jane bought |^ of a yard of ribbon, and Caro-
line bought I" of a yard? How many sixths did
both buy ? How many sixths are |-, |- and ^ ?
6. A farmer sold |- of a bin of wheat to one man,
and f to another. How many sevenths did he sell?
7. How many eighths are f, |- and J?
I
IN ARITHMETIC
97
8. William bought 2J yards of cloth for a pair of
pantaloons, f of a yard for a vest, and 4^ yards for
a coat. How many yards of cloth did he buy?
9. A man plowed 1 j^ acres one day, and
lA
acres the next day. How many acres did he plow ?
10. A laborer bought f of a ton of coal at one
time, f of a ton at another, and ^ of a ton at another.
How much coal did he buy?
Slate Exercises.
Copy and add the following:
i + i + 4
i + f + l
l + f + l
3j^C
LESSON LTIII,
1. Lucy had ^ of a dollar, and her brother gave
her :^ of a dollar more. How much money did she
have then ?
2. How many halves
of a dollar are equal to
one dollar ?
3. How many fourths
of a dollar are equal to
one dollar?
4. How many fourths of a dollar are equal to
one-half of a dollar? How many fourths are there
ini?
9
1 - - ■
98 FIRST LESSONS
5. How many fourths of a dollar are there in ^
and J of a dollar? How many fourths in ^ and ^?
6. Draw two lines of
the same length.
7. Divide the first line
into 2 equal parts.
8. Divide the second line into 6 equal parts.
9. What is one part of the first line called ?
10. What is one part of the second line called?
11. What are three parts of the second line called?
12. How do three parts of the second line compare
in length with one part of the first line ?
13. How many sixths of a line are equal to one-
half of a line ?
14. How many sixths are there in ^ and ^? How
many sixths are there in J and |- ? In ^ and f ?
15. How many eighths are equal to one-fourth?
Hcfw many eighths are there in ^ and f ?
■ 16. Mary bought 2^ yards of lace one day, and 2^
yards the next day. How many yards did she buy ?
17. John bought 2^ pounds of raisins, and Joseph
bought 3f pounds. How many pounds did they buy ?
18. How many ninths are ^ and ^? f and |^?
19. How many eighths are ^ and f ?
Slate Exercises.
Copy and add the following :
i+i+i i+l+l i+i+i
*+i+f i+i+i i+l+A
IN ARITHMETIC. 99
liESSOlS^ I.IX.
1. Henry had 3 fourths of an orange, but gave
1 fourth of it to his cousin. How much had he left?
2. If a boy had f of a pound of candy, but gave
^ of it away, how much had he left? -| — i = ?
3. If I have f of a dollar, and spend ^ of a dol-
lar, what part of a dollar will I have left?
4. A girl having -j^ of a dollar, paid ^^ of a
dollar for thread. How much had she left?
5. From ^ take ^. From |^ take ^.
6. If Julia divides a loaf of cake into 8 equal
parts, and gives away -| of it, how many eighths
will she have left?
7. A man chopped f of a cord of wood in the
forenoon, and f of a cord in the afternoon. How
much more did he chop in the afternoon than in the
forenoon ? f — f ^^ ?
8. Gilbert owns f of a boat, and Carl the re-
mainder. What part does Carl own?
9. Oscar bought a pair of skates for -^^ of a dol-
lar, and sold them for -^-q of a dollar. What part
of a dollar did he lose? -^ — to"^^^
10. How much more than |^ of a pound is f of a
pound? f — f = ?
11. In a school f of the pupils are girls, and the
rest are boys. What part of the school is boys ?
12. How many more than 3^ are 8^ ?
13. A grocer having lOf pounds of butter, sold 4
pounds of it. How much had he left?
100 FIRST LESSONS
14. A tailor had 12|- yards of cloth, and sold 3f
yards. How many yards had he left?
Slate Exercises.
Copy and subtract the following :
4 1 7 2. 6. 3 4 1
•6 "6 ¥ 8 9 9 Z 5"
6A-¥o H-H 8f-2J 9f-3f
3j^C
1. Into how many parts is the first melon in the
picture cut? How do the parts compare in size?
2. Into how many equal
parts is each of the halves of
the second melon cut?
3. How many such parts
are there in the two halves^
or the whole melon?
4. What are these- parts called?
5. How many sixths are there in one-half?
6. From -l- subtract ^. From ^ subtract f.
7. Draw a line and divide it into 3 equal parts.
8. Draw another line of the same length, and
divide it into 3 equal parts.
9. Divide each part of the second line into 3 equal
parts.
10. How many of these smaller parts are there in
the whole line? What are these parts called?
I
IN ARITHMETIC. 101
11. How many ninths are there in one third?
12. How many ninths are there in two thirds?
13. From ^ of an orange take f of an orange.
14. Belle having f of a yard of velvet, gave away
I of a yard. How much had she left?
15. A grocer who had ^ of a barrel of beans, sold f
of a barrel. What part of a barrel did he have left?
16. How many tenths of a dollar are there in one-
fifth of a dollar? In two-fifths?
17. From f of an hour take -^ of an hour.
18. A milliner having 4f yards of silk, used 2-|
yards. How many had she left?
Slate Exercises.
Copy and subtract the following:
l-i
f-f
l-i
f-A
^-^
H-H
5i-2i
71-lA
^-^
5i-2i
^-^
6i-6A
5^#<C
IiESSO:N^ I.XI.
1. Clara had a yard of cambric. She gave Grace
J of it, and Lizzie f of it. How much had she
left?
2. A bushel of wheat was divided among three
persons. One received ^ of it, another i of it, and
the third the rest. What part did the third per-
son receive?
102 FIRST LESSONS
3. George paid ^ of a dollar for a slate, | of a
dollar for a reading-book, and ^ of a dollar for a
writing-book. What did he pay for all?
4. A man dug f of a ditch one day, ^ of it the
second day, and the rest of it the third day. What
part of the ditch did he dig the third day ?
5. From ^ + | take i. From ^ + ^ take ^.
6. From f + ^ take ^. From f + |- take |-.
7. To the difference between ^ and f add ^.
8. To the difference between -^-^ and f add ^.
9 24-i_l-3 2—9 l-|-2._i_2. 1—9
10. Peter had f of a dollar. His father gave him
-^ more, and his mother gave him enough to make
the dollar. How much did his mother give him?
11. James paid ^ of a dollar for a book, -J of a
dollar for a slate, and f of a dollar for writing-paper.
How much did he pay for all? i + i + f^?
12. How much more did he pay for the book than
for the slate? i— ^=?
14. William owns f of a sled, and his brother the
remainder. What part of the sled does his brother
own?
Slate Exercises.
Find the value of the following :
H + H 3f + 5i 4I + 6A 8| + 10i
6|-5f 8^-4f H-Si^ m-H
2| + 3^ 5| + 3^ 6} + 2f 5t + 3i
H-H 9f-4i 8^-4^ 6^-3^
IN ARITHMETIC. 103
liESSOlS^ liXII.
1. If one pint of peanuts costs 1 half of a dime,
what will 5 pints cost ? 5 times |^ = ?
