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m:
AUT
I
New Revised Edition,
JUVENILE
MENTAL ARITHMETIC;
AN INTRODUCTION TO THE
"AMERICAN INTELLECTUAL ARITHMETIC."
BY JOHN F. STODDARD, A.M.,
AUTHOE OF THE " NORMAL MATHEMATICAL SERIES," ETC.
TOEONTO:
PUBLISHED BY ADAM MILLER
1869.
STEr.EOTYPED BY
THE GLOBE POINTING COMPANY,
TOEOKTO. *
PREFACE.
The foundation for- a thorough education is laid in
youth. The habits of thought and modes of reasoning
then acquired will exert an influence favoralde or un-
favorable to intellectual development in after j'ears.
It is hoped that this little book, in its s('ope and
arrangement, and in the discussion of the subjects of
which it treats, is adapted to the capacity of j'ouug
pupils ; and that by proper instruction acid ctireful
study, it will produce the desired effect i!poii the
mind, and afford the information it is designed to
impart.
Addition, Subtraction, Multiplication, Division, the
Tables of Weights and Measures, and the elcmeutaiy
parts of Common Fractions have been introduced and
illustrated by appropriate exami)le&.
SUGGESTIONS TO TEACHERS.
For the benefit of those whose experience is limited, I
make the following suggestions in regard to the most
approTect methods of teaching this important branch of
study :
The lesson should be assigned previous to recitation, to
afford the pupils an opportunity for its examination : the
use of the book, by the pupil, during class exercise, should
be iJrohibited.
A question should be read slowly and distinctly, and
the i)upil required to repeat and analyse it without inter-
ruption, unless it be to make a necessary criticism or cor-
rection.
The pupils should not be called upon promiscuously and
not ill rotation, to take part in the recitation.
Care should be taken that the language they use be
strictly correct as to construction and articulation.
If not carefully guarded, joupils, in their hurried solu-
tions, pronounce many simple words incorrectly. For
instance, the words— a?i(?, of, if, for, ivith, what, which,
ivhere, when, costs, quarts, &c,, are not unfrequently pro-
nounced — an, off, ef, fur, withe, wat, witch, ware, wen, coss,
quats, &c.
By careful attention to these particulars, a lesson in
Mental Arithmetic is a practical lesson in elocution, gram-
mar, rhetoric and logic, as well as a lesson in the science
of numbers.
It is respectfully suggested that the particular forms
given for the analysis of questions be adhered to, unless
better ones should be devised by the teacher. J. F. S,
• Those wishing to becoms thoroughly acquainted with Fractions and
arithmetical questions of almost every kind, are referred to Stoddard's
"American Intellectual Arithmetic."
I
1 \
mm
ARITHMETIC.
A number expresses how many.
Numbers are expressed in three ways :
1. By words ; as one, two, three, four, &c.
2. By figures ; as 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0.
3. By letters; as, I, V, X, L, C, D, and M.
The method of expressing numbers by figures
is called the Arabic Method.
The method of expressing numbers by letters
is called the Koman Method.
Count the number of stars in each row, also,,
the number in each column, and express the
number in each by the different methods:
One.
Two.
Three.
Four.
Five.
Six.
Seven.
Eight.
Nine.
Ten. *
*
*
*
•X-
*
*
*
*
*
*
* *
*
*
*
*
*
*
*
*
*
*
*
*
*
1.
2.
3.
4.
5.
6.
7.
8.
9.
I, II, III, IV, V, VI, VII, VIII, IX, X.
1 '2. 3.
4. 5, 6.
8.
9, 10.
MENTAL ARITHMETIC.
H
ARABIC AND ROMAN NUMBERS.
The Arabic and Eoman Methods of expressing
numbers are as follows:
»5
'^ h B3 >4
1 I
2 II
3 III
4 IV
6 V
6 VI
7 VII
8 VIII
9 IX
10 X
11 XI
12 XII
13 XIII
U XIV
15 XV
16 XVI
17 XVII
18 XVIII
19 XIX
NUMBERS.
Naught.
One.
Two.
Three.
Four.
Five.
Six.
Seven.
Eight.
Nine.
Ten.
Eleven.
Twelve.
Thirteen.
Fourteen.
Fifteen.
Sixteen.
Seventeen.
Eighteen.
Nineteen.
gs
< ft
20
21
22
23
24
25
25
27
28
29
30
40
50
CO
70
80
90
100
500
1000
fr PS
O u
NtTMBBRS.
XX Twenty.
XXI Twenty-one.
XXII Twenty-two!
XXIII Twenty-three,
XXIV Twenty-four.
XXV Twenty-five.
XXVI Twenty-six.
XXVII Twenty-seven.
XXVIII Twenty-eight.
XXIX Twenty-nine.
XXX Thirty
XL Forty.
L Fifty.'
LX Sixty.
LXX Seventy.
LXXX Eighty.
XC Ninety.
C One Hundred.
T> Five Hundred.
^I ' One Thousand.
ADDITION.
Lesson I,
1. How many are 2
Analysis. — Two and one are 3.
2. How many are 2
3. How many are 2
4. How many are 2
5. How many are 2
• 6. How many are 2
7. How many are 2
8. How many are 2
9. How many are 2
10. How many are 2
2 and 2 are how
and 1 ?
11.
12.
13.
14.
15.
16.
17.
18.
19.
and
and
and
and
and
and
and
and
2?
3 ?
4?
5 ?
6 ?
7?
8 ?
9?
2
2
2
2
5
2
2
2
and 5 are liow
and 9 are how
and 8 are how
and 6 are how
3
are how
are how
7 are how
and 10 are how
and
and
and
and 10 ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
Lesson II.
1, Henry had 4 apples, and bought 2 more ;
how many did he then have ?
Analysis. — If Henry had 4 apples, and should _buy 2
more, he would then have 4 apples and 2 apples, which are
6 apples.
8
ADDITION.
2. Harvey had 5 books, and James had 2 ; how
many books did both liave ?
3. Mary has 3 peaches, and John gave her 2
more ; how many peaches did she then have ?
4. Moses had 2 cents, and his father gave him
8 more ; how many cents did lie tlien have ?
5. Edwin had 10 marbles, and found two more ;
how many marbles did he then have ?
6. Catharine had G pinks, and Mary gave her 2
more ; iiow many had Catharine then ?
7. Alice found 9 pins, and her mother gave her
2 more ; how many did Alice then have ?
8. Francis spelled 7 words coiTectly and 2
incorrectly ; how manv words were given to
him ?
Lesson ill.
•
].
How
many
are
3
and 1 ?
i
How
many
are
3
and 2 ?
3.
How
many
are
o
O
and 3 ?
4
How
many
are
o
O
and 4 ?
>.
How
many
are
3
and 5 ?
?.
How
many
are
and 6 ?
7.
How
many
are
and 7 ?
8.
How
many
are
3
and 8 ?
9.
How
many
are
3
and 9 ?
10.
How
many
• are
o
and 10 ?
11.
4 and 3
are
how
many ?
12.
3 and 3-
are
how
many ?
13.
2 and 3
are
how
many ?
14.
and 3
are
how
many ?
I i
ADD.r/ON.
9
15.
16.
17.
■•s.
19.
8 and 3 are how many ?
3 and 10 ore how many ?
3 and 7 are how many ?
5 and 3 are liow many ?
11 and 3 are how many ?
Lesson IV.
1. If a ball cost 6 cents, and a top cost 3 cents,
how much will both cost ?
Analysis. — If n ball cost G cents, (xdu a top cost 3
cents, l)oth will cost the sum of 6 cents and 3 cents, which
is 9 cents.
2. A boy paid 3 cents for a cake, and 2 cents for
an orange ; how much did he pay for both ?
3. Emily bought a melon for 10 cents, and a
lemon for 3 cents ; what did she give for both ?
4. There were 9 boys on one bench, and 3 on
'another; liow many boys were on both ?
5. Harriet had 8 sweet apples and 3 sour ones ;
how many apples had she in all ?
6. Kozekiah shot 5 red squirrels and 3 gray
ones ; how many squirrels did he shoot in all ?
7. Darius had 3 books, and his father gave him
3 more ; how many books had he then ?
8. Fanny had G plums, and her sister gave her
3 more ; how many plums had she then ?
9. Betsy gave 7 cents for tape, and 3 cents for
thread ; what did she pay for both ?
10. Thedagave 11 cents for.a comb, and 3 cents
for some hair pins ; how many cents did she pay
for all?
I
10
ADDITION.
: ( t -i
m
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
How many-
How many
How many-
How many-
How many-
How many
•How many
How many
How many
How many
4 and 3
4 and 6
2 and 4
4 and 4
7 and 4
4 and 8
5 and 4
10 and 4
9 and 4
4 and 11
are 4
are 4
are 4
are 4
are 4
;.re 4
are 4
are 4
are 4
are 4
are how
are how
are how
are how
are how
are how
are how
are how
are how
are how
and
and
and
and
and
and
and
and
and
1 ?
2 "
s: ?
4?
5 ?
6 ?
7?
8 ?
9?
and 10 ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many .?
!?f
Lesson VI.
1. Sarah had 4 rings on one finger, and 3 on
another ; how many had she on both fingers ?
2. Walter has 9 chickens, and William 4 ; how
manv have both ?
It'
3. Bought a penci*! for 6 cents, and a i3iece of
rubber for 4 cents ; what did I pay for both ?
ADDITION.
11
4. Bought a bottle of ink for 10 cents, and a pen
for 4 cents ; what was the cost of both ?
5. If a lemon cost 4 cents, and a peach cost 2
cents ; what was the cost of both ?
6. Gave 4 dollars for a hat, and 4 dollars for a
vest ; what was the cost of both ?
7. Jane gave 7 cents for raisins, and 4 cents for
cinnamon ; what did she pay for all ?
8. If a Avriting-book cost 5 cents, and a box of
pens cost 4 cents, what did all cost ?
9. After a cat caught four of Nancy's chickens,
she had but 11 left; how many had she at
first ?
10. A boy, after losing 4 marbles, had only 12
remaining ; how many had he at first ?
Lesson VII
1.
How
many
are
2.
How
ma :y
are
3.
How
many
are
4.
How
many
are
0.
How
many
are
6.
How-
many
are
7.
How
many
are
8.
How
many
are
9.
How
many
are
10.
How
many
are
11.
3 and 5 ;
iire
12.
2 and 5 j
ire
13.
6 and 5 j
ire
5
5
5
5
5
5
5
5
FT
and
and
and
and
and
and
and
and
and
1 ?
2 ?
3 ?
4?
5 ?
6 ?
7?
8 ?
9 ?
licw
how
hcAv
and 10 ?
many ?
many ?
many ?
I
12
^^a
■■;ft
ADDITION.
14.
15.
16.
17.
18.
19.
20.
5
and
and
7 and
9 and
5 and
10 and
11 and
4
5
5
5
8
5
5
how many ?
how many ?
how many ?
how many ?
ctrtj how many ?
are how many ?
are liow^ many ?
are
are
are
are
are
Lesson VIII.
1. If Charles walk 4 miles in one day, and 5
miles in another, how far does he walk in the two
days?
2. If Eebecca has 5 roses, and Mary gives her
3 more, how many will she have then ?
