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9. Reduce y of a pint to the fraction of a hhd, Ans. sto 10. Reduce of a pound to the fraction of a guinea.

Compounded thus, of 39 of 7s. Ans. 11. Express 5} furlongs in the fraction of a mile.

Thus 5=\ of =1Ans. 12. Reduce of an English crown, at 6s. 8d. to the fraction of a guinea at 28s.

Ans. Á of a guinea.

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To find the value of a fraction in the known parts of the

integer, as of coin, weight, mcasure, &c.

RULE.

Multiply the numerator by the parts in the next inferior denomination, and divide the product by the denominator; and if any thing remains, multiply it by the next inferior denomination, and divide by the denominator as before, and so on as far as necessary, and the quotient will be the answer.

Note. This and the following Case are the same with Problems H. and III. pages 70 and 71; but for the scholar's exercise, I shall give a few more examples in each.

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EXAMPLES.

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1 What is the value of 71% of a pound? Ans. 8s. {{d. 2. Find the value of 7 of a cwt. Ans. 3 qrs.3.0, 10z.124 de & Find the value of 7 of 33. Bilo Ans. 3s. 0 d. 4. How much is of a pound avoirdupois ?

Ans. 70%. 10 dr. állow much is # of a hhd. of wine ? Ans. 45 gala; 6. What is the value of It of a dollar? Ans. 6s. 716. 7 What is the value ofs of a guinea ?

Ans. 185

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

Ans. 2 oz. 3 grs. 9. How much is of 51. 9s.? Ans. £4 13s. 5 d. 10. How much is į of of of a bhd. of wine ?

Ans. 15 gals. 3 qts.

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. 401

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

Ans. 38

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

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

17 lb.

Ans. 7 8 oz.?

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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, (hy Case VI. Rule II.) then the sum of the numerators written over the common denominator will be the sum of the fractions required.

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1. Add 54 i and oftogether.

5=Y and of 7-14 Then Y, , 4 reduced to their least common denominator

by Case VI. Rule II. will become . . * Then 132+18+14=1463; or 64 Ans.

2. Add , , and together.

ANSWERS. 17 3. Add , , and together.

17 4. Add 12; 3and 4 together.

2011 5. Add { of 95 and 7 of 141 together.

4417 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.

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1.

6. Find the sum of 52, 74 and 15.
I find the sum of and to be i=111

Then 12+5+7+15=2871 Ans.
7. Add ; and 174 together.

ANSWERS. 1776 8. Add 25, 8 and of of po

33,4 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 terms. 9. Add of a shilling to of a pound. 1st method

2d method. 4 of 25=145£.

£=7s. 6d. Oqrs. Then tot=£.

45.=0 6 33 Whole value by Case VIII. is 8s. Od. 34 qrs. Ans.

Ans. 8 0 31

By Case VIII. Reduction. 10. Add lb. Troy, to fof a pwt.

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

Ans. 12 cwt. I qr. 8 lb. 12%, 0%. 12. Add of a mile to o of a furlong. Ans. 6 fur. 28 po. 13. Add of a yard, of a foot, and / of a mile together.

Ans. 1540 yds. 2 ft. 9 in. 14. Add ; of a week, 1 of a day, of an hour, and fd a minute together. Ans. 2 da. 2 ho. 30 min. 45 sec.

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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.

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EXAMPLES.

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1343

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

Therefore 9–7= the Ans. 2. From take 4

Answers. 47 3. From id take it 4. From 14 take i 5. What is the difference of s and 17 ? 6. What differs tb from } ? 7. From 14. take of 19

17 8. From 37 takes

O remains. 9. From 11 of a pound, take of a shilling. of doin£. Then from 1. £. take to £. Ans. £.

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

10. From 15£. take 37 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 3 weeks, take of a day, and of of of an hour.

Ans. 3 w. 4 da. 12 ho. 19 min. 171 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 denominator, and placing the remainder ose 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 differen' integers to the same; then multiply all the numerators together for a new numerator, and all the denominators to gether for a new denominator.

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EXAMPLES,
1. Multiply i by

Answers. =
2. Multiply by
3. Multiply 51 by }
4. Multiply of 7 by

-311
5. Multiply 131 by z
6. Multiply of 8 by 1 of 5

131
7. Multiply 7} by 91

69
8. Multiply of by of 3
9. What is the continued product of of, 7, 54 and

Ans. 47

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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.

EXAMPLES

4 X 5 1. Divide by

Thus,

3 X 7 ! 2. Divide i by

Answers, 1 m 3. Divide of by 4. What is the quotient of 17 by f?

591 5. Divide 5 by to

77 6. Divide of of 1 by of

3) 7. Divide 4 by of 4 8. Divide 71 by 127 9. Divide 5205} by of 91

711

= Ans.

230

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