2. If one yard of cloth costs 2 fourths of a dollar,
what will 3 yards cost? 3 times f = ?
3. If it takes 2 eighths of a yard of lace for one
veil, how much lace will it take for 3 veils ?
4. How many sevenths are 2 times 2 sevenths ?
5. How many ninths are 3 times 3 ninths ?
6. 3 times | == ? 7 times f = ? 4 times | = ?
7. If a man earns 2 dollars in one day, how much
will he earn in 1 half-day ? ^ of 2 = ?
8. If 1 yard of cloth costs 9 dollars, what will 1
third of a yard cost ? ^ of 9 = ?
9. When coal is 7 dollars a ton, what will 1 seventh
of a ton cost ? What will 2 sevenths of a ton cost ?
10. Mary is 15 years old, and her sister is 2 fifths as
old. How old is her sister? 15 X f = ?
11. 6 multiplied by ^=^2 By |? By ^? By |?
12. 10 multiplied by | = ? By|? Byf? By ^L?
13. A boy having 20 pennies gave ^ of them to one
boy, and ^ of them to another. How many did he
give to both ? How many had he left ?
14. If a pound of cinnamon costs 21 cents, what
will ^ of a pound cost? What will |^ of a pound cost?
15. If a barrel of sugar is worth 25 dollars, what is
^ of it worth ? What are f of it worth ?
16. What is the product of f multiplied by 6? 6
multiplied by f ?
104 fikst lessons
Slate Exercises.
Find the value of the following :
6 times j-,
or f X 6.
|X5.
iX2
5 times f ,
or 1 X 5.
iX5.
iX5
f of 6,
or 6 X |.
8X|.
6X|
1 of 12,
or 12 X f .
9X1.
12Xf
^>^c
LESSON liXIII
1. At |- of a dollar each, how many books can be
bought for 1 dollar? How many times is ^ contained
in 1?
2. At 2 fifths of a dollar per yard, how much cloth
can be bought for 4 fifths of a dollar? How many
times are f contained in |^?
3. If a boy can earn 2 eighths of a dollar per day,
how long will it take him to earn 6 eighths of a dol-
lar? How many times are f contained in f?
4. If a man can mow f of an acre in one hour,
how long Will it take him to mow j- of an acre? How
many times are f contained in -f^?
5. A boy having f of a pound of candy, divided
it equally among his playmates, giving to each f of
a pound. How many playmates had he ?
6. A grocer having ^ of a barrel of vinegar, sold
3^ of a barrel each day until it was all sold. In how
many days did he sell it?
IN AKITHMETIC. 105
7. How many times are -^ contained in 3^, or
what is the vahie of 9 tenths -^ 3 tenths?
8. How many times are -^ contained in 3^, or
what is the value of it "^ IT ^
9. How long will it take a boy to earn ^ of a
dollar, by earning ^ of a dollar per day? How
many times are -fy contained in 3^ ? -fs "^ A ^^ ^
10. How many times are f contained in ^? 3^ in
M? A in if? A in if? ^ in H?
11. How long a time will be required to fill a cis-
tern, if ^ of it is filled every hour ? lor^-^-^ = ?
Slate Exercises.
Find the value of the following :
¥
2
3>®^C
liESSOK I.XIV.
1. If William divides 4 oranges equally between
his 2 sisters, how many will each receive ?
2. What is one-half of 4 cents ? What is one-half
of 4?
3. By what number do you divide to find one-half
of any number ?
4. How many pears is 1 third of 3 pears ?
5. How many pears are 2 thirds of 3 pears?
^1-
¥^*-
¥^l-
¥-^l
^i-
¥^i-
¥^f-
¥-^1
H-
i^h
8^1.
7-^1
106 FIRST LESSONS
6. By what number do you divide to find one-
third of any number? How do you find 2 thirds
of a number?
7. How many roses are one-half of 8 roses?
8. If a woman divides 5 loaves of bread equally
between 5 persons, what part will each person receive ?
9. How many loaves are 3^ of 5 loaves? f of 5
loaves? f of 5 loaves?
10. How is ^ of a number found ? f of a number ?
11. If 14 marbles are equally divided between 2
boys, how many marbles does each boy receive?
12. How many are ^ of 14 ? How many are ^ of 14?
13. One-fourth of 20 cents is how many cents?
14. By what number do you divide to find one-
fourth of any number ?
15. A man shot 12 pigeons and sold ^ of them.
How many had he left?
16. A boy saAv 18 fowls, |- of which were white.
How many were white ?
17. A boy having 40 cents, paid 4 of his money for
pencils and -^ of it for paper. How much did he
have left?
18. A farmer sold 7 bushels of wheat for 28 dollars.
What did he receive for one bushel?
19. How many bushels are ^ of 28 bushels?
20. How many bushels are ^ of 28 bushels?
21. What is J^ of 20? What is | of 56 ?
22. If 25 dollars is divided equally among 5 men,
what part of the money will each receive? How
much will each receive?
IN ARITHMETIC.
107
^
NGTATiONA NUMERATION
tif
LESSOIS^ I.XV.
A single thing is called a Unit,
How many units make one ten? Two tens?
Copy and read
10 12
16 64
27
73
35
42
90
59
99
4. Express in figures the following :
Ten. Forty-eight. Eighty -five.
Thirteen. Sixty-fi3ur. Ninety.
Twenty-five. Seventy-nine. Ninety-three.
Thirty-two. Eighty-one. Ninety-nine.
5. Express in figures the
One ten, no units.
Five tens, six units.
Six tens, four units.
Two tens, seven units.
Seven tens, one unit.
Three tens, five units.
Eight tens, six units.
Foui; tens, five units.
Nine tens, nine units.
following :
One ten, one unit.
Five tens, two units.
Six tens, six units.
Two tens, one unit.
Seven tens, three units.
Three tens, four units.
Eight tens, one unit.
Four tens, six units.
Nine tens, one unit.
108 FIRST LESSONS
6. When two figures are written side by side what
does the one at the right represent? What does the
one at the left represent?
7. How many tens and units in ninety-nine ?
8. If one is added to the 9 units, what is the result?
9. How many are 9 tens and 1 ten ?
10. How many tens make one hundred ?
11. Copy
and reac
1:
100
104
108
116
138
149
157
168
173
123
188
199
205
316
423
216
304
229
12. Express the following in figures ;
One hundred, two tens, and five units.
Four hundreds, five tens, and no units.
Seven hundreds, five tens, and six units.
Eight hundreds, nine tens, and one unit.
Three hundreds, nine tens, and eight units.
Five hundreds, three tens, and seven units.
Two hundred. Nine hundred.
Two hundred, forty. Nine hundred, forty.
Eight hundred, five. Six hundred, seventy.
Three hundred, fifty. Five hundred, eighty.
Three hundred, forty. Five hundred, twenty.
Five hundred, ninety. Seven hundred, thirty.
13. When three figures are written side by side,
what does the one at the right represent? ^ The one
next to it? The one at the left?
IN .
A.IIITHMETIC
. Copy and read
:
314 268
572
681
372
465
200 2G0
350
580
673
856
371 426
842
730
307
406
184 755
862
985
422
999
109
15. Express in figures the following:
Two hundred, ten.