3. If Joshua has 5 cakes, and Jane gives him 2
more, how many will he tlien have ?
4. Thomas gave 8 apples to his companions,
and had 5 remaining; how many had he at
first ?
5 Gave 5 dollars for a pair of pantaloons, and
^ 6 dollars for a hat ; what did both cost ?
^ 6. Andrew caught 9 birds, and Anthony 5-
how many did both catch ? . "^ '
7. Baldwin, after spending 5 cents, had only
7 cents remaining ; how many had he at first ?
8. Martha bought a ribbon for 10 cents, and
thread for 5 cents; what was tho cost of
both ?
9. Caroline had 5 flowers, and Clarinda had 5 •
how many did both have ? '
ADDITION.
13
10. Bought a book for 11 cents, and liad 5 cents
remaining ; how much had I at first ?
1
Lesson IX.
8 1.
How
nrany
are
6
and 1 ?
m 2.'
How
many
are
6
and 2 ?
m 3. '
How
many
are
6
and 3 ?
■ ^'
How
many
are
6
and 4?
■ 5.
How
many
are
6
and 5 ?
9 6.
How
many
are
6
and 6 ?
1 B0
H 7.
How
many
are
7
and 6 ?
, and
1 1 J
S 3^
How
many
are
8
and 6 ?
the two
m ^'
How
many
are
9
and 6 ?
ves her
■ 10.
How
many
are
6
and 10 ?
1 11.
3
and C
are
how
many ?
him 2
1 -^^'
6
and 4
are
how
many ?
1 13.
6
and 8
are
how
many ?
)anions,
I -'^^'
6
and 2
are
how
many ?
he at
■ 15.
6
and 5
are
how
many ?
H 16.
7
and 6
are
how
many ?
ns, and
1 -^^'
9
and G
are
how
many ?
■ 1^-
10
and 6
are
how
many ?
Dny 5;
1 -'-^'
6
and 6
are
how
many ?
1 2^-
6
and 11
are
how
many ?
St?
ts, and
;ost of
had 5 ;
Lesson X.
1. Augustus killed 6 birds, and John 2; how
many did both kill ?
2. Gave 5 cents to Franklin, and 6 cents to Fos-
ter ; how many cents did both receive ?
U
ADDITION.
'I
N
:Ut
S. Granville gave me 4 apples, and Mary gave
me 6 ; how many did both give me ?
4. A farmer having 6 cows, purchased 3 more -
how many had he then ? *
5. Jackson bought 8 papers, and found 6 more ;
how many had he then ?
6. Anna had 6 pictures, and her brother gave
her 6 more ; how many had she then ?
7. A farmer sold horses, and had 6 remaining? •
how many had he at first ?
8. A market-woman sold 6 oranges, and had 7
remaming ; how many had she at first ?
9. A boy sold 10 apples, and had 6 remaining :
now many had he at first ?
^ 10. After losing 6 chestnuts I had 11 remain-
mg ; how many had I at first ?
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
Lesson XI
How many are 7
How many are 7
How many are 7
How many are 7
How many are 7
How many are 7
How many are 7
How many are 7
How many are 7
How many are 7
7 and 4 are how
2 and 7 are how
7 and 5 are how
and
anci
and
and
and
and
and
and
and
1 ?
2 ?
3?
4?
5 ?
6 ?
7?
8 ?
9?
and 10 ?
many ?
many ?
many ?
-♦*
reuiam-
iDDITION.
14.
3
and
7
are
how.
many ?
15.
7
and
6
are
how
many ?
16.
7
and
9
are
how
many ?
17.
7
and
7
are
how
many ?
18.
10
and
are
how
many ?
19.
8
and
7
are
how
many ?
20.
7
and
11
are
how
many ?
15
Lesson XII.
1. A merchant bought 4 barrels of sugar, and 7
barrels of molasses ; how many barrels did he then
have ?
2. Albert is 7 years old, and Austin is 6 ; what
is the sum of their ages ? -
3. Alfred solved 8 questions in arithmetic, and
Abraham 7 ; how many did both solve ?
4. If it take 7 yards of calico for a dress, and
2 yards of cloth for a cloak, how many will it take
for both ?
5. Isaac bought 7 sheets of paper, and 3 more
were given to him ; how many had he then ?
6. If a peck of apples cost 7 cents, and a peck
of pears 10 cents, what did both cost ?
7. J^acob walked 9 miles and rode 7 ; how far
did he go ?
8. In 1 certain class there are 7 boys and 7 girls ;
how many pupils are there in the class ?
9. Jeremiah found 5 quiUs, and John found 7 ;
how many did both find ?
10. In a certain recitation there were 11 ques-
tions correctly answered, and 7 incorrectly answered;,
how many questions were asked ?
16
1.
2.
3.
4
6.
6.
7.
8.
0.
10.
11.
12.
13.
14.
}5.
16.
17.
18.
19.
20.
ADDITION.
Lesson XIU
How many are 3
How many ' are 8
How many are 8
How many are 8
How many are 8
How many are 8
How many are 8
-lIow many are 8
How many are 8
How many are 8
8 and 2 are how
and
and
and
and
and
and
and
and
and
1 ?
2?
3?
4?
5 ?
6?
7?
8?
9?
8 and
8 and
i and
8 and
3
7
4
are how
are how
are how
are how
8 and 6 are how
8 and 9 are how
8 and 10 are how
8 and 8 are how
11 and 8 are how
and 10 ?
many ?
many ?
many ?
many ?
many ?
miiny ?
many ?
many ?
many ?
many ?
1
Lesson XIV.
1. A beggar met two boys; one gave him 7 cents
and the other gave him 8 cents ; how many cents
did both give him ?
-•, -\ J^'^n t.ought a hat for 5 doUars, and a vest
lor » dollars ; what was the cost of both ?
3. Tliere were 8 boys sitting, and 3 standing ;
how many boys were there in all ?
11
ADDITION.
17
4. Eachel gave her teacher 8 pinks, and 2 roses ;
how many flowers did she give her ?
5. Barlow caught 8 squirrels, and Denton caught
4 ; how many did both catch ?
6. If we learn 6 pages this week, and 8 the next,
how many shall we leajrn in the two weeks ?
7. If in one Held there are 8 sheep, and in
another 9, how many are in both ?
8. Charles caught 8 fish, and Matthew caught
8 ; how many did both catch ?
9. George shot 10 pigeons, and James shot 8 ;
how many ^id both shoot ?
10. If one insect has 6 legs, and another insect
has 8, how many legs are on both insects ?
1.
2.
3.
4
5.
6.
7.
8.
9.
10.
11.
12.
13.
14
15.
Lesson XV.
How many are 9
How many are 9
How many are 9
How many are 9
How many are 9
How many are 9
How many are 9
How many are 9
How many are 9
How many are
9 and 3 are bow
9 and 5 are liow
7 and 9 are how
9 and 9 are how
9 and 4 are how
and 1 ?
and 2 ?
and 3 <
and 4 ?
and 5 ?
and 6 ?
and 7 ?
and 8 ?
ajid 9 ?
9 and 10 ?
many ?
many ?
many ?
many ?
many ?
18
ADDITION.
16.
17.
18.
19.
20.
9 and 6 are how many ?
8 and 9 are how many ?
9 and 2 are how many ?
9 and 10 are how many ?
9 and 11 are how many ?
Lesson XVI
1. Two boys, John and James, gave some money
to a beggar; John gave him 9 cents, and James
gave^him 4 cents ; how many cents did both give
2. Gave 6 cents to Henry, and 9 cents to Hiram :
now many cents were given to both ?
3. Gave 7 nuts to one boy, and 9 to another •
now many nuts did both receive ? '
4 Bought strawberries for 9 cents, and plums
lor 5 cents ; what did both cost ?
5. Bought a knife for 11 cents, and a whistle for
y cents ; what was the cost of both ?
6. Gave 10 cents for an arithmetic, and 9 cents
tor a slate ; what did both cost ?
7. Euphemia learned 9 lessons, and Maria learned
« ; now many did both learn ?
8 A boy bought raisins for 9 cents, and a cake
lor 6 cents ; what was the whole cost ?
9. A lady bought some tape for 9 cents, and
some thread for 2 cents ; how much did both
cost ?
10. Gave 12 dollars for a cow, and 9 dollars for
a sheep ; what was given for both ?
ADDITION.
19
1.
2.
3.
4.
B,
a
7.
8.
10.
11.
12.
13.
14
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
26.
29.
50.
5
Lesson XVH
How many are 10 and 1 ?
How many are 10 and 2 ?
How many are 10 and 3 ?
How many are 10 and 4 ?
How many are 10 and 5 ?
How many are 10 and 6 ?
How many are 10 and 7 ?
How many are 10 and 8 ?
How many are 10 and 9 ?
How many are 10 and 10 ?
3 and 10 are how many ?
and 10 are how many ?
2 are how many ?
4 are how many ?
8 and 10 are how many ?
9 and 10 are how many ?
10 and 6 are how many ?
10 and 10 are how many ?
10 and 7 are how many ?
10 and 11 are how many ?
How many are 11 and 2 ?
How many are 11 and 5 ?
How many are 6 and 11 ?
How many are 11 and 3 ?
How many are 11 and 4 ?
How many are 11 and 7 ?
How many are 9 and 11 ?
How many are 11 and 10 ?
How many are 11 and 12 ?
How many are 11 and 14 ?
10 and
10 and
1,1
20
ADDITION.
Lesson XVni.
1. Mary bought a pencil for 6 cents, a book lor
8 cents, and a slate for 10 cents; how much did
all cost ?
2 Joseph had 3 marbles, John 6, and James
10; how many did all have?
3. Bought a cow for 14 dollars, and a calf for 6
dollars; what did both cost?
4. Bought a bottle of ink for 6 cents, some paper
for o cents, and some pens for 10 cents; what was
paid for all ?
5. Susau is 11 years old, and Nancy is 9; what is
the sum of their ages ?
6. If a pound of beef cost 8 cents, and a pound
of pork 11 cents, what did the two pounds
cost J
7. A lady bought pins for 11 cents, and ribbon
lor 7 cents; what was the whole cost?
8 B. sold 9 cows to one man, and 7 cows to
anoth- ; how many did he sell to both?
9 . drover bought 4 cows of one man, 6 of
another, and 11 of another; how many did he
buy? "^
10. A boy gave 10 cents for a whistle, 8 cents
lor a whip, and 6 cents for a top; how much did
he give for all?
11. A merchant sold 12 barrels of flour one
week, and 8 the next week; how many barrels
Old he sell durmg the two woeks ?
12. A farmer bought sugar for 14 doUars, and
molasses for 6 dollars; what cost both?
AJiDniOTH.
21
I
I book tor
much did
ad James
calf for 6
>me paper
what was
9; what is
a pound
• pounds
id ribbon
cows to
lan, 6 of
y did he
, 8 cents
nuch did
lour one
y barrels
lars, and
13. Simeon gare 8 cents for a melon, 6 cents for
a j.Ji\e -apple, i-nd had G cents remaining; how
much haa he at first ?
14. Abner found 12 eggs, and Alice found 10 ;
how many did botli find ?
15. A boy saw 7 pigeons on one tree, 8 on an-,
other, and 5 on another ; how many did ho see in
aU?
