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8. Required the value of 107 of a pound apothecaries.

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Ans. 2oz. 3grs. Ans. £4 13s. 54d.

of of of a hogshead of wine ? Ans. 15gals. 3qts.

CASE IX.

reduce any given quantity to the fraction of any great

er denomination of the same kind.

[See the Rule in Problem III. page 75.]

EXAMPLES FOR EXERCISE.

Reduce 12lb. Soz. to the fraction of a cwt.

Ans.

2. Reduce 15cwt. 3qrs. 20lb. to the fraction of a ton. Ans.

S. Reduce 16s. to the fraction of a guinea. Ans. 4. Reduce 1 hhd. 49 gals. of wine to the fraction of a buan. Ans.

5. What part of 4cwt. 1qr. 24lb. is Scwt. Sqrs. 17lb. 3oz..

Ans.

ADDITION OF VULGAR FRACTIONS.

RULE

REDUCE compound fractions to single ones; mixed numbers to improper fractions; and all of them to their east common denominator (by Case VI. Rule II.) then he sum of the numerators written over the common denominator, will be the sum of the fractions required.

EXAMPLES.

1. Add 51 and of together.
5 and of 7=14

Then

reduced to their least common denominator by Case VI. Rule II. will become

Then 132+18+14=-63% or Answer.

2. Add and together.

S. Add and together.

4. Add 124 33 and 4 together.

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5. Add of 95 and 3 of 14 wogether.

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NOTE 1. In adding mixed numbers that are not com pounded with other fractions, you may first find the sum of the fractions, to which add the whole numbers of the given mixed numbers.

6. Find the sum of 53 73 and 15.
I find the sum of and to be {}=1}}
Then 14+5+7+15=281 Ans.
Ans. 17

7. Add and 17 together.

8. Add 25, 81 and 2 of 3 of

Ans: 35

NOTE 2.-To add fractions of money, weight, &c. reduce fractions of different integers to those of the same.

Or, if you please you may find the value of each fraction by Case VIII. in reduction, and then add them in their proper termis.

9. Add of a shilling to of a pound.

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SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

PREPARE the fractions as in Addition, and the difference of the numerators written above the common denominator, will give the difference of the fraction required.

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7. From 14 take of 19

8. From 37 take 118

11

31 208

13,

5

10

O remains.

9. From of a pound, take of a shilling.
of £. Then from 1. take. Ans.

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NOTE. In fractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reduction) and then subtract them in their proper terms.

10. From take shilling. Ans. 5s. 6d. 2grs. 11. From of an oz. take

12. From of a cwt. take

of a pwt.

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Ans. 11pwt. 3gr.

of a lb. Ans. 1gr. 271b. 6oz. 10, dr. 15. From S weeks, take of a day, and of of of ns. Sw. 4da. 12ho. 19min. 174sec

an hour.

*In subtracting fixed numbers, when the lower fraction is greater than the upper one, you may, without reducing them to improper fractions, subtract the numerator of the lower fraction from the common denominator, and to that difference add the upper numerator, carrying one to the unit's place of the lower whole number.

Also, a fraction may be subtracted from a whole number by taking the numerator of the fraction from its denominator, and placing the remainder over the denominator, then taking one from the whole number.

MULTIPLICATION OF VULGAR FRACTIONS.

RULE'.

REDUCE whole and mixed numbers to the improper fractions, mixed fractions to simple ones, and those of different integers to the same; then multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.

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6. Multiply of 8 by 7 of 5

7. Multiply 7 by 91

8. Multiply of by

of 34

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9. What is the continued product of of 3, 7, 5, and

} of ?

Ans. 4

DIVISION OF VULGAR FRACTIONS.

RULE.

PREPARE the fractions as before; then, invert_the divisor and proceed exactly as in multiplication :-The products will be the quotient required.

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2. Divide 17 by

Answers. 1

3. Divide of by 3

4. What is the quotient of 17 by ??

5. Divide 5 by 7%.

6. Divide of 4 of 7 by of

7. Divide 4 by & of 4

8. Divide 71 by 127

9. Divide 5205) by of 91

591

74

RULE OF THREE DIRECT IN VULGAR
FRACTIONS.

RULE.

PREPARE the fractions as before, then state your question agreeable to the Rules already laid down in the Rule of Three in whole numbers, and invert the first term in the proportion; then multiply all the three terms continually together, and the product will be the answer, in the same name with the second or middle term.

EXAMPLES.

1. If of a yard cost of a pound, what will of an Ell English cost?

As

{yd.={ of of =2% or 4 Ell English.

Ell. £. Ell.

54

s. d. qrs And ××=.=10 3 14 Ans 2. If of a yard cost of a pound, what will 40 yds

come to ?

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Ans. £59 Ss. 61d. 3. If 50 bushels of wheat cost 17. what is it per bush

el?

to?

Ans. 7s. Od. 12yrs. 4. If a pistareen be worth 143 pence, what are 100 pistareens worth? Ans. £6 5. A merchant sold 54 pieces of cloth, each containing 244 yds. at 9s. jd. per yard; what did the whole amount Ans. £60 10s. Od. Syrs. 6. A person having of a vessel, sells of his share for 312.; what is the whole vessel worth? Ans. £780 7. If of a ship be worth of her cargo, valued at 800l. what is the whole ship and cargo worth? Ans. £10051 14s. 11d.

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PREPARE the fractions and state the question as be fore, then invert the third terin, and multiply all the three terms together, the product will be the answer.

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