Five hundred, fifty.
Two hundred, forty.
Seven hundred, five.
Eight hundred, four.
Nine hundred, fifteen.
Five hundred, sixteen.
Eight hundred, twelve.
Five hundred, fifty-five.
Four hundred, sixty-six.
Nine hundred, forty -five.
Six hundred, forty-seven.
Eight hundred, fifty-four.
Seven hundred, forty-one.
Nine hundred, ninety-nine.
Eight hundred, sixty-three.
Three hundred, ninety-nine.
Seven hundred, twenty-nine.
The method of expressing numbers by figures is
called the Arabic notation.
The method of reading numbers is called NumeV"
ation.
110 FIRST LESSONS
LESSOIS^ I.XTI.
1. If 1 be added to nine hundred ninety-nine,
how many hundreds will there be?
2. To what are 10 hundreds equal ? One thousand,
3. One thousand is expressed thus: 1^000,
4. Copy and read the following :
1,000 1,004 1,016 1,323 1,548
2,000 2,159 3,872 5,625 7,822
8,465 6,372 4,189 9,786 9,999
5. Express in figures the following:
Seven thousand, two hundred, fifty-six.
Nine thousand, nine hundred, ninety-five.
Five thousand, three hundred, twenty-eight.
6. How many are 9 thousand and 1 thousand?
7. Ten thousand is expressed thus: 10^000,
8. Copy and read the following:
10,000 18,000 ' 22,005 35,012
87,482 96,856 13,729 88,543
9. Express in figures the following:
Ninety thousand, nine hundred, fifty-six.
Eighty -four thousand, five hundred, forty.
Seventy-five thousand, eight hundred, fifty.
Fifty-three thousand, two hundred, twenty.
Eighty thousand, seven hundred, forty-four.
Ninety thousand, nine hundred, ninety-nine.
IN ARITHMETIC. Ill
10. How many are 90 thousand and 10 thousand?
11. One hundred thousand is expressed thus:
100,000.
liESSON I.XTII.
1. Copy and read the following:
" 100,000 120,000 562,000 159,725
540,805 723,016 986,784 684,379
2. What do the three figures at the right repre-
sent? Units, tens, and hundreds,
3. What do the three figures at the left repre-
sent? Units, tens, and hundreds of thousands.
4. A group of figures containing the units, tens,
and hundreds of any denomination is called a Period.
5. How many periods are there in the number
132,654?
6. What is the denomination of the first period?
7. What is the denomination of the second period?
8. Copy and read the following:
354,728
639,955
845,762
876,953
423,872
635,476
82,675
400,800
8,005
264,361
315,008
216,040
9. How many figures must there be in a period?
10. How are the periods separated from each other ?
112 FIEST LESSONS
Express in figures the following:
11. Two hundred eight thousand, five hundred sev-
enty-four.
12. Seven hundred fifty-four thousand, two hundred
twenty-five.
13. Eight hundred sixty-three thousand, four hun-
dred eighty-nine.
14. Eight hundred sixty-five thousand, three hun-
dred thirty-seven.
15. Eighty-four thousand, five hundred eighty-four.
16. Nine hundred thirty-three thousand, six hun-
dred twelve.
17. Three hundred thousand, six hundred.
18. Eight hundred ninety-four thousand, six hun-
dred twenty-four.
19. Five hundred eighty thousand, seven hundred
ninety-seven.
20. Three hundred eighty-nine thousand, seven
hundred eighty-one.
21. Seven hundred eighteen thousand, nine hundred
eighty-seven.
22. Six hundred thousand, one.
23. Six hundred twenty-four thousand, three hun-
dred twenty-nine.
24. Eight hundred thirty-nine thousand, five hun-
dred sixteen.
25. Nine hundred, thirty-five thousand, eight hun-
dred twenty-six.
26. Nine hundred sixty-eight thousand, nine hun-
dred thirty-seven.
IN ARITHMETIC. 113
-^=7^^
LESSON I.XVIII.
1. Helen solved 6 examples, Martha solved 5,
and Jennie solved 9. How many examples did
they all solve ?
2. How many goblets are 3 goblets, 8 goblets,
and 9 goblets?
3. James learned 5 lessons on Monday, 6 lessons
on Tuesday, and 3 lessons on Wednesday. How
many lessons did he learn in the three days?
4. How many marbles are 5 marbles, 4 marbles,
6 marbles, and 2 marbles?
5. After spending 2 cents for a slate-pencil and 5
cents for a lead-pencil, James had 5 cents left. How
much had he at first?
6. How many dollars are 10 dollars and 8 dollars?
DEFINITIONS.
The process of finding one number that is equal
to two or more numbers is called Addition,
The result in addition is called the Sum,
The Sign of Addition is an upright cross : -f- ,
called plus.
The Sign of Equality is two short horizontal
lines: =.
10
114 FIRST LESSONS
1. What is the sum of 5, 4, 7, and 6 ?
PROCESS. Explanation. — For convenience the numbers
n to be added are arranged so that tliey stand in a
column.
"* We begin at the bottom to add, thus: 6, 13,
7 17, 22, and write the sum beneath.
/» Hence, the sum is 22.
In adding say 6, 13, 17, 22, instead of 6 and 7
22 are 13 and 4 are 17 and 5 are 22.
Slate Exercises.
Copy and add the following :
(2.)
(3.)
(4.)
(5.)
(6.)
4
5
6
8
3
2
6
5
2
2
3
3
3
3
5
5
4
2
3
1
7. William shot 6 squirrels, Henry shot 8, John
shot 5, and James shot 7. How many squirrels did
they shoot?
8. Oscar owned 4 cows, Herbert owned 5, George
owned 3, and Clarence owned 6. How many cows
did the four boys own?
9. A merchant received 5 boxes of oranges one
day, 6 the next, and 4 the next. How many boxes of
oranges did he receive?
10. A farmer sold 6 cords of wood to one man, 3
cords to another, 8 to another, and 2 to another.
How many cords of wood did he sell ?
IN ARITHMETIC. 115
Slate Exercises.
Copy and add the following :
(11.)
(12.)
(13.)
(14.)
(15.)
4
6
3
4
6
7
5
6
7
2
8
7
9
2
3
2
8
2
3
9
3
5
6
5
3
4
1
2
4
2
3j^C
liESSON I.XIX.
1. What is the sum of 217, 853, and 365?
PROCESS. Explanation. — For convenience the num-
o 1 Y bers to be added are arranged so that units
Q ^ ey stand under units, and tens under tens, etc.
Beginning at tiie right hand, each column
*^ o " ' is added separately.
2^ z|. 3 5 Thus, 5 + 3-1-7 = 15, the sum of the units.
15 units are equal to 1 ten and 5 units. The 5
is written under the column of units, and the 1 is reserved to add
with the tens.
1 reserved +6 + 5 + 1=13, the sum of the tens. 13 tens are
equal to 1 hundred and 3 tens. The 3 is written under the column
of tens, and the 1 is reserved to add to the column of hundreds.