16. A man bought a watch for 15 dollars, and
had 10 dollars remaining ; how many dollars had
lie at first ?
17. Egbert gave 4 cherries to Oliver, 7 to Ed-
win, and kept 12 himself; how many had he at
first?
18. Elizabeth picked 8 quarts of blackberries,
Ellen 5 quarts, and Helen 7 quarts; how many
quarts did all pick ?
19. Samuel gave 2 dimes for his breakfast, 4
dimes for his dinner, and had 14 dimes left ; how
much had he at first ?
20. A boy travelled 14 miles one day, and
11 the next; how far did he travel in the two
days ?
21. Henry gave 4 roses to Anna, 6 roses to
Mary, and had 5 roses remaining ; how many roses
had Henry at first ?
22. James picked 6 quarts of blackberries, John
picked 8 quarts, and Maggie picked 12 quarts;
how many quarts did all pick ?
23. Moses bought 7 marbles of John, 9 of Albert,
and 11 of Jackson ; how many did he buy in
aU?
ciUBTRACTION. ^
1. 3
• Analysis
2. 4
3. 5
4. 6
6. . 7
6. 8
7. 9
8. 10
9.
10.
11.
?2.
13.
14.
15.
17.
18.
19.
20.
21.
22.
3
4
5
6
7
8
9
less
.— Threr
less
less
less
less
less
less
less
less
less
less
less
less
less
less
Lesson I
1 are how
lesa one are two.
1 are
1 are
1 are
1 are
1 are
1 are
1 are
2
2
2 are
are
are
2
are
are
are
liow
how
low
How
low
low
low
[low
low
low
low
tiow
[low
16. 10 less
5
fr
I
8
9
23. 10
24.
25,
4
5
less
less
less
less
less
less
less
less
2
2
2 are how
2 are how
3 are how
3 are how
3 are how
3 are how
3 are how
3 are how
3 are how
4 are how
4 are how
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many t
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
SUBTRAOTIOfi.
23
Lesson II.
1. If I have 3 apples, and give 1 of them to
Jamea, liow many have I left?
Analysis. — If I have 3 apples, and give one of them to
James, I will liave remaining the ditterence l»etweeii 3
apples and 1 apple, which is 2 apples.
2. A boy had 4 chestnuts, and gave 1 away
ho w many had ho left ?
3. Catharine had 6 pins, and gave 1 away; how
many had she left ?
4. Rebecca bought G cakes, and ate 2 of them ;
how many had she left?
5. Eachel had 4 apples, and gave 2 of them to
George; how many had she left?
6. Alice iDought 5 cakes, and ate 3 of them for
her dinner; how many had she left?
7. Agnes had G quart? of berries, and sold 2
quarts of them; how many had she remaining?
8. Anna had 5 books, and lost 3 of them; how
many had she remaining ?
9. Weston had 9 marbles, and gave 2 of them
to John ; how many had he remaining ?
10. Eliza had 8 oranges, and gave her sister 2 of
them; how many had she remaining?
11. Sarah had 9 pinks, and gave her teacher 2
of them; how many had she left?
12. Isaac saw 10 pigeons on a tree; 2 of them
flew away; how many remained?
13. David had 6 apples, and gave 3 to his brother;
how many had he remaining?
14. Sold some apples for 9 cents, and some
24
SITFrRACTION.
pears for 4 cents; how much more did I get for
the apples than for the pears ?
15. Louise had 8 roses, and gave 4 of them to
Ann; how many had she remaining?
16. Walter gave 9 cents for a book, and 4.cents
tor a pencil; how much more did the book cost
than the pencil ?
17. A farmer sold a calf for 12 dollars, and a
sheep for 4 dollars; how much more did he receive
tor the calf than the sheep?
18. Jane is 10 years old, and Susan is 6; how
many years older than Susan is Jane?
19. Mary found 12.quiUs, and lost 5 of them •
how many had she remaining? '
20. Pamella gave 13 cents for a comb, and 9
cents for seme tape? how much more did the comb
cost than the tape?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
Lesson ill.
1.
5
less
5
are
JlOW
2.
6
less
5
are
how
3.
7
less
5
are
how
4.
8
less
5
are
how
5.
9
less
5
are
how
6.
10
less
5
are
how
7.
12
less
5
are
how
8.
6
less
6
are
how
0.
7
less
6
are
how
,lp.
8
less
6
are
how
11.
9
less
6
are
how
12.
10
less
6
are
how
many ?
many ?
many ?
many ?
many ?
SUBTRACTION.
13.
11
less
6
are
how
14
6
less
j
are
how
15.
7
less
5
are
how
16.
10
less
7
are
how
17.
9
less
7
are
how
18.
8
kss
5
are
how
19.
12
less
7
are
how
29.
14
less
6
are
how
21.
12
less
2
are
how
22.
13
less
3
are
how
23.
14
less
4
are
how
24.
15
less
5
are
how
25.
12
less
9
are
how
26.
12
less
10
are
l!ow
27.
12
less
7
are
how
2&.
12
less
5
are
how
29.
9
less
7
are
how
30.
13
less
7
are
how
25
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
Lesson IV.
1. Edward had 9 oranges, and gave 5 of them
to his sister ; how many had he left ?
2. A boy had 11 rabbits, 3 of which were killed
by a dog ; how many had he left ?
3. A farmer, having 8 bushels of apples, sold 5
bushels of them ; how many were left ?
4. A boy had 9 birds and 4 squirrels ; how many
more birds had he than squirrels ?
5. There "were 15 questions asked during a reci-
tation, 5 of which were answered incorrectly ; how
many were correctly answered ?
3
96
SUBTRACTION.
lU (^eorge sold some marbles for 11 nn^f
which was 4 cents more than thei? cos • w\.f *''
their cost ? ^^^^ » what was
than t& sponge? *^"^ ^'^^ ''^''*^ <=«st
much ought he to reS back ' '"" '^'' ^°^
itfo1^^TS*--5-J-s,ana.M
be left ? ^"' ^""^ '^^J^ ^l^-fe panes will
sJi, picked
7
3 of whom
s for can-
used 3 of
used ?
n cents,
what was
MTTLTIPLICATION.
Id it for
Id it for
dollars,
Jl; how
Lesson I.
TABLE.
2 times 1 are 2.
3 tim
2 *
2 ^
' 4
3 "
2 '
3 *
' 6.
3 "
2 '
4 '
' 8.
3 "
2 '
5 '
' 10.
3 «
2 '
6 '
' 12.
3 "
2 '
7 ^
' 14.
3 '
2 '
8 '
' 16.
2 '
9 '
' 18.
3 "
2 *
' 10 '
' 20.
3 "
2 '
' 11 '
' 22.
3 "
2 '
' 12 '
' 24.
3 "
2
3
4
5
6
7
9
10
11
12
11
a
ti
It
((
ti
<(
((
(C
«
((
6.
9.
12.
15.
18.
21.
24.
27.
30.
33.
36.
1. How many are 2 times 2 ?
Analysis. — Two times two are fonr.
2.
How
rn any-
are
3.
How
Ill any
are
4.
How
many
are
5.
How
many
are
6.
How
m,any
are
7.
How
many
are
8.
How
many
are
9.
How
many
aro
10.
How
many
are
11.
How
many
are
two times 4 ?
two times 8 ?
two times 3 ?
two times 6 ?
two times 7 ?
two times 9 ?
two times 7 ?
two times 11 ?
two times 10 ?
two times 12 ?
28
MULTIPUCATIOK.
12.
13.
14.
15.
16.
17.
IS.
19.
20.
21.
22.
How
How
How
How
How
How
How
How
How
How
How
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
many
are
three
times 4 ?
times 2 ?
times 3 ?
times 5 ?
times 8 ?
times 7 ?
times 10 ?
times 12 ?
times ll ,?
times 6 ?
times 9 ?
Lesson IJ.
1. What cost 2 lemons, at 4 cents each ?
. Analysis.— If l lemon costs 4 cents, 2 lemons will cost
two times 4 cents, which are 8 cents.
2. What cost 2 apples, at 4 cents each ?
6 \V hat cost 2 peaches, at 3 cents each ?
K )irr^* ^^^^' ^ ^^P^' ^^ ^ <^"^es each ?
5. What cost 3 melons, at 11 cents each ?
b. What cost 3 books, at 12 cents each ?
Q Tm:^^^ ^°^* ^ ^'^^*^^' '^'^ '^ ce^ts each ?
o -vS^^^. ^^^^ ^ pencils, at 6 cents each ?
ound ? ''''^* ^ ^'''''''^^ of raisins, at 12 cents a
J?* ^^^^ "^""^^ ^ pine-apples, at 9 cents each ?
11. What cost 3 lamps, at 4 dimes each ?
each ? ^^ '''''^ ^ looking-glasses, r^i 6 dimes
each ? ^^^^^ '''''^ ^ writing-hooks, at 3 dimes
MULTIPLICATION.
29
es
4?
9S
2 ?
33
3 ?
3S
5?
JS
8 ?
5S
7?
JS
10?
5S
12?
S
lii?
S
61
S
9?
s will cost
?
1?
1?
?
cents a
each ?
3 dimes
5 dimes
14. What cost 3 candlesticks, at 5 dimes each?
15. What-cost 3 inkstands, at 7 cents each ?
16. What cost 2 balls of tape, at 10 cents a
ball?
17. What cost 2 hammers, at 11 cents each ?
18. What cost 3 papers of needles, at 8 cents
a paper ?
19. Wliat cost 2 baskets of strawberries, at 7
cents a basket ?
•
i
Lesson III
TABLE,
4
times 1
are
4.
5
times
1
are 5.
4
2
«
8.
5
«
2
" 10.
4
3
«
12.
5
((
3
" 15.
4
4
((
16.
5
<<
4
" 20.
4
5
(t
20.
I**
D
((
5
" 25.
4
6
((
24.
5
((
6
" 30.
4
" 7
((
28.
5
<(
7
" 35.
4
" 8
((
32.
5
«
8
" 40.
4
9
((
36.
5
a
9
" 45.
4
" 10
IC
40.
5
a
10
" 50.
4
" 11
«
44.
5
(I
11
" 55.
4
" 12
C(
48.
5
((
12
" GO.
1.
Four
times 3
are
how
many ?
2.
Four
times 6
are
how
many ?
3.
Four
times 8
are
how
many ?
4.
Four
times 7
are
how
many ?
5.
Four
times 4
are
how
many ?
6.
Four
times 2
are
how
many ?
•
30
It i
\f f
■•r
;
MULTIPLICATION.
7.
Fcnir
times
11
are
how
8.
Five
times
3
are
how
9.
Five
times
5
are
how
10.
Five
times
4
are
how
11.
Five
times
6
are
how
12.
Foiir
times
10
are
how
la
Five
times
2
are
how
14.
Four
times
2
are
how
15.
Five
times
9
are
how
16.
Five
times
8
are
how
17.
Five
times
10
are
how
18.
Four
times
11
are
how
19.
Five
times
11
are
how
20.
Four
times
12
are
how
21.
Five
times
12
are
how
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
many ?
fnany ?
many ?
many ?
many ?
many ?
Lesson IV.
1. Wliat cost 4 pair of shoes, at 3 dollars a
pair?
2. What cost 5 pounds of mutton, at 6 cents
a pound ?
