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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 25.=, Ans. 11. Express 5] furlongs in ti.e

Thus, 5)=3 of =it Ans.

ply a mile. 12. Reduce of an English crown, at Os. 8d. to the fraction of a guinea at 285.

Ans. of a guinea. CASE VII.

To find the value of the 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 mferior 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 examples in each.

EXAMPLES

1. What is the value of go of a pound ?

Ans. 8s. 9 d. 2. Find the value of 'n of a cwt.

Ans. Sgrs. 3lb. 1oz. 12 dr 3. Find the value of 3 of 3s. 6d Ans. 3s. uid. 4. How much is not of a pound avoirdupois ?

Ans. 7oz. 10dr. 5. How much is of a hhd. of wine ? Ans. 45 gals. 6. What is the value of 15 of a dollar ?

Ans, 5s. 71d. 7. What is the value of it. of a guinea ? Ans. 185.

8. Required the value of 1.7 of a pound apothecaries.

Ans. 2oz. Sgrs. 9. How much is of 5l. 9s.,? Ans. £4 135. 54d. 10. ilow much is suf of of a hhd. of wine ?

Ans. 15gals. Sats.

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

Ans. 125

1707 2. Reduce 13 cwt. 3 qrs. 20 lb. to the fraction of a ton.

Ans. 3. Recluce 16s. to the fraction of a guinea.

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

Ans. 5. What part of 4 cwt. 1 qr. 24 lb. is 3 cwt. 3 qrs 17 lb.

Ans.

Ans.

8 02.

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 53 # and of together.

5=' and of 7= Then reduced to their least common denominator by Case VI. Rule II. will become 132 18

是结 Then 132+18-+-14=*=635 or 6 Answer.

2. Add and together
3. Add į and together.
4. Add 12 3 and 4 together.
5. Add 1 of 95 and 7 of 141 together.

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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 nuinbers of the given mixed numbers.

6. Find the sum of 51 7 and 15.
I find the sum of and to be t=11%

Then ili +5+7+15=281 Ans. 7. Add 1 and 17 together.

Ans. 17's 8. Add 25, 84 and off of

Ans. 3315 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 f of a pound. 1st Method.

2d Method. of o£

=7s. 6d. Oqrs.
Then hotérilik s. 30 6 3
Whole value by Case VII
is 8s. Od. 3 qrs. Ans.

Ans. 8 03
By Case VIII. Reduction.

fir.

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10. Add { lb. Troy, to f of a pwt.

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

Ans. 12cwt. 1qr. 8lb. 12 i80%. 1. Add of a mile to jo of a furlong.

Ans. 6fur. 28po 18. Add f of a yard, { of a foot, and 7 of a mile together.

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

SUBTRACTION OF VULGAR FRACTIONS.

RULE.* PREPARE the fractions as in Addition, and the difference of the numerators written above the common de. nominator', will give the difference of the fraction required,

EXAMPLES.

11 42

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31

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206

5 378

1. From take of
of j =i=1 Then and 1=11

Therefore 97=1= the Ans. 2. From take

inswers. 3. From take 4. From 14 take 13

1345 5. What is the difference of it and }} ? 6. What differs is from } ? 7. Froin 141 take of 19 8. From take 116

O remains. 9. From ti of a pound, take of a shilling: of id=6o. Then from £takeAns.

Note.--In fractions of money, weight, &c. you may, if you please, find the value of the given f actions (by Case Vill. in Reduction) and then subtract them in their pro

10

171 17

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per terms.

10. From ;'. take 37 shilling. Ans. 5s. 6d. 2{qrs. 11. From of an oz. take of a put.

Ans. liput. 3gr. 12. From } of a cwt. take of a lb.

jins. Igr. 27lb. 6oz. 10., dr. 13. From 3 weeks, take of a day, and fof} of j of

Ans. 3w.4da. 12ho. 19min. 174sec

an hour.

*In subtracting mixed numbers, when the tower fraction is greater than the upper one, you may, without reducing them to iinproper fractions, subtract the numerator of the lower fraction from the coinmon denoninator, 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 FRACTIONI.

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.

EXAMPLES.

35

1. Multiply by

Answers. He 2. Multiply by 3. Multiply 54 by 4. Multiply of 7 by

311 5. Multiply it by 12 6. Multiply of 8 by 1 of 5 7. Multiply 7t by 91

69 8. Multiply of by of 5 9. What is the continued product of of, 7, 54 and of ?

Ans. 45€

131

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.

=i Ans.

4 X 5 1. Divide by Thus,

3 X 7
2. Divide 17 by

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

599 5. Divide 5 by 1o

71 6. Divide 4 of 4 of by 1 of

3
7. Divide 45 by of 4
8. Divide 71 by 127
9. Divide 5205} by of 91

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