1 reserved +3 + 8 + 2 = 14, the sum of the hundreds. 14
hundreds are equal to 1 thousand and 4 hundreds, which are written
in thousands' and hundreds' places in the sum.
In adding, name results only. Thus, instead of saying, 5 and 3
are 8 and 7 are 15, say 5, 8, 15.
116 first lessons
Slate Exercises.
Copy and add the following :
(2.)
(3.)
(4.)
(5.)
678
852
338
852
153
365
466
738
261
472
^53
645
(6.)
(7.)
(8.)
(9.)
235
512
832
893
415
416
142
416
268
304
624
842
317
497
615
249
10. A man traveled 250 miles by railroad, 325 by
steamboat, and 190 by stage. How many miles did
he travel ?
11. What is the sum of three thousand five hundred
twenty-six, eight thousand one hundred twelve, six
thousand nine hundred eighteen?
12. A butter-buyer bought 326 pounds of butter
from one dairy, 518 pounds from another, and 168
pounds from another. How many pounds of butter
did he buy?
13. Find the sum of six hundred seventy-nine,
three hundred twenty-eight, and fourteen.
14. Three persons deposited money in a bank. The
first put in 192 dollars, the second 466 dollars, and
the third 825 dollars. How much money did they
deposit ?
I
IN ARITHMETIC. 117
15. A man paid 400 dollars for a span of horses,
150 dollars for a carriage, and 75 dollars for a harness.
How much money did he pay for all ?
Copy and add:
(16.) (17.) (18.)
6,231 27,638 25,789
1,354 13,925 32,644
4,872 53,164 58,793
3,125 41,538 62,461
3,258 31,604 58,261
4,123 58,643 21,469
(19.)
(20.)
(21.)
6,843
13,462
46,845
2,754
26,541
27,891
6,281
32,716
84,263
4,156
42,683
38,419
7,123
94,275
32,981
8,142
24,239
19,497
(22.)
(23.)
(24.)
4,265
68,465
48,634
3,789
31,892
31,299
4,573
47,468
87,109
4,684
39,210
46,296
4,591
40,009
37,415
8,743
32,567
45,984
4,268
26,849
51,846
5,745
45,265
74,695
118
FIRST LESSONS
SUBTRACTION
liESSOI^ I.XX
1. Herbert earned 19 dollars and gave 7 dollars for
a coat. How much had he left?
2. Mary painted 18 pictures and sold 6 of them.
How many had she left?
3. If a man earns 15 dollars a week and uses 8
dollars, how many dollars will he have left?
4. A grocer having 22 pounds of lard, sold 11
pounds of it. How many pounds had he left?
5. William had 12 marbles, but gave away 5 of
them. How many had he left?
6. 25 pencils are how many more than 10 pencils?
7. From a piece of cloth containing 22 yards, 16
yards were cut. How many yards remained?
8. From a cistern containing 40 gallons of water,
10 gallons were drawn out. How many gallons re-
mained ?
9. There are 24 pupils in a school, of whom 13 are
boys. How many are girls?
10. One piece of cloth contained 26 yards, and
another contained 13 yards. How many yards more
were there in the larger piece ?
11. A farmer who had 23 horses, sold 11 of them.
How many horses had he left?
IN ARITHMETIC. 119
DEFINITIONS.
The process of finding the difference between two
numbers is called Subtraction.
The greater of the two numbers is called the
Minuend.
The lesser of the two numbers is called the Sub-
trahend.
The result obtained by subtracting is called the
Meniainder or Difference,
The Sign of Subtraction is a short horizontal
line : — , called minus.
1. From 768 subtract 425.
PKOCESS. Explanation, — For convenience the less
- ^ „ number is written under tlie greater, units
under units, tens under tens, etc.
4 2 5 Beginning at the right hand, each figure
3 4 3 ^^ ^^^^ subtrahend is subtracted from the cor-
responding figure of the minuend.
8 units minus 5 units equal 3 units, which are written under
the units.
6 tens minus 2 tens equal 4 tens, which are written under the
tens.
7 hundreds minus 4 hundreds equal 3 hundreds, which are
written under the hundreds. Hence the remainder is 343.
Slate Exercises.
Copy and subtract the following :
(2.)
(3.)
(4.)
(5.)
(6.)
635
876
957
543
665
421
453
835
320
543
120 FIUST LESSONS
I.ESSOX LXXI.
1. From 7425 subtract 2536?
PROCESS. Explanation. — For convenience the
.,. , ^ . f^ r less number is written under the greater.
Minuend 7425 .^ , .^, ,, ,,/
units under units, tens under tens, hundreds
Subtrahend 2536 under hundreds, etc.
Remainder 4 8 8 9 Beginning at the right hand, each fig-
ure of the subtrahend is subtracted from
the corresponding figure of the minuend.
Since 6 units can not be subtracted from 5 units, 1 ten is united
with the 5 units. 1 ten is equal to 10 units. 10 units and 5 units
are 15 units. 6 units from 15 units leave 9 units. The 9 is writ-
ten in units' place.
Since 1 of the tens was united with the units, there is but 1 ten
left. Because 3 tens can not be subtracted from .1 ten, 1 hundred is
united with the 1 ten. 1 hundred is equal to 10 tens. 10 tens and
1 ten are 11 tens. 3 tens from 11 tens leave 8 tens. The 8 is writ-
ten in tens' place.
Because 5 hundreds can not be subtracted from 3 hundreds,
1 thousand is united with the 3 hundreds. 1 thousand equals 10
hundreds. 10 hundreds and 3 hundreds equal 13 hundreds. 5 hun-
dreds from 13 hundreds leave 8 hundreds. The 8 is expressed in
hundreds' place.
Since 1 thousand was added with the hundreds, there are but
6 thousands left. 2 thousands from 6 thousands leave 4 thousands.
The 4 is written in thousand's place in the remainder.
Hence the remainder is
Slate Exercises.
Copy and subtract the following :
(2.)
(3.) •
(4.)
(5.)
(6.)
6825
8541
3412
1694
3728
4376
7285
1589
469
1963
I
IN ARITHMETIC. 121
Copy and subtract the following :
(7.) (8.) (9.) (10.) (11.)
4328 6351 4211 6253 4101
2579 5472 3587 4897 2853
12. A paid 8,728 dollars for his farm, and B paid
5,935 dollars for his. How much more did A^s farm
cost than B\s?
13. There were manufactured in a cotton factory
1,857 yards on Monday, and 2,139 yards on Tuesday.
How many yards more were manufactured on Tues-
day than on Monday ?
14. A man who owned 8,754 acres of land, sold
3,215 acres to one company, and 2,154 acres to an-
other. How many acres were unsold?
15. From eight thousand, five hundred sixteen,
subtract three thousand, six hundred twenty-four.
16. A mill was purchased for 13,850 dollars, and
afterward sold at a loss of 2,175 dollars. How much
was received for it?
Copy and subtract the following:
(17.) (18.) (19.) (20.) (21.)
15,862 14,684 28,465 35,469 99,846
9,839 13,299 13,984 24,983 31,985
(22.) (23.) (24.) (25.) (26.)