3. What cost 4 barrels of sugar, at 8 dollars a
barrel ?
4. What cost 5 pounds of sturgeon, at 10 cents
a pound ?
5. What cost 4 pounds of almonds, at 11 cents
a pourd ?
6. What cost 5 barrels of pork, at 9 dollars a
barrel ?
7. What cost 4 pounds of candles, at 10 cents
a pound ?
MULTIPLICATION.
h
8. What cost 5 coats, at 4 dollars each ?
9. What cost 4 handkerchiefs, at 5 dimes
«aeh ?
10. AVhat cost 5 lamps, at 3 dimes each ?
11. AAHiat cost 4 plows, at 7 dollars each ?
12. What cost 5 boxes of caps, at 11 cents a
box?
13. Wh it cost 4 quires of paper, at 12 cents a
quire ? •
14. What cost 5 letter-folders, at 11 cents
each ?
15. Wliat cost 4 oranges, at 7 cents each ?
16. What cost 5 pen-knives, at 12 cents
each ?
17. What cost 4 bunches of grapes, at 9 cents a
bunch?
18. What cost 5 pine-apples, at 8 cents each ?
19. What cost 4 spools of cotton, at 6 cents
each ?
20. What cost 5 pounds of ginger, at 7 cents a
pound ?
Lesson V.
TABLE.
6
times
1
are 6.
6
times
. 7 are
42.
6
2
" 12.
6
8 "
48.
6
o
" 18.
6
9 "
54
6
4
" 24.
6
10 "
60.
S
5
" 30.
6
11 "
66.
€
6
" 36.
6
12 "
72.
^^ift^i*
32
MULTIPLICATION.
7
7
7
7
7
7
1.
2.
iS.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24
25.
26.
times
((
(I
(C
((
1
2
3
4
5
6
are 7.
14.
21.
28.
35.
42.
7
7
7
7
7
7
times
((
7
8
9
10
11
12
Six times 2 are how many ?
Six times 5 are how many ?
Seven times 5 are how many ?
Seven times 2 are how many ?
Six times 8 are ho^^' many ?
Six times 7 are how many ?
Six times 10 are how many ?
Seven times 7 are how many ?
Seven times 8 are how many?
Seven times 10 are how many ?
Six times 3 are how many ?
Six times 6 are how many ?
Six times 4 are how many ?
Seven times G ai-e how many ?
Seven times 3 are how many ?
Seven times 4 are how many ?
Six times 9 are how many ?
Six times 12 are liow many ?
Six times 21 are how many ?
Seven times 11 are ho^^r many ?
Seven times 9 are how many ?
Seven times 12 are how many ?
Seven times 13 are how many ?
Seven times 15 are how many ?
Six times 15 are how many ?
Six times 20 are how many ?
are
49.
56.
63.
70.
77.
84
MULTIPLICATION
33
Lesson VI
1. "Wliat cost 6 quarts of cherries, at 4 cents a
quart ?
2. "Wliat cost 7 quarts of raspberries, at 4 cents
a quart ?
3. What cost 6 lead pencils, at 5 cents each ?
4. What cost 7 pens, at 3 cents each ?
5. What cost 7 lead pencils, at 5 cents each ?
6. What cost 5 cakes, a*-j 3 cents each ?
7. What cost 7 figs, at 2 cents each ?
8. What cost 5 pictures, at 6 cents .each ?
9. What cost 5 tomatoes, at 2 cents each ?
10. What cost 6 ounces of cinnamon, at & cents
a^ ounce ?
\ 11. What cost 5 pounds of cheese, at 8 cents a'
pound ?
j^ 12. What cost 7 pounds of prunes, at 9 cents a
: pound ?
Y 13. What cost 5 fish-hooks, at 9 cents each ?
'y- 14. What cost 7 yards of calico, at 8 cents a
yard ?
*-*— -15. Wliat cost G skeins of silk, at 8 cents 4
skein ?
r 16. What cost G pounds of starch, at 12 cents a
.pound ?
^^ 17. What cost 7 barrels of fiour, at 10 dollars a
barrel ?
18. What cost 6 bushels of potatoes, at 9 dimes
a bushel ?
" 19. What cost 7 primers, at 11 cents each ?
20. What cost 7 coats, at 12 dollars each ?
u
MULTIPLICATION.
Lesson Vn.
i
*
\k
■
TABLE.
8 times 1
8
8
8
8
8
8
8
8
8
8
8
1.
2.
3.
4.
5.
G.
7.
8.
9.
10.
11.
12.
13.
14.
15.
IG.
(C
«
«
<(
<(
((
((
((
<<
2
3
4
5
G
7
8
^9
10
11
12
are
(I
((
<(
((
c<
<(
tc
<(
8.
16.
24.
32.
40.
48.
56.
64
72.
80.
88.
96.
9
9
9
9
9
9
9
9
9
9
9
9
times
((
((
((
Cl
(I
((
<(
(C
((
1
2
3
4
5
G
7
8
9,
10
11
12
^ight times 4 are how many ?
Eiglit times 6 are liow many ?
Eight timep 3 are how many ?
Eight times 2 are liow many ?
Eight times 5 are how many ?
Nine times 4 are how many ?
Nine times 3 are liow many ?
Nine times G are how many ?
Nine times 5 are liow many ?
Nine times 2 are how many ?
Eight times 12 are how many ?
Nine times 7 are how many ?
Eight times 1 1 are how many ?
Nine times 8 are how many ?
Nine times 10 are how many ?
Eight times 10 are how many ?
are. 9.
18.
27.
36.
45.
54.
63.
72.
81.
90.
99.
" 108
((
((
<c
<c
,(
II
(I
((
((
MULTIPLICATION.
M
17 Ei"lit times 9 are how many ?
18. Nine times 11 arc how many ?
19 Eight times 8 are how many ?
20* Nine times 12 are how many ?
Lesson VIIl
1. What cost 9 sticks of tape, at 4 cents a
'^'2^ What cost 8 yards of calico, at 12 cents a
^^3 What cost 9 combs, at 2 cents each 1
4 What cost 8 pine-apples, at 11 cents each ^
5'. What cost 9 spools of thread, at 11 cents a
^"^t What cost 8 brushes, at 10 cents each ?
7! What cost 9 cakes of paint, at o dimes a
^^ a What cost 8 yards of miisUn, at 9 cents a
^% What cost 9 citrons, at 9 cents each ?
lb. What cost 8 boxes of caps, at 8 cents a
11 What cost 9 orangt- , at 6 cents each ?
12. What cost 8 boxes of figs, at 7 dimes a
^13 What cost 9 lemons, at 7 cents each ?
14 Wliat cost 9 feet of boards, at 8 cents a
^""^5. What cost 9 bushels of oats, at 11 cents a
bushel ?
*
I
II
36
MULTIPLICATION.
i;
16. What cost 8 yards of merino, at 3 dimes a
^'Tt. What cost 9 yards of broadcloth, at 5 dollars
^ ^iT What cost 9 plows, at 10 dollars each ?
19 What cost 8 chickens, at 5 cents each ?
20. What cost 9 pigeons, at 12 cents each ?
Lesson IX.
TABLE.
10 times 1 are 10. I H times 1 are 11.
10
10
10
10
10
10
10
10
10
10
10
((
«
((
i(
((
it
((
2
3
4
5
6
7
8
9
10
11
12
20.
30.
40.
50.
60.
70.
80.
90.
" 100.
" 110.
" 120.
((
11
11
11
11
11
11
11
11
11
11
11
((
((
<(
«
«
C(
c.
C(
{(
2
3
4
5
6
7
8
9
10
11
12
22.
33.
44.
55.
66.
77.
88.
99.
" 110.
" 121.
" 132.
(C
Lesson X.
1. If ahoy travel 5 miles in one day, how far
will he go in 10 days ?
2. If a boy earn 5 cents a day, how many cents
will he earn in 11 days ? . , i , n
3. If James has 3 marbles, and John has ii
times as many, how many has he ?
MULTIPLICATION.
IT
4. If a hare run 3 rods in a-eccond,howfar wiU
fthe run in 10 seconds ? , . ^ ^ . .
5.Tacob ia 7 years old, ancl.Tosiah is 11 times as
old as Jacob ; how old is Josiah ?
6 If I pay 7 cents for riding, one mde. how
mudi must I pay for riding 10 miles ?
7. Mary has 2 roses, and fearah has 10 tuaes as
manv ; how many has she ? , ^ ^.
8^%ert killed 2 birds, and saw 11 times as
-TSl t:r?L^o:^i^ lO times as '
To'^ yr; gri Itei^s L a piece of pie ; what
would 11 pieces cost at the same rate ?
11. If a stage-coach go G miles in one hour, how
far i«ll it eo in 11 hour? ?
Vr If a man shear C sheep in one day. how
manv can he shear in 10 days ? . .,
13^ Henry is worth 8 dollars, and Hiram is wortn
11 times as much; how much is Hiram worth?
14. What wUl 8 tons of hay cost, at 10 douars
"" *15. mat wiU 9 firkins of butter cost, at 11
'°?rw£will 9 pounds of fish cost, at 11 cents
^ ^riunson caught 10 fish and Marvin 10
times as many ; how many did Marvm catch?
18. What cost 11 .parts ot wahiuts, at 10 c«nt3
^ Ta'A farmer sold 11 cattle, at 11 dollais.each ;
what did he receive for them all ?
4
«
38
irULTIPLICATION.
Lesson XI
TADLB.
12
12
12
12
12
12
12
12
12
12
12
12
How
How
How
How-
How
How
How
How
How
liX How
Twelve
Twelve
Twelve
Twelve
Twelve
Twelve
Twelve
1.
»>
mi.
• k
o.
4
a
times
«
«
luanv
luanv
lUiiiiy
manv
manv
luauv
immv
manv
uiany
many
timecji
times
times
times
times
times
times 6
S
12
11
o
9
•»
o
1
5
6
7
8
10
11
12
are
are
ai-e
an?
art'
are
are
Lxn.»
are
are
are
are
are
are
are
ore
are
are
u
((
((
a
u
<(
<t
«
12
12
12
12
12
12
12
12
12
12
how
bow
how
how
how
hov/
how
12.
24
36.
48.
60.
72.
84
96.
108.
120.
132.
144
times
times
times
times
times
times
times
3 ?
5 ?
4 i
2 ?
6 ?
7 ?
9 ?
times 11 ?
times 12 ?
times 10 ?
miiny 1
manv ;
manv {
w
manv ?
many I
manv ?
mau-#- 1
MFLTIPLICATION.
39
Lesson XXI.
"TlTa Bchool-room arc 12 benches, and
bovs on each bench; ho. many boys m the
Tin a corn-field are 12 -ws and 12 hills in
each row; 1-- --^ ^""Cte fen s a ponnd,
J?-aJnc:air;el^lo„nd?.hat
'^f Ttanerlld U bushcb of potatoes, and had
12tints~any bushels remaining; how many
n^l^'r^y^oWrS^'l^ rows of seats, and
seis in eatrow; 1- -ny 3 -^^^^^^
8. What cost 8 pounds oi chocolate, ai i-
" n^boy earned 35 cents a day a;-) paul 25
cents aday for his board; how much had he lett
at the expiration ot days ^^j_
10 A farmer bought '.) aoies ot una, at
lart an acre; what did it all costs
f w
III
40
MULTIPLICATION.
