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8. Required the value of 147 of a pound apothecaries.

Ans. 2oz. Sgrs. 9. How much is of 51. 9s. ? Gus. £4 135. 5 d. 10. How much is of į of f of a hogshead of wine ?

Ans. 15yals. 3q's.

CASE IX.

To 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.

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1. Reduce 12b, Soz. to the fraction of a cut.

Ans. 195 2. Relace 19ewt. Sqrs. 201b. to the fraction of a ton.

Ans. 39 3. Reduce 16s. to the fraction of a guinea. Ans.

4. Reduce 1 hhd: 49 gals.'ut wine to the fraction of a cun,

ins. 5. What part of 4cwt. Igr. 2411. is Scwt. 3qus. 171). 302.

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ADDITION OF VULGIR FRACTIONS.

RULE.

REDUCE compound fractions to single ones; mixeil 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 compión de nominator, will be the sum of the fractions required.

EXAMPICS.

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1. Add siiani of together.

513 and of Then I reduced to their luasi coamon denom matur

by Case VI. Rule II. will becilie H Thien 132+18+14=19*=0 or 6 Anster:

13 14

2

32

18

Ans. 2012

Ans. 33 12

2. Add and together.

Ans. 13 3. Ada and together.

Ans. 11 4. Add 1943 and 4. together. 5. Add } of 95 and 7 of 141 together. Ans. 4433

Note 1.-In adding mixed numbers that are not compounderl with other tractions, you may first find the sun of the fractions, to which add the whole numbers of the.. given mixed numbers. 6. Find the sum of 57 and 15. I find the sum of and to be !=1

Then 10+5+7+15=2827 Airs. 7. Add and 17! together.

Ans. 176 8. Add 25,81 and of j of 15

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 threw in their

proper terms. 9. Aud of a shilling to of a pound. 1st Method.

2d Method. of 'To!.

$£.=75. 6d. Oqrs. Then tots =;

S. =0
Whole value by Case VIII.
is 8s. Od. 3.qrs. Ans.

Ans. 8
By Case VIII. Reduction.

452

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10. Add 3 lb. Troy, to fof a pwt.

Ans. 7oz. 4pwt. 13}gr 11. Add of a ton, to i of a cwt.

Ans. 12cwt. 1gr. 8lb. 12,goz. 12. Add of a mile to Io of a furlong.

Ans. 6fur. 28po. 13. Add í of a yard, of a foot, and of a mile to. gether.

Ans. 1540yds. 2ft. 9in. 14. Add } of a week, of a day, of an hour, and į of

를 a minute together. Ans. 2da. 2ho. 30min. 45 sec.

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.

EXAMPLES.

7

12

2

11

1

31 205

31

2 +0

1. From take ţ of
of == Then and 1=1' in

Therefore 9-7=*= the Ans. 2. From take

Answers. 3. From it take

TG 4, From 14 take 13

13 5. What is the difterence of ii and 17 ? 6. What differs ib froin ? 7. From 141 take of 19

115 8. From šī take to

O remains. 9. From of a pound, take of a shilling: of th=rict. Then from { £. take Ans. 16.

zo it Note.--In tractions of money, weight, &c. you may, if you please, find the value of the given fractions (by Case VIII. in Reluction) and then subtract them in their per terms.

10. From 15. take 3 shilling. Ans. 5s. 6d. 2391's. 11. From of an oz. take of a pwt.

Ans. 11put. 3gr. 12. From j of a cwt. take of a lb.

Ans. 1qr. 271b. 6oz. 108, nr. 13. From 3} weeks, take of a day, and ļ of of of an hour.

Ans. 3w. 4da. 12o. 19min. 17 sec.

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*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 denominalor, and placing the remainder over the denominator, then taking one from the whole number,

MULTIPLICATION OF VULGAR FRACTIONS.

RULE. REDUCE whole and miscil 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 de. nominators together for a new denominator.

EXAMPLES.

1. Multiply by

Answers. me 2. Multiply by 3. Multiply 51 by's 4. Multiply of 7 by en 5. Multiply by 6. Multiply of 8 by 01 5 7. Multiply by 91

69 8. Multiply of by of 5 9. What is the continued product of 1 of s, i, 57 and of?

Ans. 4.5

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DIVISION OF VULGAR FRACTIONS.

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

EXAMPLES.

- Ans.

4 x 5 1. Divide 4 by

Thus,

S X7 2. Divide 11 by

Ansicers. 1-23 3. Divide of by 4. What is the quotient of 17 by i ?

59. 5. Divide 5 by 15 6. Divide i of of it by } of i 7. Divide 4 by of 4 8. Divide 71 by 127 9. Divide 5205 by of 91

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RULE OF THREE DIRECT IN VULGAR

FRACTIONS.

RULE. PREPARE the fractions as before, then state your question agrecable 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.

a

20

s. d. grs.

.

54

come to

1. Iff of a yard cost of a pound, what will is of a Ell English cost ?

fyd.=of of = or Ell English. Ell. fo. Ell. As } ::: And {xxis=15:=10 3 16, Ans. 2. If of a yard costs of a pound, what will 40% yds.

Ans. 4,59 8s. 61d. 3. If 50 bushels of wheat cost 17l. what is it per bushel

ns. 7s. Od. 12 yrs. 4. If a pistareen be worth 14 pence, what are 100 pistareens worth: :

5. A merchant sold 53 pieces of cloth, each containing 24} yds. at Is, 3d. per yard; what did the whole amount to ?

Ans. £ 60 10s. Odl. 3qrs. 6. A person having 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?

Ans. f10031 14s. 11.10.

Ans. £o

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PRISPARE 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.

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