85,724 27,869 35,321 73,814 125,269
46,689 13,780 15,094 15,209 48,736
li
122
FIRST LESSONS
MULTIPLICATION
--^-
LESSON I.XXII.
1. What will 9 sheep cost at 6 dollars a head ?
2. What will 10 quarts of milk cost at 6 cents a
quart ?
3. What will be the cost of 4 wagons at 30 dol-
lars apiece?
4. Since 12 inches make one foot, how many
inches are there in 3 feet?
5. At 11 cents a quart, what will 9 quarts of ber-
ries cost?
6. If a laborer can work but 13 days per month,
how many days can he work in 3 months?
7. In one week there are 7 days. How many
days are there in 12 weeks?
8. If one hogshead of sugar is worth 40 dollars,
what are 2 hogsheads of sugar worth ?
9. If one apple-tree yields 14 bushels of apples,
how many bushels will 2 such trees yield?
10. If a man plants 20 apple-trees in one row,
how many trees will he plant in 5 such rows?
11. When loaf-sugar is worth 15 cents a pound,
how much will 4 pounds cost?
12. What will 9 dozen of peaches cost at 10 cents
per dozen?
I
IN ARITHMETIC. 12»3
13. What will be the cost of 3 copy-books at 20
cents each?
14. What will be the cost of 4 yards of muslin at
30 cents a yard ?
15. If you give 25 cents to each of 3 beggars,
how much will you give them?
DEFINITIONS.
The process of taking one number as many times as
there are units in another, is called Jlultiplication,
The number to be taken or multiplied is called the
Mu ltix> Ilea iid.
The number which shows how many times the
multiplicand is taken is called the 3£ultiplie7\
The result obtained by multiplying is called the
JProduct.
The Sign of Multiplication is an oblique
cross : X . It is read times or multiplied by,
1. Multiply 421 by 3.
■ PROCESS. Explanation. — For convenience the
i ct 1 multiplier is written under the multipli-
Multiplicand 421 jr.-- ... -ixi-ji
cand. Beginning at the right hand each
Multiplier 3^ figure of the multiplicand is multiplied
Product 12 6 3 ^y t^^e multiplier.
Thus 3 times 1 unit are 3 units. The
3 is written in units' place in the product. 3 times 2 tens are 6 tens.
The 6 is written in tens' place in the product.
3 times 4 hundreds are 12 hundreds, which equal 1 thousand and
2 hundreds. The 1 thousand is written in thousands' place and the
the 2 hundreds in hundreds' place in the product.
Hence the product is 1263.
124 first lessons
Slate Exercises.
Copy and multiply the following :
(2.) (3.) (4.) (5.)
6102 5233 5212 7342
4 3 3 2
(7.) (8.) (9.)
5234 3123 4123
2 3 3
liESSOX I.XXIII
1. How many are 8 times 196?
PROCESS. Explanation. — For convenience the mul-
1 Q ^ tiplier is written under the multiplicand. Be-
ginning at the right each figure of the multi-
^ plicand is multiplied by the multiplier.
;[ 5 g g Thus, 8 times 6 units are 48 units. 48 units
are equal to 4 tens and 8 units. The 8 is written
in units' place in the product, and the 4 is reserved to add with the tens.
8 times 9 tens are 72 tens, plus the 4 tens reserved, are 76 tens.
76 tens are equal to 7 hundreds and 6 tens. The 6 is written in tens'
place in the product, and the 7 is reserved to add with the hun-
dreds.
8 times 1 hundred are 8 hundreds, plus 7 hundreds reserved,
are 15 hundreds. 15 hundreds are equal to 1 thousand and 5
hundreds, which are written in hundreds' and thousands' places in
the product.
Hence the product is 1568.
The accuracy of the work may be tested by reviewing it.
IN ARITHMETIC. 125
Copy and
multiply :
(2.)
(3.)
(4.)
(5.)
1345
3824
6325
7863
6
7
(7.)
4
(8.)
5
(6.)
(9.)
7581
6274
6235
7341
3
9
8
2
10. If a ship sails 368 miles in one week, how
many miles will she sail in 7 weeks?
11. There are 5280 feet in a mile. How many
feet are there in 9 miles?
12. What will 6 yoke of cattle cost at 184 dollars
a yoke?
13. If 1 horse is valued at 275 dollars, what is the
value of 6 such horses?
14. If a ship sails 895 miles in 1 week, how far
will she sail in 9 weeks?
15. What is the product of 457 multiplied by 7?
16. What is the product of 784 multiplied by 4?
17. If a clerk receives a salary of 972 dollars a
year, how much will he receive in 5 years?
18. Since there are 365 days in 1 year, how many
days are there in 9 years?
19. Multiply 3452 by 3. Multiply 1472 by 5.
20. Multiply 6841 by 6. Multiply 5261 by 7.
21. Multiply 7186 by 3. Multiply 9167 by 8.
22. Multiply 2041 by 8. Multiply 9380 by 9.
126 FIRST LESSONS,
23. Multiply 4926 by 6. Multiply 4829 by 7.
24. Multiply 3624 by 4. Multiply 1684 by 2.
25. If it takes 5428 shingles for the roof of a house,
how many shingles will it take for 5 such houses?
Copy and multiply :
(26.) (27.)
4753 6529
5 3
(28.)
8881
6
(29.)
9573
4
(30.)
2469
8
(31.)
6382
6
(32.)
4629
7
(33.)
3265
9
(34.)
8475
8
(35.)
8463
4
3^#^C
liESSON^ I.XXIV.
1. Multiply 435 by 37.
FIRST PROCESS. EXPLANATION. — The numbers are
written as before. Since in multiply-
"^^^ ing we multiply by the parts of a
3 7 number, to multiply by 87 we multi'
7v425= 2975 ^^^ ^^ ^^ ^"^ ^^ ^' ^"^ ^^^ ^^^ ^^'
30X425 --^ 12750 7 ^j^^^g 425 ^re 2975, the first par-
37X425=:15725 tial product ; 30 or 3 tens times 425
are 1275 tens or 12750, the second
partial product. The sum of these partial products will be the
entire product.
Hence the entire product is 15725.
IN ARITHMETIC. 127
SECOND PROCESS. EXPLANATION. — In this process the
cipher at the right of the partial prod-
^ uct is omitted and the significant figures
3 7 placed in their proper places. Thus, in
7y42.5= 2975 multiplying by 3 lois, the product is
_ ^' 1275 tens or 12 thousands 7 hundreds
o A 4 -^ L Z i ^^^ g j.gj^g^ which are written in their
15 7 25 proper places in the partial product.
In multiplying by tens the lowest denomination of
the product is tens, in multiplying by hundreds it is
hundreds, by thousands it is thousands. Hence,
The first figure of each product should he placed
under the figui^e by which we multiply.
Slate Exercises.
(2.)
Multiply 3468
By 12
(3.)
4126
31
(4.)
7824
23
(5.)
6846
43
(6.)
7125
37
(7.)
Multiply 4685
By 76
(8.)
7235
83
(9.)
4986
49
(10.)
5843
121
(11.)
1987
316
(12.)