Note.— Tlie sign of Multiplication is x, and is
times. The sign of equality is =, and is read equais,
read nvltiplied by, or
or equal to.
IX 1= 1
2X 1= 2
3X 1= 3
4X 1= 4
5X 1= 5
6X 1= 6
7X 1- 7
8X 1= 8
9X 1= 9
lOx 1= 10
IX 2= 2
2X 2= 4
3X 2= 6
4X 2= 8
5X 2= 10
6X 2= 12
7X 2= 14
8X 2= 16
9X 2= 18
lOx 2= 20
UX 1= 11 llX 2= 22
12x 1= 12I12X 2= 24
IX 3=
2X 3=
3X 3=
4X 3=
5X 3=
6X 3=
7< 3=
8X 3=
9X 3=
10 X 3--=
IIX 3-
12 X 3=
3
6
9
12
15
18
21
24
27
30
33
30
IX
2X
3)^
4X
5X
6X
7X
8X
9X
lOX
IIX
12X
4= 4
4= 8
4= 12
4= 16
4= 20
4= 24
4= 28
4= 32
4= 36
4= 40
4= 44
4= 48
IX 5- 5
IX 6-
2X 5= 10
2V '\z=z
3X 5— 15
3.C 6-
4X 5= 20
4X 6=
5X 5— 25
5X 6=
6X 5= 30
TX 5= 35
8X 5= 40
9X 5= 45
lOX 5= 50
UX 5= 55
12X 5= 60
6, IX 7=
12 1 2X 7 =
18
24
30
6X 6=r 36
7X 6= 42
8X 6= 48
9X 0= 54
lOX 6= 60
3X 7 =
4X 7 =
5X 7=
6X 7 =
7X 7 =
8X 7=
OX 7=
lOX 7 =
UX 6= 66 UX 7 =
7
14
21
28
35
42
49
56
03
70
77
84
IX 8 =
2X 8 =
3X 8 =
4X 8=
5X 8 =
6X 8 =
7X 8 =
8X 8 =
9X 8-
lOX 8-
UX 8 =
12X 8 =
IX 9= 91 1x10= lOi 1 xll =
2X 9= 181 2x10= 20 2x11 =
3x11 =
4xU =
3X «= 27
4X 9= 36
5X 9= 45
6X 9= 54
7X 9= 63
8X 9= 72
9X 9= 81
lOX 9= 90
3x10= 30
4x10= 40
5x10= 50
6x10= 60
IIX
12X
9= 99
9 = 108
7x10 =
= 70!
8x10 =
= 80
9 X 10 =
= 90
10x10 =
= 100
11x10 =
= 110
12 X 10 -
= 120
5 xU =
6x11 =
7x11 =
8x11 =
9x11 =
10x11 =
U xll =
12x11 =
U
22
33
44
55
66
77
88
99
110
121
132
8
16
24
32
40
48
56
64
72
80
38
96
1x12 =
2x12 =
3x12 =
4x12 =
5x12 =
6x12 =
7x12 =
8x12 =
9x12 =
10x12 =
U xl2 =
12x12
12
24
36
48
60
= 72
= 84
= 96
= 108
= 120
= 132
= 144
DIVISION
Lesson I
1 4 are liow many
ANALYBIS.-4 are as many times
tin;esiu4,wliichare2^tmies.
2.
times 2 ?
2, as 2 is contained
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.,
13.
14
15.
16.
17.
18.
2 are how many
G are liow many
8 are how many
10 are how many
12 are how many
14 are how many
16 ave how many
3 are how many
9 are how many
G are how many
12 are how many
15 are how many
18 are how many
21 are how many
18 are how many
20 are how many
22 are how many
times 2 1
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times 2 ?
times o 5
times
times
times
times 3 ?
tunes •-> ^
tunes o ^
times 2 ?
times 2 ?
times 2 ?
3 ?
3?
Lesson II.
l.IfI<,ivefovoneapple2cents,howmany
42
DIVISION.
i I
II'
2. At 2 cents each, how many pears can I buy
for 6 cents ?
3. At 2 cents each, how many oraiiges can I
buy for 8 cents ?
4. At three dimes a yard, how many yards of
tcalico can he had for 12 dimes ?
5. At 3 cents each, how many lemons can be had
for 9 cents ?
6. At 2 cents a yard, how many yards of tape
<;an be bought for 10 cents ?
7. At 2 dimes a bushel, how many bushels of
apples may be had for 12 dimes ?
8. How many baskets of strawberries, at 3 cents
a basket, can be had for 15 cents ?
9. How many pounds of ginger, at 2 dimes a
pound, may be liad for 14 dimes ?
10. For 18 dollars, how many yards of cloth can
be had, at 2 dollars a yard ?
11. For 16 apples, how many oranges can be
had, by giving. 2 apples for 1 orange ?
12. How many primers, at 2 cents each, can be
had for 26 cents ?
13. How many barrels of flour, at 2 dollars a
barrel, can be bought for 24 dollars ?
14. For 22 dollars, how many sheep may be
bought, at 2 dollars each ?
15. How many melons, at 3 dimes each, may be
had for 18 dimes?
16. At 3 cents each, liow many tops may be
had for 6 cents ?
17. If 1 peck of beans cost 3 dimes, how many
pecks can be bought for 21 dimes ?
DIVISION'.
43
X 8 are
2. 12 are
3. 16 are
4 5 are
5. 10 are
6. 20 are
7. 15 are
8. 28 are
9. 20 are
10. 32 are
11. 36 are
12. 28 are
13. 30 are
14 25 are
15. 35 are
16. 36 are
17. 27 are
18. 36 are
19. 48 are
20. 48 are
Lesson IH
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
how many
times 4 ?
times 4 ?
times 4 ?
times 5 ?
times 5 ?
times 4 ?
times 5 ?
times 4 ?
times 5 ?
times 4 ?
times 2 ?
times 2 ?
times 5 ^
times 5 r
times 5 ?
times 4 ?
times 3 ?
tim^s 3 ?
times 4 ?
times 3 ?
Lesson IV.
. 1. If4 Ijoota- cost 8 cents, ^Tllat mil 1 book
^° t irrs^roriJ cents. ...t .^ 1
orange cost ?
I
u
DIVISION.
3. If 4 lemons cost 16 cents, what will 1 lemon
cost ?
4. If a boy walk 20 miles in 4 days, how far
does he walk in 1 day ?
5. If a boy divide 10 apples equally among 5 of
his playmates, how many will each receiw^ '^
G> A boy distributed 15 walnuts equally among
5 of his playmates ; how many did each receive ?
7, A man gave 28 dollars for 4 hogs; how much
did they cost each ?
a A boy sold 5 baskets of berries for 20 cents ;
how much did he get for one basket ?
9. Mary gave 35 cents for 5 pencils ; how much
were they each ?
10. Margaret gave 36 cents for 4 spools of thread ;
how much did she pay for each ;
11. Thornton walked 27 miles in 3 days; how
far did he walk each day?
12. If 3 inkstands cost 36 cents, what will 1
inkstand cost?
13. If 2 yards of calico cost 36 cents, how much
will one yard cost ;
14. If 4 pounds of beef cost 32 cents, what will
1 pound cost ?
15. If 2 balls of cotton cost 28 cents, what will
1 ball cost ?
16. If 3 melons cost 30 cents, what will 1 melon
cost ?
17. A man sold 3 cows for 48 dollars ; how much
was that for each ?
18. Albert gave 36 marbles for 4 oranges ; how
many marbles did he give for 1 orange?
MUtTIPLIOATIOH AND DIVI5I0S.
i!>
Lesson V.
Multiplication and DiviMm CmMrud.
L 3 times 4 are how many times 2?
A.NAWSIS -3 times 4 are 12. 12 is a? mauy time^ 2 «
3 it!Sed times in 12. which are 6 Umes. ^
2 3 times 6 are how many times 2 .
3 3tiiiies 8 are how many times 2 ?
4 3 times 10 are how many times 2 ?
t 3 toes 12 are how many times 2 ?
6 3 times 12 are how many times 2 ?
7 4 times 4 are how many times 2 ?
8 4 times 5 are how many tunes 2 ?
9 4 times 6 are how many imes 3 ?
- 4 times 7 are how many times 2 ?
4 times 8 are how many times ^ ■
4 times 9 are how many imes b ^
4 times 10 are how many times b ■
4 times 11 are liow many times 2 .
4 times 12 are how many times 6 .
4 times 12 are how many times o ■
5 times 6 are how many times 6 .
5 times 8 are how many times 4 ?
5 times 9 are how many times 3 !
5 times 10 are how many times 2 ?
How many times 4 are 5 times 12 ?
How many times 3 are 6 times 4?
How man^ times 3 are 6 times 7?
How many times 3 are 6 times 5 .
How many times 4 are 6 times 8?
How many times 3 are C times 10 ?
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
'y
W
46
MULTrPLICATION AND DIVISION.
27. How
28. How
29. How
30. How
31. How
32. How
33. How
34. How
35. How
36. How
37. How
38. How
39. How
40. How
many
many
many
many
many
many
many
many
many
many
many
many
many
many
times
times
times
times
times
times
times
times
times
times
times
times
times
times
3 are
10 are
4 aie
6 are
5 .ire
3 are
6 are
15 are
6 are
7 are
5 are
7 are
9 are
4 arf.
6 time&
8 times
8 times
8 times
8 times
9 times
9 times
9 times
9 times
2 times
10 times
3 times
12 times
12 times
11?
5?
7?
9?
10?
or
8?
10 T
12?
14?
7?
14?
6?
P?
Lesson VI
Practical QitestiortSf combining Midtip^icatio'n aiid Division.
1. If 2 pears cost 4 cents, what will 3 pears
cost?
Analysis.— If 2 pears cost 4 cents, 1 pear will cost one-
half of 4 cents, which is 2 cents. If 1 pear cost 2 cents, 3
pears will cost 3 times 2 cents, which are 6 cents.
2. If 2 pens cost 6 •cents, what will 5 pens
cost?
3. If 2 melons cost 24 cents, what will 3 melons
cost?
4. If 2 lemons cost 8 cents, what will 4 lemons
cost?
5. If 2 books cost 10 dimes, what will 6 books
cost?
MULTIPLICATION AND DIVISION.
47
6. If 2 oranges cost 6 cents, what will 10 oranges
^"^ 7.* If 3 pine-apples cost 36 cents, what will 7
^tTs'lT^^^ cents, what wiU 5 cost?
9. If 3 pencils cost 18 cents, what will 6 pencils
'""to Ii 3 pens cost 9 cents, what will 8 cost?
11. If 3 caps cost 12 dimes, what will 10 caps
^^12^ If 3 pairs of shoes cost 6 dollars, what will
8 P^^^^j^^^^^^ ^^^, ,,,n 18 doUars a week, how
many dollars can 8 men earn in a week ?
14. If 3 candies cost 6 cents, what wiU .^
'^If IfTcIves cost 16 dollars, what will 9 calves
""""iG. If 4 sheep cost 12 dollars, what will 12 sheep
^""iV. If 4 men cut 8 cords of wood, how many
cords will 9 men cut ? . ^\ -m
18 If 7 quarts of milk cost 35 cents, what will
^ T9''^HoTmanv coats can be cut out of 36 yards
of cloth, if 4 coats can be cut out of 12 yards oi
the same kind of cloth? ^ . ..
