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CASE II.
To subtract a simple fraction, or a mixed number,

from a whole number, Ruli.Subtract the numerator of the fraction from its denominator, and put the denominator of the fraction under the remainder ; and carry one to be deducted from the whole number.

Examples.
1. It is required to subtract from 12.

12 — }=113 Ans. 2. It is required to subtract 27from 32.

Ans. 4

49 97

3. What is the difference between 12 and 21 ?

Ans. 87

1

8

10.

4. What is the difference between 101 and 100

Ans. 7 000

99 ?

100

CASE III.

To subtract fractions having different denominators.

RULE..Reduce the fractions to a commop de nominator, by case 5th, in Redaction; and the difference of the numerators is the difference required.

Examples.

19 20

45 22

83 are equal to dif.

Ans. 45

180 180 180

171 88

19 and

2. What is the difference between and

15

Ans, 5

10

. 30

CASE IV.

To distinguish the largest of any two fractions, &C..

Rule.-Reduce them to a common denominator, (by case 5th in Reduction,) and the one that has the largest numerator is the largest fraction..

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Example.
1. Which is the greatest fraction is or 11?
It reduced to a common denom. is equal to 16

reduced to a common denom. is equal to

54
60

10

1

Ans.

60

Therefore is the largest fraction.

CASE V.

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To subtract a mixed number from a mixed number,
when the fraction which is to be subtracted
is greater than the one which it is to

be taken from.
RULE.-Reduce the fractions to a common denom-
inator ;, then subtract the numerator of the greater:
from the common denominator, and to the remain-.
der add the least numerator, and the sum of them
must be set over the common denominator ; and
carry one to the whole number, and subtract the
whole number. as in simple subtraction.. .

12

Examples
1. It is required to take 8 from 122..
reduced to a common denom. is equal to
reduced to a common denom. is equal to

129. less by 89

19

72 114

57

I14 ୨9

Anson 114

3

114

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To subtract when the fractions are of different de.

nominations, such as parts of cwt. qr. lb. &c. RULE.Find the value of the fraction (by case 10th in Reduction, then subtract as in compound subtraction. If fractions happen in finding the value of the parts, reduce them to common denominators and subtract as in case third.

Examples. 1. It is required to take of a cwt. from of

a ton.

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2. Required to take ing of a cwt. from 12 cwt.

Ans. 12 cwt. O qrs. 18 lb. 10 oz. 103 dr. MULTIPLICATION OF VULGAR FRACTIONS.

CASE I. RULE.Reduce compound fractions to simple multiply the numerators all together for a new nuones ; mixed numbers to improper fractions; then merator, and the denominators for a new denomi

nator.

Examples.
1. It is required to multiplyš byg of of:
of of 1= x=392= Ans.

2

%. It is required to multiply 24, by 1 of gi

Ans.

66

64

164

5

9

3. It is required to multiply iz by io

Ans.

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IVISION OF VULGAR FRACTIONS, Rule.-Reduce compound fractions to simple ones; mixed numbers to improper fractions ; theninvert the divisor(that is put the numerator for the denominator) and multiply the numerators together for a new numerator, and the denominators together for a new denominator ; and the fraction thus found is

the quotient required.

Examples.
1. It is required to divide f by

inverted is x Ans. 2. It is required to divide by si

100

Ans..7

3. It is required to divide 10 by off.

Ans. 3316

4. It is required to divide 10% by 7

249 Ans. 1

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6

540

Miscellaneous Questions in Vulgar Fractions:

1. A schoolmaster being asked one dày how many scholars he had, made answer that one fifth of them sat on one seat, one tenth on another, two fifths on another, two tenths on another, and 6 on another ; I demand the number his school consisted of.

of 2 of

=.54 to 6. = 60 Ans,

2. A man, having returned from a journey, was asked by a friend, what his expenses were ; the answer was, that he spent in Boston of his money ; between Boston and New York }; in New York ; beyond New York sto; and he brought home $40; I demand the sum he. carried, and also what he spent.

Ans. carried $160, and spent $120..

1 1 2 2

10 tof-t -X-10--9 = 1=5 10 5 10 10

1

10

1

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RULE OF THREE IN VULGAR.FRACTIONS:.

RULE.-State the question as in the Rule of Three Direct, invert the divisor, and multiply the numerators together, and the denominators together, and the frac. tion thus found is the fourth term or answer ; com.pound fractions must be reluced to simple ones, and mixed numbers to improper fractions.

Examples.

1

75

2

1

75

3

As

:

2

100

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1. If - bushel of corn cost of a dollar, what will

100 of a bushel come to ?

Dols. 2 x

x 3 inverted is

Ans: 1 X 100 X 4 2. If 104 bushels of potatoes cost $34; how many may be had for $121?

44 Ans:

39

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400

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3. If 4 of of a ship is worth of 16000 dollars ; show much is of of her worth?

Ans. $4571.42.8384

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