Multiply 5964
By 73
(13.)
6842
39
(14.)
2723
64
(15.)
8962
135
(16.)
8462
216
(17.)
Multiply 8964
By 62
(18.)
3562
36
(19.)
7825
47
(20.)
3265
234
(21.)
9268
327
128
FIRST LESSONS
uMMm
D I V I S I O N
tzz=i
1. How many barrels of flour at 8 dollars a barrel,
can be bought for 72 dollars?
2. If there are 3 feet in a yard, how many yards
are there in 27 feet?
3. At 4 dollars a cord, how many cords of wood
can be bought for 40 dollars?
4. If a man can walk 4 miles per hour, how long
will it take him to walk 36 miles?
5. If 5 paces are a rod of distance, what is the
length in rods of a piece of land which is 30 paces
long ?
6. If paper is put in packages containing 6 sheets
each, how many packages can be made out of 48
sheets ?
7. If 5 bushels of wheat make a barrel of flour,
how many barrels of flour can be made from 40
bushels of wheat?
8. At 6 dollars a ton, how many tons of hay can
be bought for 54 dollars?
9. If a man can build 7 rods of fence in one day,
in how many days can he build 35 rods?
10. If a teacher earns 9 dollars a week, in how
many weeks can she earn 90 dollars? .
IN ARITHMETIC. 129
DEFINITIONS.
The process of finding how many times one num-
ber is contained in another is called JDivision,
The number to be divided is called the Divi-
dend.
The number by which the dividend is to be di-
vided is called the Divisor.
The result in division is called the Quotient,
The part of the dividend remaining when the di-
vision is not exact is called the Remainder,
The Sign of Division is -f-, read divided by.
Til us, 24 -f- 6 is read, 24 divided by 6.
1. How many times is 3 contained in 369?
FIRST PROCESS. EXPLANATION. — For Convenience
Divisor. Dividend. Quotient. the divisor is written at the left of the
3)36 9(100 dividend, and the quotient at the right.
Beginning at the left we divide.
3 is contained in 369 I hundred
times and a remainder. The 100 is
placed in the quotient, and the divisor
is multiplied by it. The product 300
is written under the dividend. Sub-
tracting there is a remainder of 69.
3 is contained in 69, 20 times and a remainder. The 20 is
placed in the quotient and the divisor multiplied by it. The
product 60 is written under the partial dividend. Subtracting the
remainder is 9.
3 is contained in 9, 3 times and no remainder. The 3 is placed in
the quotient, and the divisor multiplied by it. The product 9 is writ-
ten under the partial dividend. Subtracting, there is no remainder.
The true quotient is therefore the sum of the partial quotients,
which is 123, and 3 is contained in 369, 123 times.
300
20
69
3
60
123
9
9
130 FIRST LESSONS
SECOND PROCESS. EXPLANATION. — The second process is
•§ g i the same as the first, except that the ciphers
QNQAQ/'IOQ ^^^ omitted from the right of the quotient
o)oov[iAo figures and partial products, the value of
^ figures being indicated by their position.
g Thus, the figures of the quotient are 1 hun-
Q dred, 2 tens, and 3 units, which are written
— — ' in succession so that each figure represents
" its proper value.
^ The products 3 hundreds, 6 tens and 9
units are placed under hundreds, tens, and
units in the partial dividends.
Slate Exercises.
Copy and divide the following :
(2.) (3.) (4.) (5.)
4)488( 5)550( 3)699( 2)264(
liESSOI^ I.XXVI.
1. How many times is 6 contained in 1398 ?
PROCESS. Explanation. — For convenience the di-
fi^l ^98^2*^'^ visor is written at the left of the dividend
-I 9 and the quotient at the right. Beginning
at the left of the dividend we divide.
1 «^ 6 is not contained in 1 thousand any
1 8 thousand times, therefore the quotient can
2 g not be higher than hundreds. Hence we
-I Q must find how many times 6 is contained
in all the hundreds of the dividend.
1 thousand is equal to 10 hundreds. 10
hundreds plus 3 hundreds equal 13 hundreds. 6 is contained in
IN ARITHMETIC,
131
13 hundreds 2 hundred times and a remainder. The 2 is written
in hundreds' place in the quotient and the divisor multiplied by it.
Subtracting this product from the partial dividend, 13 hundreds,
there is a remainder of 1 hundred.
1 hundred remainder is equal to 10 tens. 10 tens plus 9 tens
equal 19 tens. 6 is contained in 19 tens 3 tens times and a re-
mainder. The 3 is written in tens' place in the quotient, and the
divisor multiplied by it. Subtracting this product from the partial
dividend, 19 tens, there is a remainder of 1 ten in the quotient.
The 1 ten remainder equals 10 units. 10 units plus 8 units
equal 18 units. 6 is contained in 18 units 3 times and no re-
mainder. The 3 is written in units' place in the quotient, and the
divisor multiplied by it.
Hence the quotient is 233.
Slate Exeecises.
Copy and divide the following:
(2.) (3.) (4.)
5)32860( 8)72880( 6)63546(
(6.)
4) 87564 (
(10.)
6) 38412 (
(7.)
7) 67326 (
(11.)
5) 42865 (
(8.)
9) 27819 (
(12.)
8) 32848 (
(5.)
3) 56841 (
(9.)
7) 58562 (
(13.)
4) 48264 (
(14.) (15.) (16.) (17.)
7) 54285 ( 9) 32616 ( 8) 42856 ( 9) 49842 (
The solution of examples having a small divisor,
may be shortened by performing the multiplications
and subtractions without waiting the results. This
process is called Short Division.
132
FIRST LESSONS
PROCESS.
6)1398
233
The solution of Example 1, by short division, is:
Explanation. — 6 is contained in 13 hun-
dreds 2 hundred times and 1 hundred remain-
der. The 2 is written in the quotient under
units of the same order in the dividend.
1 hundred remainder and 9 tens make 19
tens. 6 is contained in 19 tens 3 tens times and 1 ten remainder. The
3 is written in the quotient under tens in the dividend.
1 ten remainder and 8 units make 1<S units. 6 is contained in
18 units 3 times. The 3 is written in the quotient under units.
Hence the quotient is 233.
Solve by short divisio
Q :
18. 4761 -^ 3.
37.
6435^5.
19. 5848-^4.
38.
3280 -4- 8.
20. 3725 -f- 5.
39.
3689-4-7.
21. 4865-^7.
40.
8262^9.
22. 2844-^6.
41.
5984 ^ 4.
23. 7254^9.
42.
6975-^5.
24. 9328 -f- 8.
43.
4284^7.
25. 6832-^7.
44.
6720-^8
26. 9745-^5.
45.
9873 -^ 9.
27. 6835-^5.
46.
3248-^8.
28. 7281 -^ 9.
47.
5274 -^ 6.
29. 3234-^6.
48.
8245 ^ 5.
30. 5948 -f- 4.
49.
3824 ^ 4
31. 4275-^3.
50.
4920-4-8
32. 3577 -f- 7.
51.
3915^9
33. 3486-4-6.
52.
4823 -4- 7
34. 9648^8.
53.
4625-4-5
35. 8936^9.