20. What will 30 pounds of sugar cost, U
pounds cost 30 cents ? .4. ;f c r^rimida
21. Whatwilll8poundsof vealoost,if6pOui^a^
cost 42 cents? ^ . , -ri r.
5>2. What wiU 13 pounds of pork cost, li t)
pounds cost 48 cents ?
48
MULTIPLICATION AND DIVISION.
f
IS
23. What will 20 weeks* board come to, if 6
weeks' board conies to 12 dollars ?
24. What will be the cost of 25 bushels of
applet, if 9 bushels cost 90 cents ?
25. "What will 14 pounds of cheese cost, if 8
pounds cost 40 cents ?
26. If 6 men can do a certain piece of work in
18 days^ in how many days can 12 men do tlie
same work ?
27. Gave for a quantity of cotton 72 dollars, and
sold it for 12 yards of cloth ; how much did the
cloth cost a yard ?
28. What cost 10 cows, if 3 cows cost 45 dollars ?
29. If 4 oranges are worth 16 apples, how many
apples are 12 oranges worth?
30. How many men can, in 4 days, do as much
work as 8 men can in 7 days ?
' 31. How many men can, in 3 days, do as much
work as 9 men in 5 days ?
32. How many days will it take 5 men to do
what it takes 6 men 10 days to perform ?
33. What will 12 pounds of fish cost, if 8 pounds
cost 72 cents ?
34. What will 15 yards of cloth cost, if 7 yards
cost 35 dollars ?
35. What cost 14 geese, if 9 cost 72 dimes ?
36. What cost 13 locks, if 7 cost 70 cents ?
37. What cost 16 ducks, if 5 cost 100 cents?
38. How far can a boy travel in 9 days, if in 7
days he travel 63 miles ?
39. How far could a man ride for 120 cents, if
for 40 cents he could ride 8 miles ?
f!^
•igmim^''
COMPOUND DENOMINATE
NUMBERS.
Lesson I.
Table of United States Cubrenct.
10 Mills make 1 Cent, marked ct
10 Cents " 1 l>inie, d^-
10 Dimes, or ) « ^ Dollar, " $•
100 Cents i , ^ i n v
10 Dollars 1 Eagle, ■''"
1 dollar^
1. How many mills in 6 cents ?
Analysis Ist.-Ih 1 cent there are 10 mills, therefore
10 tfmeX number of cents equal the number of mills.
10 times 6 are CO mills.
Analysis 2ND.-In 1 cent there are 10 mills, and in 6
cents there are 6 times 10, Avhich are 60 miUs.
2. How many mills in 1 cent? in 2 cents? in 3
cents ? in 4 cents ? in 5 cents ? „ , . o
3. How many cents in 1 dime? in 3 dimes?
in 4 dimes ? in 2 dimes ? in 5 dmies ? m 6
dimes? ^ i n o
4. How many dimes in 1 doUar? in 2 dollars?
in 4 doUars ? in 3 dollars ? in 7 dollars ? m 8 dol-
lars ? in 9 dollars ? in 6 dollars ?
5 How many doUars in 1 eagle ? in 4 eagles i
in 3 eagles ? in 5 eagles ? in 9 eagles ?
50
COMPOUND NUMBERS.
G. In 50 mills how many cents ?
11
Analysis.— There are 10 mUlw in 1 cent, therefore one-
tenth of the number of milb equals the number of cents,
One-tentli of 50 in 5 cents.
7.
8.
9.
10.
11.
12.
13.
14
15.
16.
17.
18.
In 20
In 30
In GO
In 70
In 80
In 00
In 20
In 30
In 90
In 80
In 40
In 60
mills how many cents ?
cents liow many dimes ?
cents how many dimes ?
cents how many dimes ?
cents how many dimes ?
cents how many dimes ?
dimes how many dollars ?
dimes how many dollars ?
dimes how many dollars ?
dimes how many doUars ?
dollars how many eagles ?
dollars how many eagles ?
po
po
ai
ai
Lesson II.
Table of English Mosey.
4 Farthings [tjr.] make 1 Penny, marked d.
12 Penes " 1 Shilling, " a.
- 20 Shillings " 1 Pound, " £.
1. How many pence in 5 shillings ?
Analysis. — In one shilling tliere are 12 pence, therefore
12 times the number of shillings equal the number of pence
12 times 5 are 60 pence.
2. How many farthings in 2 pence? in 4 pence?
in 7 pence ? in 5 pence ? in 9 pence ?
3. How many pence in 4 shillings ? in 3 shil-
lings ? in 7 shillings ? in 8 shillings ?
COMPOUND NUMBERS.
M
4 How many shillings in 2 ponncls ? in 4
ponnds ? in 3 pounds ? in 7 pounds ? m 8
pounds?
5. How many farthings in 2 shillrngs, 2 pence
and 2 farthings ? , ^ , .„• o
6. How many pence in 1 pound, 6 shilUngs r
7. How many farthings in 1 pound, 2 shiUinga
and 3 pence?
Lesson ni.
Table OF Troy WFJOirr.
84 Grains [gr.] rrmke 1 Pennyweight, marked M.
20 Pennyweights " 1 Ounce, ^^ oz.
J2 Ounces " 1 Po^^'** "^'
1 How many grains in 2 penny weights ?
AvATTSis —There are 24 grains in 1 penny weight, there-
fort 24 S the n^mb^^
of grains. 24 times 2 are 48 pennyweights.
2. How many pennyweights in 2 ounces ? in a
ouncee ? in 6 ounces ?
3. How many ounces in 2 pounds? m 4 pounds^
in 5 pounds ?
4. How many pounds in 60 ounces?
Analysis —There are 12 cunces in 1 pound, therefore
onttweSh of tie number of ounces equals the number of
pounds. One-twelfth of 60 is 5 pounds.
5. How many ounces in 80 pennyweights?
6. How many pounds in 84 ounces ?
'^■n-^i
$2
COMPOUND NUMBERS.
i 1
X
\4 i
Lesson IV.
Table of Apothecaries' Wegiht.
■20 Grains [gr.] make 1 Scruple, marked 3
(<
((
z
lb
3 Scruples '« i Dram,
8 Drams « i Ounce,
12^ Ounces " j Pound,
1. In 3 scruples how many grains ?
2. In 4 drams how many scruples ?
o. In 3 pounds how many scruples ?
4. In 5 drams and 2 scruples how manv
grams ? ^aujr
5, In 1 pound 3 scruples, how many grains
b. In 2 drams, 3 scruples and 4 grains, ho\r
many grams ? 5 , lauw
7. In 48 drams, how many ounces ?
8, In 96 drams, how many pounds ?
Lesson V.
Table of Advoiedupois "Wi^ght
25 &s . 1 ^Qr4 :: ^/; .
• 1- How many drams in 1 ounce ? in 2 ounces ?
m 5 ounces ? m 4 ounces ?
^ 2, How many ounces in 2 pounds ? in 3 pounds ?
in 4 pounds ? in 5 pounds ? ^ '
3 How many pounds in 2 quarters ? in 3 quar-
ters ? m 4 quarters ? in 8 quarters ?
COMPOUND NUMBERS.
53
4 How many quarters in 2 hundred-weiglit ?
5. How many hundred-weight in 4 tons? m
3 tons? in 5 tons?
6. How many ounces in 32 drams ?
7. How many pounds in 48 ounces ?
8. How mp-ny quarters in 75 pounds ?
9. How many hundred-weight in 12 quarters ?
lb. How many tons in 60 hundred weight ?
aany
ho\r
vt.
r
les?
ds?
lar-
Lesson VI
Table of Cloth Meastjbe.
2i Tnclies [in.] make 1 Nail, marked na.
f Nails ;; iQuarter-ofayard, " qr •
4 Quarters " 1 Yard, 2/a-
NoTE.--The Flemish. EngUsh and Frenc'i ells are no lodger used.
1. In 1 yard how many quarters?
2. In 3 yards and 3 quarters how many quai-
ters?
3. In 3 quarters how many nails ?
4. In 2 qr. and 3 na. how many nails ?
5. In 2 yards how many nails ?
6. In 3 yards how many quarters ?
7. In 32 nails how many yards ?
8. In 64 nails how many yards ?
9 In 3 yards and 3 quarters how many quarters f
lb. In 4 yards and 2 quarters how many
quarters
11. In 4 yards and 5 quartci:s how many quar-
ters?
6
Ua^
'?m^
54
COMPOUND NUMBEBfif.
3
12 Inches
3 Feet
5J Yards, or 164 Feet
40 Rods, or 220 yards
8 Furlongs
3 Miles
60 Geographic, or )
694 Statute Miles j
360 Degrees
Lesson VH
Table of Long Measctie.
Inch,
Foot,
Yard,
Rod.
Furlong
Mile,
League,
Degree,
Barley-€oms [ftc] make 1
1
xnorked in^
A
ret.
fur,
tni.
deg. or'
the Circumference of the earth*
1. In 2 yards how many inches ?
2. In 4 rods how many yards ?
3. In 3 feet how many barley-corns ?
4. In 2 furlongs how many yards ?
5. In 4 miles how many rods ?
6. In 190 inches how many yards ?
7. In 320 rods how many miles?
8. In 48 furlongs how many leagues ?
9. In 5280 feet how many miles?
10. In one mile how many feet ?
Ill
Lesson VUL
;?ABLE OF LAND OR SQUARE MEAStJRE.
144 Square in. [sq. in.'] make 1 Square foot, marked sq. ft.
9 Square feet
30^ Sq. yd., or 272i ft.
40 Sq. rod, or poles
4 Roods
640 Acres
1 Square yard,
1 Square rod,
1 Rood,
1 Acre,
1 Squaremile,
sq.yd.
sq. rd.
B.
A.
sq.Jf.
1. In 2 square feet how many square inches ?
COMPOUND -NUMBERS.
65
2. In 2 square feet how many square inches ?
3. In 27 sq. ft. how many square yards ?
4. In 1 square rod how many square feet ?
5. In 1 acre how many rods ?
6. In 4 acres how many rods ?
or'
L.
Lesson IX.
Table cf Solid or Cubic Measure.
1728 Cubic in. [cm. in.'] make 1 Cubic foot, marked cu.ft.
27 Cubic feet "1 Cubic yard, " - cu. yd.
40 ft. round tim., or) «« ^ Ton ** T.
60 ft. hewn timber j *
16 Cubic feet *' 1 Cord foot, " c.fi.
^ o5 S^'l^ %^\ """"l "1 Cord of wood, " cd.
128 Cubic feet )
A pile of wood 8 feet long, 4 feet wide, and 4 feet high, is a
ccord.
1. In 2 cords how many cord feet ?
2. In 2 cords how many cubic feet ?
3. In 3 cubic yards how many cubic feet ?
4. In 256 feet how many cords ?
5. In 54 cubic feet how many cubic yards ?
^.yd.
q. rd.
R.
A.
I?
Lesson X.
Table of Wine Measure.
