8. Required the value of of a pound apothecaries.

1

Ans. 2 oz. 3 grs.

Ans. £4 18s. 54d.

10. How much is

of of of a hihd. of wine?

Ans. 15 gals. 3 gts

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 71.]

EXAMPLES FOR EXERCISE.

1. Reduce 12 lb. 3 oz. to the fraction of a cwt.

Ans.

2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton.

Ans.

Ans.

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

iin.

5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3

5 oz.

?

Ans. qrs. 17 lb. Ans. 1

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 off together.

Then,,

51 and 3 of 7=11

reduced to their least common denominator by Case VI. Rule II. will become, H, Then 132+18+146 or 6 Ans.

4. Add 121 33 and 4 together.

ANSWERS. 17

17

2011

4417

5. Add 1 of 95 and 1 of 141 together.

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 51, 74 and 15.

7. Add

I find the sum of and to be 1=1}
Then 11+5+7+15=2811 Ans.

and 17 together.

8. Add 25, 8 and of of

ANSWERS. 17.

33

NOTE 2.-To add fractions of money, weight, &c. redu 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 thei proper terms.

9. Add 4 of a shilling to of a pound.

1st method

11. Add 4 of a ton, to of a cwt.

12. Add of a mile to
201
13. Add of a yard,
导

14. Add of a week, ■ minute together.

Ans. 12 cwt. 1 gr. 8 lb. 12 oz.

of a furlong. Ans. 6 far. 28 po. of a foot, and of a mile together Ans. 1540 yds. 2 ft. 9 in.

of a day, of an hour, and of Ans 2 da. 2 ho. 30 min. 45 sec.

SUBTRACTION OF VULGAR FRACTIONS.

RULE.*

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

6. What differs

H

1

8. From 2 take

O remains.

3. Fromake

4. From 14 take }}

5. What is the difference of and 17?

from ?

7. From 14 take of 19

9. From of a pound, take of a shilling. } of {£. Then from 1. take T. Ans. 1£. 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 3 shillings. Ans. 5s. 6d. 23 qrs. 11. From of an oz. take of a pwt. Ans. 11 pwt. 3 gr. 12. From of a cwt. take of a lb.

Ans. 1 qr. 27 lb. 6 oz. 10 dr. 13. From 33 weeks, take of a day, and of of ‡ of an hour. Ans. 3 w. 4 da. 12 ho. 19 min. 174 sec.

* 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 ver the denominator, then taking one from the whole number

MULTIPLICATION OF VULGAR FRACTIONS

RULE.

Reduce whole and mixed numbers to the improper frac tions, mixed fractions to simple ones, and those of differen integers to the same; then multiply all the numerators to gether for a new numerator, and all the denominators to gether for a new denominator.

8. Multiply of by

of 34

of &?

9. What is the continued product of of 4, 7, 5 and 1

Ans. 45'

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.

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?

off of = or Ell English.

s. d. qrs.

And ××£10 3 1

Ans.

Ans. £59 8s. 6d.

2. If of a yard cost of a pound, what will 403 yards eome to ? 3. If 50 bushels of wheat cost 1737. what is it el ?

per bushAns. 7s. Od. 123 qrs.

4. If a pistareen be worth 143 pence, what are 100 pista reens worth? Ans. £6 5. A merchant sold 5 pieces of cloth, each containing 241 yards at 9s. d. per yard; what did the whole amount to? Ans. £60 10s. Od. 3 qrs. 6. A person having of a vessel, sells of his share for 3127.; what is the whole vessel worth?

Ans. £780 7. If of a ship be worth of her cargo, valued at 80007. what is the whole ship and cargo worth?

Ans. £10031 14s. 111⁄2'¡d.

. INVERSE PROPORTION.

RULE.

Prepare 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.