54.
9441 ^ 3.
36. 8532^6.
55.
8928 -4- 6.
IN ARITHMETIC.
133
liESSON LiXXVII.
1. Divide 4825 by 26.
PROCESS,
pivisor. Dividend. Quotient
26)4825(185
26
222
208
145
130
Explanation.— 26 is not contained
in 4 thousands any thousands times,
hence, the thousands are united with
the hundreds, making 48 hundreds. 26
is contained in 48 hundreds 1 hundred
times and a remainder. The 1 is writ-
ten in hundreds' place in the quotient
and the divisor multiplied by it, giving
a product of 26 hundreds. Subtracting
this product from the partial dividend
48, there is a remainder of 22 hundreds.
22 hundreds united with 2 tens
make 222 tens. 26 is contained in 222 tens 8 tens times and a re-
mainder. The 8 is written in tens' place in the quotient and the
divisor multiplied by it, giving a product of 208 tens. Subtracting
this product from the partial dividend there is a remainder of 14 tens.
14 tens united with 5 units make 145 units. 26 is contained in
145 units 5 times and a remainder. The 5 is written in units' place
in the quotient and the divisor multiplied by it, giving a product of
130 units. Subtracting, there is a remainder of 15.
Therefore the quotient is 185, and the remainder, 15.
Remainder 1 5
Divide :
Divide :
2. 864 by 12.
10.
3358 by 73
3. 845 by 13.
11.
4788 by 84
4. 906 by 21.
12.
3696 by 66
5. 1188 by 22.
13.
1904 by 28
6. 2016 by 32.
14.
3277 by 29
7. 1486 by 33.
15.
5706 by 46
8. 2016 by 30.
16.
45658 by 37
9. 2397 by 51.
17.
55484 by 26
134 FIRST LESSONS
liESSOX I.XXTIII.
UNITED STATES MONEY.
The money of the United States is called United
States Money,
The standard unit is the dollar,
TABLE.
10 Mills are equal to 1 Cent.
10 Cents " " " 1 Dime.
10 Dimes " " " 1 Dollar.
The denomination dimes is not generally used.
The Sign of Dollars is %, a supposed combination of U. S.
1. How many mills are there in 2 cents? In 5
cents ? In 10 cents ?
2. How many cents are there in 2 dimes ? In 4
dimes? In 7 dimes? In 10 dimes or 1 dollar? In
5 dimes or one-half of a dollar ?
3. How many cents are there in |2 ? In $3 ? In
$4? In $5?
4. How many dollars are there in 200 cents? In
300 cents? In 400 cents? In 500 cents?
5. In 450 cents how many dollars are there, and
how many cents besides? In 375 cents? In 425
cents ? In 870 cents ? In 684 cents ? In 296 cents ?
IN ARITHMETIC.
135
1. In expressing dollars and cents by figures, a period called the
decimal point, is placed between the dollars and the cents. Thus,
265 cents are equal to $2.65, which is read, 2 dollars, 65 cents.
2. When less than 10 cents are written, a cipher must be written
before the number. Thus, 5 cents are written, $.05.
3. Mills are written after the cents. Thus, $2,655 is read, 2
dollars, 65 cents, 5 mills.
6. Read the following:
$3.25; $6.38; $7.24; $6.05; $2.46; $7.24;
$5.18; $7.36; $3.02; $5.07; $2.15; $4.16.
7. Write the following :
Five dollars twenty-nine cents.
Seven dollars sixty-eight cents.
Eight dollars seventy-seven cents.
Forty-eight dollars sixteen cents.
Thirty-four dollars nine cents.
Sixty-eight dollars nineteen cents.
3^^C
liESSOX I.XXIX
Slate Exekcises.
Copy and add the following :
(1.) (2.) (3.)
$63.28 $32.18 $24.16
47.15 25.16 37.18
21.15 17.24 22.39
(4.)
(5.)
$38.24
$29.66
29.16
18.39
45.77
14.27
136
FIEST LESSONS
Copy and subtract the following:
(6.) (7.) (8.) (9.) (10.)
$69.84 $63.18 |36.27 $17.64 $33.64
21.39 24.24 28.39 8.89 17.25
(11.) (12.) (13.) (14.) (15.)
$16.00 $45.10 $46.00 $28.76 $64.35
13.28 33.49 25.18 18.87 57.47
Arrange in columns and add :
16. $12.27, $15.34, $18.29, $64.38, $15.92, $2.68.
17. $8.37, $28.05, $36,
18. $5.06,- $2.18, $.34,
19. $3.25, $4.26, $8.35,
20. $8.29, $4.34, $5.69,
21. $14.24, $8, $3.46,
$14.29, $25, $1.25.
$.08, $5.22, $18.
$13, $15.92, $14.96.
$8.34, $7.29, $6.84.
$.75, $2.84, $7.50.
How many are
How many are
22. 3 times $18.24?
28. 18 times $16.24?
23. 7 times $21.36?
29. 30 times $45.61?
24. 12 times $34.29?
30. 24 times $8.64?
25. 15 times $34.09?
31. 35 times $16.80?
26. 5 times $19.26?
32. 32 times $18.25?
27. 8 times $34.18?
33. 25 times $15.24?
What is
What is
34. ^ of $24.35?
38. i of $38.43?
35. i of $13.30?
39. -jV of $34.24?
36. i of $24.36 ?
40. j\ of $9.40?
37. I of $32.48?
41. -^ of $74.26?
IN ARITHMETIC. 137
IjESSON liXXX.
MEASURES OF LENGTH.
The measures used in determining length, or the dis-
tance of one place from another, are called Measures
of Length.
TABLE.
12 Inches are
equal to 1 Foot.
3 Feet
" " 1 Yard.
b\ Yards') «
16^ Feet i
" " 1 Rod.
320 Rods
" " 1 Mile.
1. How many inches are there in 2 feet? In 3
feet ? In 5 feet ? In i of a foot ? In J of a foot ?
2. How many feet are there in 24 inches? In 36
inches? In 48 inches? In 60 inches? In 72 inches?
3. How many feet are there in 3 yards? In 4
yards? In 8 yards? In 9 yards?
4. How many inches are there in 1 yard? In 2
yards? In 4 yards?
5. How many feet are there in 2 rods? In 2 rods
and 5 feet ? In 2 rods and 10 feet ? In 2 rods and
2 yards?
6. How many rods are there in 2 miles ? In 3
miles? In 5 miles?
7. This line is 1 inch long I i I ■ I ■ I ■ I. Cut
a string a foot in length. A yard in length. A rod
in length.
8. Name two places a mile apart. Two miles.
12
FIRST LESSONS
r.Esso:Nr i^xxxi
LIQUID MEASURES.
The measures used in measuring all kinds of liquids
are called Liquid Measures,
TABLE.
4 Gills are equal to 1 Pint.
2 Pints " " " 1 Quart.
4 Quarts " " " 1 Gallon.
In estimating the capacity of cisterns, reservoirs, etc., 31 J gallons
are considered a barrel, and 63 gallons a hogshead.
1. Name some articles that are bought and sold
by the gallon, quart, pint, or gill.
