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

64

Ans. 2oz, Sgrs. Ans. £4 13s. 54d. hogshead of wine? Ans. 15gals. Sets.

CASE IX.

To reduce any given quantity to the fraction of any greater denomination of the same kind.

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

EXAMPLES FOR EXERCISE.

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

Ans. 195 7792

2. Reduce 13ewt. Sqrs. 20lb. to the fraction of a ton.

Ans. 39

35

5. Reduce 16s. to the fraction of a guinea. Ans. 4. Reduce 1 hld. 49 gals. of wine to the fraction of a tun. Ans.

5. What part of 4cwt. 1gr. 24lb. is Scwt. Sqrs. 17lb.

302.

ADDITION OF VULGAR FRACTIONS,

RULE.

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

EXAMPLES.

1. Add 5 and 3 of 7 together.

Then

5 and of j = 1 4 reduced to their least common denominator by Case VI. Rule II. will become V3 1 14 Then 132+18+14=16*=63% or 63 Answer.

132 18

NOTE 1.-In adding mixed numbers that are not compounded 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 74 and 15.
I find the sum of 3 and to be 311,
Then 11+5+7+15=281 Ans.
Ans. 17 9
Ans. 33

7. Add and 171 together.

8. Add 25, 81 and of of 15

12

NOTE 2.-To add fractions of money, weight, &c. rẹduce 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 terms.

9. Add of a shilling to of a pound.

4

SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

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

1. From take of

EXAMPLES.

=

3 of 7=14=1 Then and ùá

Therefore 9-7=}=} the Ans.

4. From 14 take 13

15

Answers.

5. What is the difference of and 17?

6. What differs from

7. From 144 take 3 of 19

8. From take 11

24

?

O remains.

9. From of a pound, take of a shilling.

of 2%. Then from 4. take. Ans. 16. 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 7 11. From

take 37 shilling. Ans. 5s. 6d. 23qrs. of an oz. take 3 of a pwt.

Ans. 11pwt. 3gr,

12. From of a cwt. take of a lb.

Ans. 1qr. 27lb. 6oz. 108, dr. 13. From 33 weeks, take of a day, and of 3 of 3 of an hour. Ans. Sw. 4da. 12o. 19min. 174sec.

*In subtracting mixed 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.

8. Multiply

of?

EXAMPLES.

of 7 by 4

135

by

of 8 by
by 91

of by of s

Answers. 12:

cler

9. What is the continued product of 4 of 3, 7, 59 and

Ans. 4

DIVISION OF VULGAR FRACTIONS.

RULE.

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

2. Divide 17 by

3. Divide of by

4. What is the quotient of 17 by ?

5. Divide 5 by

6. Divide of 4 of 7 by 4 of

7. Divide 45 by 5 of 4

8. Divide 71 by 127

9. Divide 5205 by of 91

Answers. 1-22

63

59

711

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 19 Ell English cost? fyd.

As

Ell. £. Ell.

of 4 of 20 or 1 Ell English.

54

of a

s. d. qrs.

And 2x4x10 3 1 Ans 2. If 3 of a yard cost of a pound, what will 403 yds.

come to?

Ans. 59 8s. 61d. 3. If 50 bushels of wheat cost 1731. what is it per bushel f Ins. 7s. Od. 133qrs. 4. If a pistareen be worth 143 pence, what are 100 pistareens worth? Ans. £6 5. A merchant sold 53 pieces of cloth, each containing 243 yds. at 9s, 3d. per yard; what did the whole amount Ans. £60 10s. Od. 33qrs.

6. A person having 3 of a vessel, sells of his share for 3121.; what is the whole vessel worth? Ans. £780 7. If of a ship be worth of her cargo, valued at 8000l. what is the whole ship and cargo worth? 10031 14s. 11d.

Ans.

INVERSE PROPORTION.

RULE.

PRIPARE the fractions and state the question as before, then invert the third term, and multiply all the three terms together, the product will be the answer.