4 Gills [^i.]
2 Pints
4 Quarts
314 Gallons
42 Gallons
€3 Gallons, or 2 barrels
2 Hogsheads (126 gallons)
2 Pipes, 4 hhds., or 252 gals.
make 1 Pint,
1
1
1
1
1
1
1
Quart,
Gallon,
Barrel,
Tierce,
Hogshead,
Pipe,
Tun,
marked ^it
qt.
gal
bhl.
ti.
hhd.
pi.
T.
' —"m^mtf.
H
COMPOUND NUMBERS.
1. How many gills in 4 pt ? in 5 pt. ? in 3
pt.?
2. How
3. How
5 gal. ?
4. How
5. How
6. How
many pints in 3 qt. ? in 2 qt. ? in 5 qt.?
many quarts in 2 gal. ? in 4 gal. * in
many gallons in 2 tier. ? in 3 tier. ?
many gallons in 2 hhd. ? in 3 lihd. ?
many liogsl^e^.ds in 2 pipes ? in 4
pipes ?
7. How many gills in 1 qt. ? in 3 qt. ? in 5 qt ?
8. How many pints in 3 gal. ? in 4 gal. ?
9. How many pints in 1 pipe ?
10. How many qts. in 32 gills ? in 64 giUs ?
11. How many gallons in 32 pt. ? in 16 pt,?
12. How many gallons in 64 gills ?
13 How many hogsheads in 504 qts.?
Lesson XI.
Table of Dry Measfiie.
2 Pints [pt. ] make 1 Quart,
8 Quarts " 1 Peck,
4 Pecks " 1 Bushel,
6 Bushels " 1 Quarter,
36 Bushels ** 1 Chaldron,
marked qt.
ph,
hu,
qr.
ch.
((
(<
1. In 2 quarts how many pints ?
2. How many pints in 3 qt. ? in 4 qt.?
3. How many pints in 1 pk.? in 2 pk.?
4. How many qt. in 3 pk. ? in 5 pk. ?
5. How many qt. in 2 biu ? in 3 bu. ?
6. How many bu. in 8 pk. in 20 pk. ?
COMPOUND NUMBERS.
57
7. How many pecks in 16 qt.? in 24 qt.,?
8. How many qt. in 12 pt? in 18 ptJ
9. How many pecks in 64 pt.? in 32 pt.
10. How many bu. in 32 qt.? in 64 qt?
11. How many pecks in 1 chaldron ?
12. How many quarts in 1 chaldron ?
Iiesson XIL
60 Seconds [«ec.]
60 Minutes
24 Hours •
7 Days
4 Weeks
12 Calenclar months
52 Weeks
make 1 Minute, marked mi.
1 Hour,
1 Day,
1 Week,
1 Month,
1 Year,
1 Year,
(I
hr.
da.
wh.
mo.
yr.
yr.
The following table exhibits the names of the
months, and the number of days in each :—
Names.
1st month, January,
" " February,
March,
April,
May,
June,
July,
August,
September,
October,
November,
Days.
31.
28, in leap-year, 29^
31.
30.
31.
30.
31.
81.
30.
31.
30.
((
December, 31.
68
COMPOUND NUMBERS.
The following lines may aid in rememberins the
number of days in each month : —
"Thirty days hath September,
April, June, and November;
All the rest have thirty -one,
Excepting February, all alone.
Which hath twenty-eight in fine,
Except in leap-year, twenty-nine. "
1. Name the Winter months, and the number
of days in each month.
2. Name the Spring months, and the number
of days in each month.
3. Name the Summer months, and the number
of days in each month.
4 Name the Autumn months, and the number
of days in each month. . . o • ^
5. How. many seconds in 2 mmutes ? m 4
minutes ? in 3 minutes ? . o i, o
6. How many minutes in 2 hours ? m o hours f
in 4 hours ? ^ ^ • r a o \
7. How many hours in 2 days ? m o aays ? lu
3 days ? in 4 days ? , . . . i o
8. How many days in 3 weeks ? m 4 weeks ?
in 6 weeks ? in 2 weeks ? , , . ^ ,. ,
9. How many weeks in 4 months? m b montns f
in 3 months ? in 2 months ? in 5 months ?
10. How many weeks in 2 years ?
11. How many months in 6 years ?
COMPOUND NUMBERS.
59
2 the
imber
amber
amber
umber
? in 4
tiours ?
ys? iu
.veeks ?
lontlis?
12. How many minutes in 180 seconds? in
240 seconds ? ' .
13. How many hours in 120 mmutes ? m 6b0
minutes?
14. How many days in 48 hours ? in 96 hours ?
in 72 hours ?
15. How many weeks in 21 days ? hi 28 days ?
in 49 days ? , ^ • o.i
16. How many months in 12 weeks ? m ^4
-weeks ? in 36 weeks ?
17. How many hours in 3600 seconds ?
18. How many weeks in 168 hours ?
19. How many months in 52 weeks ?
550. How many days in 3 weeks and 3 days ?
21. How many hours in 4 days and 4 hours ?
Lesson XIIL
T.VBLE OF CniCULAll MOTION
60 Seconds (") make 1 Minute, marked
60 Minutes ♦* 1 Degree, "
80 Degrees " 1 Sign,
12 signs, or 3C0 Degrees " 1 Circle,
sign.
a
1. How many degrees in 2 circles ?
2. How many minutes in 1 sign ?
3. How many seconds in 1 degree ?
4. How many degi-ees in 8 signs ?
5. If there are 60 miles in 1 degree, how- many-
miles in 4 degrees ?
6. How many degrees in 12 signs ?
60
COMPODND NUMBERED.
Lesson XIV.
MISCELLANEOUS TABUES.
Advoirdupois Weight.
A gallon of train-oil weighs
A stone of wire '
A stone of iron, or horseman's weight, is
A peck of salt weighs
A bushel of salt
A lirkin of butter
A quintal of fish
A faggot of steel
A barrel of flour
A barrel of beef or pork | *
A barrel of potash
A fother of lead
Long Measure.
4 Inches make 1 Hand. Used for meas. horses.
iUsed by sailors for
meas. ropes, the depth
of water, &c.
7^^ Inches make 1 Link of a surveyor's chain.
100 Links, or 66 feet, or 4 rods, make 1 chain.
80 Chains, or 320 rods, or ) «« , -i
1760 yards, or 5280 feet i ^^
Solid Measure.
231 cubic inches make 1 Wine gallon.
282 cubic inches make 1 Beer gallon,
cubic inches make 1 Bushel.
(<
(C
74
lb.
104
((
14
<< .
14
t<
56
<<
5a
((
100
{<
120
(<
196
((
200
«
200
i<
19cwt.2qr3.
21501^
Liquid Measure.
10 Gallons make 1
18 Gallons make 1
42 Gallons make 1
84 Gallons make 1
9 Gallons make 1
18 Gallons make 1
86 Gallons make 1
54 Gallons make 1
108 Gallons make 1
Anker.
Eundlet,
Tierce.
Puncheon.
Firkin of beer.
Kilderkin of beer.
Barrel of beer.
Hogshead of beer.
Butt.
COMPOON0 NUMBERS.
61
Table.
12 Single thinp make 1 Do«n, marked ^.
iiaiudo.)'. oSGn«. ;; V
20 Single things " 1 Score, 8^-
5 Scoter ^^^•
Table OF Pa* £11.
24 Sheets of paper make 1 Qniro.
20 Quires ** 1 5^^™:
20 Quires
2 Beams
10 Reams
1 Bundle.
1 Bale.
Table of Parchment.
12 Skina °i^^« ^ ^^'^^
6 Dozen, or 60 Skins
«< 1 Roll.
size.
<(
<(
«(
Table of Books.
When a sheet of paper makes :
2 leaves or 4 pages, the book is called ^foUo
\ leaves' or 8 ?ages the hook is called a quarto
t leaves' or 16 mges, the hook is called ^nodavo^
if ^eaves' or 24 pales the hook is called a duodecimo
is leaves', or 36 p^es', the hook is called an Cf/Weamo
Arithmetical Signs.
1 The symbol + is called flus, and is the sign cf
addition ^us, 2 + 4 indicates the addition of 2
""""^ The svmbol - is called min^*, and is the sign of
snbii^tfon^ Thus, 5 - 2 indicates the subtraction of 2
^TThe symbol X is the sign of -i^^tipU^^^^^^^^^
3 X 5 indicates that 3 is to be multiplied by 5, or o
^^4The symbol - is the sign of division. Thus, 8 -4- 2
indicates the division of 8 by 2. ^nn«1itv Thus,
5. The symbol = is the sign of equality, inus,
4 4. 6 = 10.
62
COMPOUND NUMBERS.
Aliqtjot, oil Equal Par73 op a Dollail
il
100
76
50
33i
25
124
10
6i
6
4
2
1
cont3
cents
cents
cents
cents
cents
cents
cents
cents
cents
cents
cent
= 1 dollar.
= J ^three-fourths)
^ (one-half)
= { (one-third)
= \ (one-fourth)
= 5 (one-eighth)
= ^y (one-tenth)
= ^ (one-sixteenth)
= j^y (one -twentieth)
^ (one-twenty-fifth)
^ (one-fiftieth)
j^ij (one-hundredth)
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar,
of a dollar.
New York Cubrency.
s. D.
are G\ cts.
1 are 12. ^ cts.
1 6 are 18| cts.
2 are 25 cts.
2 6 are 31 J cts.
3 are 374 cts-
3 6 are 43j cts.
4 arc 50 cts.
Aliquot, or Equal Parts of a Month,
83 <lay3= 1 month.
15 day3= 4 (one-half)
10 day3= I (one-third)
6 days= i (one-fifth)
5 day3= h (one sixth)
3 days= ^ (one-tenth)
2 days=.^ (one-fifteenth)
1 day = TjV (one-thirtieth)
Aliquot, or Equal Parts, oj- a Year.
of a month,
of a month,
of a month,
of a month,
of a month,
of a month,
of a month.
12
6
4
8
2
1
months =
months =
months =
months =
months =
month =
year.
(one-half)
(one-third)
(one-fourth)
(one-sixth)
^ (one-twelfth)
of a year,
of a year,
of a year,
of a year,
of a year.
FRACTIONS
half
half
Lesson I.
1. Mary has 4 apples, and Sarah 1 half as many;
how many has she? , , i, ip „.
Analysis.— If Mary has 4 apples, and Sarah 1 halt as
m^yfX must have one-hal/of 4 apples, which is 2
apples. . ^
2. Henry is 8 years old. and Harvey is i
as old ; how old is Har\^ey t , ^_ ^^, .
3. Martin has 6 marbles, and Matthew 1
as many ; how many has he ? „ , , «
4 If you divide 10 apples equally between 2
bovs what part of them will each receive ?
5.' What is 1 half of 10?
C If an orancre cost 12 c^nts, and a -omon 1
half as much, what was the cost of j^e lemcm?
7. If 3 apples cost 6 cents, what part of 6 cent^
will 1 apple cost ?
8. What is 1 third of 6 ? ^ ^ o . p in 9
9 What is 1 half of 4? of 6 ? of 8 ? of 10 ?
of 12 ?on4? of 16? of 18? of 20? of 24
10 If 3 oranges cost 9 cents, what part ot J
cents wiU 1 orange cost ? what part of 9 cents will
'nThatis'lthirdof3?of6?of9?ofl2?of
15? of 21? of 24? of 27? of 30?