2. How many gills are there in 2 pints? In 3
pints? In 5 pints? In 10 pints? In 12 pints?
3. How many pints are there in 5 quarts? In
7 quarts? 6 quarts? 8 quarts?
4. How many quarts are there in 5 gallons ? In
8 gallons? 7 gallons? 6 gallons?
5. How many pints are there in 12 gills? In
16 gills? In 15 gills? In 21 gills? In 32 gills?
6. How many gallons are there in 12 quarts?
In 16 quarts? In 15 quarts? In 25 quarts?
IN ARITHMETIC.
139
LESSOR I.XXXII.
DRY MEASURES.
The measures used in measuring grain, roots,
fruit, etc., are called Ury Measures.
TABLE.
2 Pints are equal to 1 Quart.
8 Quarts " " " 1 Peck.
4 Pecks " " " 1 Bushel.
In measuring coarse commodities the measure should be heaped.
In measuring grain, seeds, etc., the measure should be even full.
1. Name some articles that are bought and sold
by the bushel, peck, or quart?
2. How many pints are there in 4 quarts? In
8 quarts? In 2 pecks? In 3 pecks? In 4 pecks?
3. How many pecks are there in 2 bushels?
In 5 bushels? In 8 bushels? In 10 bushels?
4. How many quarts are there in 40 pints?
In 60 pints?
5. How many bushels are there in 32 pecks?
In 40 pecks?
6. What will 2 pecks of berries cost at 3 cents
a pint?
140 FIRST LESSONS
LESSOR I.XXXIII.
MEASURES OF WEIGHT.
The weights used in measuring all coarse and heavy
articles, as hay, grain, gro-
ceries, coal, flour, etc., and
all the metals except gold
and silver, and all drugs
except medicines com-
pounded in prescriptions,
are called Avoirdupois Weights.
TABLE.
16 Ounces are equal to 1 Pound.
100 Pounds " " " 1 Hundred-weight.
20 Hundred- weight " 1 Ton.
1. How many ounces are there in 3 piounds?
In 5 pounds?
2. How many pounds are there in 7 hundred-
weight? In 9 hundred-weight?
3. How many pounds are there in 1 ton? In
2 tons? In 5 tons?
4. How many tons are there in 6000 pounds?
5. How many tons and hundred-weight are
there in 4500 pounds? In 2900 pounds?
6. How many tons, hundred-weight, and pounds
are there in 4625 pounds? In 2643 pounds?
7. What will 6 hundred-weight of sugar cost at
9 cents per pound ? At 10 cents per pound?
I
IN ARITHMETIC.
141
8. If a bushel of wheat weighs 60 pounds, how
many bags that hold 2 bushels each will be required
to hold 4800 pounds?
9. What will 5 pounds of indigo cost at 5 cents
an ounce? What will 7 pounds cost?
liESSOX I^XXXIT.
MEASURES OF TIME.
The names of the ordinary divisions of time are
seconds, minutes, hours, days, weeks, months, and years.
TABLE.
60 Seconds
are
equal
to 1 Minute.
60 Minutes
iC
(C
" 1 Hour.
24 Hours
(I
u
" 1 Day.
7 Days
l(
u
" 1 Week.
30 Days
u
u
" 1 Month.
12 Months
a
It
" 1 Year.
365 Days
it
It
" 1 Year.
100 Years
i(
ti
" 1 Century
1. How many seconds are there in 5 minutes?
In 6 minutes? In 10 minutes?
2. How many minutes are there in 2 hours?
J of an hour? In i of an hour?
3. How many hours are there in
} of a day? In J of a day? In \
4. How many days are there in 4 weeks?
6 weeks? In 7 weeks? In 10 weeks?
2 days?
of a day?
In
In
In
142
FIRST LESSONS
5. What part of an hour are 30 minutes? 15
minutes? 45 minutes?
6. How many hours are there in 90 minutes?
In 120 minutes? In 180 minutes?
7. How many centuries are there in 1500 years?
8. Of what century is the year 1501 a part?
TABLE OF MONTHS.
Oi-der.
Name.
No. of Days.
Season.
Ist.
2d.
3d.
January,
February,
March,
31.
28 or
31.
29.
1 Winter.
4th.
5th.
6th.
April,
May,
June,
30.
31.
30.
V Spring.
7th.
8th.
9th.
10th.
July,
August,
September,
October,
31.
31.
30.
31.
Summei
\ Autumr
11th.
November,
30.
i
12th.
December,
31.
1 Winter.
365
\m.
1.
2.
4th?
RHYME OF THE MONTHS.
Thirty days hath September,
April, June, and November.
All the rest have thirty-one
Save February, which alone
Hath twenty-eight, and one day more
We add to it one year in four.
Kepcat the months in their order.
What is the 5th month? The 7th?
The 3d? The 10th? The 8th?
The
IN ARITHMETIC. 143
3. What are the months of Winter? Summer?
Spring? Autumn?
4. How many months have 30 days? How
many 31 days?
COUNTING.
The following denominations are used in count-
ing some classes of articles :
TABLE.
12 things are called 1 dozen.
12 dozen " " 1 gross.
12 gross " " 1 great gross.
20 things " " 1 score.
1. How many eggs are there in 6 dozen eggs?
2. How many dozen are there in 2 great gross?
3. How many are J dozen dozens of eggs?
4. How old is a man who is 3 score years of
age? 3 score and 10?
STATIONERS' TABLE.
The denominations used in the paper trade are :
*■ 24 sheets are equal to 1 qnire.
20 quires " " ** 1 ream.
1. How many sheets of paper are there in 2
quires ? In J of a quire ? In J of a quire ?
2. How many quires are there in 2 reams? In
i of a ream ? In J of a ream ?
3. What will be the cost of a ream of paper
at 20 cents a quire ? At 1 cent a sheet ?
144
FIEST LESSONS
1. The method of expressing numbers by letters
is called the Homan Notation,
Letters. I, V, X, L, C, D, M.
Values. 1, 5, 10, 50, 100, 500, 1000.
TABLE OF KOMAN NOTATION.
I
.... 1
XXII
. . . 22
II
.... 2
XXIII
XXIV
. . . 23
Ill
.... 3
. . . 24
IV .... .
.... 4
XXV
. . . 25
V
.... 5
XXVI
. . . 26
VI
.... 6
XXVII ....
. . . 27
VII
.... 7
XXVIII ....
. . . 28
VIII ....
. . . . 8
XXIX
. . . 29
IX
.... 9
XXX
. . . 30
X
.... 10
XL
. . . 40
XI
• • . . 11
L .
. . . 50
XII
.... 12
LX
. . . 60
XIII ....
.... 13
LXX
. . . 70
XIV
.... 14
LXXX
. . . 80
XV
.... 15
XC
^ . . 90
XVI .... .
.... 16
C
. . .100
XVII ....
.... 17
CC
. . .200
XVIII ....
.... 18
CCCC
. . . 400
XIX
.... 19
J^,..=:w- . .
. . . 500
XX
• • '^
. . . 800
XXI
. . /c^
. . 1000
o**
rrirnTii?
•s "
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