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Ans. 672

9. Reduce # of a pint to the fraction of a hhd. 10. Reduce of a pound to the fraction of a guinea

Compounded thus, of 4 of 8.=4 Ans. 11. Express 5} furlongs in the finction of a mile.

Thus, 51 of 1=1 Ans. 12. Reduce of an English crown, at 6s. 8d. to the fraction of a guinea at 28s.

Ans of a guinea.

CASE VIII.

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

integer, as of coin, weight, measure, &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 II. and III. pages 75 and 76; but for the scholar's exercise, I shall give a few more examp? 's in each.

EXAMPLES.

1 What is the value of 11 of a pound?

Ans. 8s. 9jd. 2. Find the value of of a cwt.

Ans. Sqrs. 3lb. 1oz. 194dr 3. Find the value of } of 8s. 6d. Ans. Ss. O d. 4. How much is t of a pound avoirdapois ?

Ans. 7oz. 10dr. 5. How much is of a hhd. of wine ? Ans. 45gals. 6. What is the value of Huf a dollar ?

Ans. 5s. 7 d. 7. What is the value of of a guinea ? Ane. 188.

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

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

Ans. 15 gals. 3qt 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.

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

Ans. 195

1792

2. Reduce 13cwt. Sgrs. 2015. to the fraction of a ton.

Ans.

39

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

4. Reduce 1 hhd. 49 gals. of wine to the fraction of a Lun.

Ans. 5. What part of 4cwt. Iqr. 241b. is 3cut. Sqrs. 17 ib. Boz.

912s.

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 deRominator, will be the sam of the fractions required.

EXAMPLES.

1. Add 53 : and of 7 together,

53= 1 and of = Then i reduced to their least common denominator

by Case VI. Rulell. berome 132 18 Then 132+18+14==off or 6. Answer.

2. Add and together.
3. Add i and together.
4. Add 122 3 and 4 together.
5. Add of 95 and 7 of 14together.

Ans. 11

fins. 11 Ans. 2011 Ans. 4441

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 ; and to be .=111

Then 121 +5+7+-15=2811 Ans. 7. Add and 17 together.

Ans. 17 18 8. Add 25, 8and of of a

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

Ars. Si

proper terms.

4 52

9. Add of a shilling to of a pound.
1st Method.

2d Method.
of Lauf

if.=7s. 6d. Oqrs. Then 14+9=1120 fir . 4s. =0 6 33 Whole value by Case VIII is 8s. Od. 3 qrs. Ans. Ans. 8 0 3

By Case VIII. Reduction. 10. Add b. Troy, to % of a pwt.

Ans. 7oz. 4pwt. 13 11. Add of a toa, to x of a cwt.

Ans. 12cwt. 1gr. slb. 12,60%. 12. Add of a mile to To of a furlong.

ins. Ofur. 2&po. 13. Add şof a yard, of a foot, and of a mile together.

Ans. 1540yds. 2ft. Sin. 14. Add of a week, I of day, of an hour, and of a minute together. Arada. 2o. 30min. 45 sec

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SUBTRACTION OF VULGAR FRACTIONS.

7

12 12

7

11 43 31 208

1345

5

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. 1. From take of of ;=14= Then and 15 Therefore 9

iz=the Ans. 2. From 28 take

nswers. 3. From I take 4. From 14 take 5. What is the distoresce of sand ?

10 172

518 6. What differs to from? 7. From 14. take of 10

17 8. From 7 take 2.13

O remains. 9. From of a round, take of a shilling. of norint: Then from 1. £. take kot. Ans. £.

Nore.-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 37 shilling. Ans. 5s. 6d. 2grs. 11. From of an oz. take z of a pwt.

Ins. 11pt. 3gr. 12. From } of a cit. take in of a lb.

ins. Igr. 97lb. 6oz. 10 dr. 13. From S? weeks, take of a day, and 3 of 4 of of an hour.

Ans. Sw. 4da. 12lo, 19 min. 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 fron, 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 OX VULGAR FRACTIONS.,

ROLE. REDUCIS 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 logether for a new bumerator, and all the denominators together for a new denominator.

EXAMPLES.

5

1. Multiply by :

Answers. 2. Multiply by S. Multiply 5 by 4. Multiply of°7 br. 5. Muliipiy by 음 6. Multiply 6 of 8 by j v 5 7. Multiply 7, by 9

693 8. Multiply of by of 3 9. What is the continued product of of 5, 7, 59 and of

Ans. 436

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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.

1

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4 x 5 1. Divide by si

Thus,

S X7 2. Divide by

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

593 5. Divide 5 by 15

77 6. Divide 3 of of by } of 7. Divide 4 by of 4 8. Divide 71 by 127 9. Divvie 52053 by of 91

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