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9. Reduce of a pint to the fraction of a hliů.
LO. Reduce of a pound to the fraction of a guinea.

Compounded thus, of 9 of 4.=Ans. 11. Express 5} furlongs in the fraction of a mile.

Thus 5!=y of lins. 12. Reduce of an English crown, at Os. 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, mcasure, &c.

RULE.

Vultipls the numerator by the parts in the next infepor denomination, and divide the product by the denomi. nator ; 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 samo 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 we value of all of a pound ?

Ans. 8s. 2. Find the value of 7 of a cwt.

Ans. 3qrs. 3lb. 102. 12. dr. 3. Find the value of of 38. Od. Ans. 35. 0/d. 4. How much is of a pound avoirdupois ?

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

Ans. 58.731. 7. Wim is the value of of a guirna ? 488, 181.

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

Ans. 2oz. 3grs. 9. How much is of 51. 9s. ? Ans. £4 13s. 510. 10. How much is } of of of a hhd. of wine ?

Ans. 15gals. Syts.

CASE I.X.

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 15. 3 ozto ine iraction of a cwt.

Ans. 195 -2. Reduce 13 cwt. 3 qrs. 20 ib. to tire fraction of a ton.

Ans. 33 3. Reduce 10$. to the fraction of a guinea.

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

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

Ans. Í

ADDITION OF VULGAR FRACTIONS.

RULE.

REDUCE compound fractions to single ones; mixed saumbers to improper fractions; and all of them to their east conimon denominator (by Case VI Rule II.) then the sum of the nume, ators written over the comnion de. nominator will be the sum of the tractions required.

EXAMPLES.

Add 5} and 3 of together.

51=\ and cf 1=14 "Then 4 reduced to their last cummon denominator

by Case VI. Rule 11. will become 131 Thor 132+-18.414-4a0for Goo Answer.

2. Add & and together.
3. Add i and , together.
4. Add 12 33 and 4 tugether
5. Add į of 95 and of 141 together.

Ans. I Ans. 17 ins. 2011 Ans. 4413

Note 1.--In adding mixed numbers that are not compounded with other fractions, you may first find the supi of the fractions, to which add the whole rumbers of the given mixed numbers.

6. Find the sum of 57 and 15.
I find the sum of land of to be 11=1}}

Then ljó+5+7+15=2816 Aus 7. Add ard 17į together.

Ans. 17

Ans. 33 12 8. Add 25, 8} and of of iso

5.=0

6 3

Note 2.—To add fractions of inoney, weight, &c. reduce fractions of different integers to those of the same.

Or, if you please you miay find the value of each fraction by Case VIII. in Reduction, and then add them in their proper terms. 9. Add 4 of a shilling to of a puund. Ist niethod.

20 Method. of zo=ito£.

*£ =7s.6d. Oqrs. Then tho+=11 Whole value by Case VIII. is 8s. Od. 3 qrs. Ans.

Ars. 8

0 3

By Case VIII. Reduction 10. Add 3 lb. Troy, to $ of a pwt.

Ans 7oz. 4prot. 13397. 11. Add. of a ton, to io of a cut.

Ans. 12cwl. 1gr. 8lb. 1217az. .12. Add i of a mile to jo of a furlong.

Ans. 6fur. 28po. 13. Add of a yard, of a fouž, and 7 of a mile to gether.

Ans. 1540yds. 2ft. Jin. 14. Add á of a week, į of a day, s of an hour, and of a minute together. Ans. 2da. 2ho, 30min. 458ec.

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.

EXAMPLEG.

3)

1345

12

1. From takes of
of == Then and isoja

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

Anewers. He 3. From id take 15 4. From 14 take 12 5. What is the difference of and it? 6. What differs from ?

Tui 7. From 14takes of 19 8. From take a

O romains. 9. From is of a pound, take of a shilling, of zorilo£. Then from 13 take jaat. Ans. 114.

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 £. iake 3 sirilling. Ans. 5s. 6d. 2grs. 11. From of an oz. take of a pwt.

Ans.11

pwt. sgr. 12. From į of a cwt: take 1 of a lb.

Ans. Iqr. 27lb. 60%. 10, 13. From 3 weeks, take ţ of a day, and of of of

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

dr.

an hour.

* 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 upit'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 mainder over the denorsnator, then taking one from the whole iombos.

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MULTIPLICATION OF VULGAR FRACTIONS.

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.

1. Multiply s by

Answers ti=; 2. Multiply by #

bo 3. Multiply 51 by 4. Multiply of 7 by

313 5. Multiply is by is

2 6. Multiply of 8 by 1 of 5

13} 7. Multiply 73 by 91 8. Multiply of hy $ of 3 9. What is the continued product of of, 7, 5, and of?

Ans. 405

69

DIVISION OF VULGAR FRACTIONS.

RULE. PREPARE the fractions as before ; then, invert the di visor and proceed exactly as in Multiplication :-The pre ducts will be the quotient required.

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EXAMPLES."

i Ans.

Answers, 14

4 X 5 1 Divide by Thus,

3 X 7 2. Divide 17 by 3. Divide off by 4. What is the quotient of 17 by ? 5. Divide 5 by 6. Divide { of off by 1 of 1 7. Divide 48 hy & of 4 8. Divide 71 by 127 9. Diviae 52053 by for 91

591 77 31 230

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