12. If 1 quart of nuts cost 12 cents, what wiU
1 third of a quart cost ?
64
FRACTIONS.
13. If 1 ton of hay cost $15, what 'mil 1 third
of a ton cost ? . «< i. i «4.
14. If 1 bushel of apples cost 21 cents, what
will i third of a bushel cost ? ^ u 4.
15. If 1 yard of shalloon cost 24 cents, what
will one third of a yard cost ? ^ ^ i, <.
16. If 1 quart of vinepr cost 9 cents, what
will i third of a quart cost ?
17 If 1 pound of candies cost 12 cents what
part, of 12 cents will 1 third of a pound cost?
what part of 12 cents will 2 thirds of a pound
cost? , n^r...
18. Wliat is 1 third of 12 ^
10. If 1 third of 12 is 4, what is 2 thirds
■P 10 9
"^ 20. What is 1 third of G? 2 thirds of G? 4
thirds of G ? 3 thirds of 6 ? 5 thirds of G ?
21. If a baiTel of flour cost 9 doUars, what will
1 third of a barrel cost ? 2 thirds ?
22. What is 2 fourths of 12 ? 1 fourth of 12 ?
3 fourths of 12 ? ^.^ -, . -n 1
23. If a barrel of fish cost sS12, what will I
fourth of a barrel cost ? 2 fourths ? 3 fourths ?
4 fourths ? . ^ . .^ /./.a.1 r 1 r 9 '^
24. mat is 1 fifth of 15? 2 fifths of 15? o
fifths of 15 ? 4 fifths of 15 ? 5 fifths of 15 ?
25. If a ton of hay cost $15, -wli^U ^i-Uw
of a ton cost ? 2 fifths ? 3 fifths ? 4 fifths ? 5 fifths ?
26. What is 2 tliirds of 24 ? 3 fourths ? 3
eighths ? 2 fourths ? „ „„ , „ . , , , „f rj. ?
27. Wliat is 3 fifths of 20 ? 7 eighths of 64 ?
4 sevenths of 56 ?
FBACTIONS.
e&
27. What do you understand by 1 fourth ? 3-
fourths ?
ANSWER.--Wheii a thing is divided into fonr equal ports^
1 of these parts is called 1 fouHh, and 3 of these imrta are
called Z fourths,
28. What do you understand by 2 fifths? 3
fifths? 4fifth8? ^ , ^ . , .
29. What do you understand by 3 sevenths ? 4
-evenths ? 5 sevenths ? G sevenths ?
30. How many thirds in 1 ?
81. How many fifths in 1 ?
82. How many fourths in 1 ?
83. How many tenths in 1 ?
84. How many ninths in 1 ?
35. How many twelfths in 1 ?
86. AVhat is 1 seventh of S28 ? 2 sevenths ot
$28? 3 sevenths? 4 sevenths? G sevenths? 5
sevenths ?
37. If a coat cost S20, and a pair of imntaloons
1 fourth as much, what is the cost of the pantaloons?
38. If a pound of cheese cost 9 cents, what will
2 thirds of a pound cost ?
39. If 12 oranges cost 3G cents, what part of
36 cents will one orange cost ? 2 oranges ? 4
oranges ? 3 oranges ? 5 oranges ? 9 oranges ? 8
oranges? „ ^« „
40 AVliat is 1 tsvelfth of 36 ? 2 twelfths of 36 ?
5 twelfths of 36 ? 4 twelfths of 36 ? 6 twelfths of
36? 9 twelfths? 8 twelfths? 10 twelfths? 11
twelfths ?
41. Eachel has 14 primers, and Anthony 5
sevenths as many ; how many has he?
66
FRACTIONS.
42. Abner is 15 years old, and Albert is 4 fifths
as old ; how old is he ? ^ i, k
43. Augustus has 40 cents, and Augusta has 5
eighths as'many ; how many has she ?
44 Martin had 25 marbles, and gave 3 fifths ot
them to Moses ; how many had he remammg, and
how many did he give to Moses; ?
45 Morgan had 21 lire-crackers, and NathaU
had 8 sevenths as many , how many had he ?
^6. Matthew had 45 apples, and Marvm had
5 ninths as many ; how many had he ? • ^
47. Dubois is 42 years old, and his l:t r is \)
sixths as old ; how old is he ?
48. A farmer, having 72 sheep, lost 1 ninth ot
them ; how many had he remaining ?
49. A man bought a horse for 60 doUars, and a
cow for 3 fifths as much ; what was the cost ot
the cow ? /^ • 1 J a
50 In a certain school there are 9 girls, and b
thirds as many boys ; required the number of boya.
and the number of boys and girls togeth'^r.
Less :n II
1 3 fourths of 12 are how many times 3 ?
ANALTSIS.-1 fourth of 12 is 3, and 3 fourths are 3 times
8 which are a 9 is as many times 3, as 3 is contained
^^7which are 3 tmies. Therefore, 3 fourths of 12 m 2
times 3. • o q
2 2 thirds of 12 are how many tunes 2. i
a 2 thirds of 15 are how many times 2 ?
FRACTIOITS*
67
r
4 9 thirds of 24 are how many times 4?
t 1 SL of 12 are how m«.y ^- 6?
6 2 fourths of 16 are how manj tm^- J^^
7 3 fourths of 16 are how M ^f 7V
R o thirds of 21 are how many times 1 .
q o thSds of 30 arc how many times 5?
in 2 thkds of 27 are how many times 6?
M- ', tSrths of 24 are how many times 9 ?
to ^- Whs of 36 are how many times 9 ?
\\ o Shs of 30 are how many ti^nes 6 ?
i-ii" -^ fourths of ?8 are how many tunes 1%
• It 3 fifth of 20 are how many times 6
\t I fifths of 20 are how many times «>
17 1 fifths of 15 are how many timos 6 ?
18 t fifths of 20 are how many tunes 2?
iS: 3 2Xf 24 are how many™
90 =i sixths of 60 are how many times - .
Il 2 i^hs of 72 are how -anyUmes^J?
22 2 sevenths of 42 are how W tmes -
oQ 1 cr-vpnths of 42 are how many times d.
fi \ evenhs o 70 are how many mes 0?
t 5 se^eX of 28 are how « ™ 2
fe, 5 eighths of 32 are how many times iu .
W fi eighths of 48 are how many times 12?
27. o eigmn!' 01 ^^^^^gg 2?
iint:o4 a Sman?times6?
lo. \ tltmis of 96 aie how ^m^^^^^
ai- 7 piahths of 64 are how many times 4
nV ? sS of 54 are how many times 3 ?
^1 7 fourths of 24 are how many tmies 6 ?
11 8 teS^ of 30 arc how « U^s 4?
35. 6 ninths of 72 are how many times
•y
68
t^HACTIONS;
K
If
I
Lesson m*
1. 4 fifths of 14 are how many times 1 half
of 12?
2. 2 thirds of 12 are how many times 1 third
of 6?
3. 2 fourths of 20 are how many times 1 half
of 20?
4. 3 fourths of 16 are how many times 1 third
of 18
5. 3 fifths of 20 are how many times 1 fouf^l
of 24?
6. 3 fifths of 30 are how many times 1 half
of 18 ?
7. 4 fifths of 30 are how many times 1 eighth
of 64?
8. 3 fourths of 24 are how many times 1 fifth of
45?
9. 5 sixths of 54 are how many times 1 third of
9?
10. 2 thirds of 36 are how many times 2 thirds
of 9 ?
11. 2 thirds of 24 are how many times 2 thirds
of 6?
12. 2 fifths of 45 are how many times 2 fifths
of 15 ?
13. 3 fifths of 50 are how many times 2 sixths
of 18?
14. 6 eighths of 48 are how many times 2 fifths
of 15?
15. 8 ninths of 27 are how many times 1 fourth
of 24 ?
i
FBACTIOSS.
e»
16. 7 eighths of 64 are how many times 2 sixths
°^n.'3 ninths of 108 are how many times 3
^"ir4feve'Jhsof 84are how many times 4 fifths
of 30 ?
#'
Lesson IV.
1. If 2 thirds of an orange cost 4 cents, what
■^oU i orange cost ? ,
' Analysis. -It 2 thirds of an orange cost 4 cents, 1 ttod
Jr'fU of 4 cent, which j two co^te-K^yl^^
of an orange cost two ceiics, 3 tlyras, or i via ^ ,
3 times 2 cents, which are G centB.
2. If 2 thirds of a melon cost 6 cents, what
win 1 thkd of a melon cost ? , a ^^a
3 If 3 fourths of a pound of sugar cost 9 cents,
what will I fourth of a pound cost ?
4 If 2 thirds of a pound of ginger rost 8 cents,
-n tVt£ota\='riee cost 12 cents,
^ tVs tif :Kjrfiyhs of a harrel of
fish what will 1 fifth of a barrel cost !
7 If 3 fourths of a pound of cinnainoncost 9
pontq what will 1 fourth of a pound cost
°' 8 What ^iill 1 sixth of a yard of cloth, cost, if
A six-ths of a Yard cost 120 cents ? , i „f
9 What will 1 seventh of a hogshead of
molasses cost, if 5 sevenths of a hogshead cost «lo ?
70
FR AUCTIONS.
fti
I*'
10. If 2 thirds of a barrel of fisb cost $8, what
will one barrel cost ?
11. If 3 fourths of a bushel of wheat cost 9
dimes, what will- 1 bushel cost ?
12. If 4 fifths of a box of raisins cost 12 dimes,
what will 1 box cost ?
13. If 6 eighths of a yard of broadcloth cost 60
dimes, what will one yard cost ? -■
14 If 3 fourths of a barrel of flour cost $6, what
will 1 barrel cost ? '
15. If 2 fifths of a barrel of fish cost $8, w
will 1 barrel cost ?
16. If 3 fourths of a pound of cinnamon cost 1^
cents, what will 1 pound cost ?
17. If 4 sixths of p barrel of sugar cost $12,
what will 1 barrel cost ? ^.^a -u ..
18. If 5 sevenths of a box of boots- cost $20, what
will 1 box of boots cost ?
19. If 4 ninths of a hogshead of molasses cost
$20, what will 1 hogshead cost ?
20. If 2 fifths of the cost of a waggon were-
what was the cost of the waggon ?
IS
'3
Lesson V.
of what number ?
1- 6 „
' Analysis.— If 2 thirds of some number is 6, 1 third of
that number is one-half of 6, which is 3. If one-third of
that number is 3, three-thirds, which is that niimber, la
3 times 3, whicli are nine. Therefore, 6 is two-thirds of 9,
2. 8 is § of what number ?
3.* 4 is § of what number ?
«•>
f*
1
♦1
- *
4. 10 is
5. 12 is
6." X2 is
7. 12 is
■^C^iI2 is
ao.
¥. ^'
25 W IS
26* is
20 is
30 is
36 is
36 is
I
2
;i
3
2
:?
3
?
6
2.
3
5
4
5
H
9
H
4
FRACTIONS.
of what
of v/hat
of wliat
of wliat
of what
of what
of what
of what
of what
of what
of what
of what
of what
of what
of what
of what
of what
71
\
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number ?
number 1
. ii
THE END.
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