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ber thereof, they may both be expunged, and the members continually multiplied (as by the rule) will produce the fraction required in lower terms.

C. Reduce of of to a simple fraction.

Thus, 2x5

4X7

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7. Reduce of 3 of of 1 to a simple fraction.

CASE VI.

Ans. 11-44

Taoduce fractions of different denominations to equivaient fractions having a common denominator.

RULE 1.

1. Reduce all fractions to simple terms.

9. Multiply each numerator into all the denominators except its own, for a new numerator; and all the denomkors into each other continually for a common denominator; this written under the several new numerators, will give the fractions required.

2 3

EXAMPLES.

1. Reduce to equivalent fractions, having a common denominator.

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9. Reduce of a pint to the fraction of a hhd.

Ans. iz

10. Reduce of a pound to the fraction of a guinea Compounded thus, of 20 ofs.

Ans. 11. Express 5 furlongs in the fction of a mile.

Thus, 5 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.

ΣΤ

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 examples in each.

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5. How much is

of a pound avoirdupois ?

Ans. 7oz. 10dr.

of a hhd. of wine? Ans. 45gals.

6. What is the value of 15 of a dollar?

Ans. 5s. 7 d.

7. What is the value of of a guinea? Ans. 18s.

8. Required the value of 14% of a pound apothecaries.

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Ans. 2oz. 3grs. Ans. £4 13s. 54d. hogshead of wine? Ans. 15gals. Sqts.

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. Sqrs. 20lb. to the fraction of a ton.

Ans. 39

56

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. A

5. What part of 4cwt. 1qr. 24lb. is 3cwt. Sqrs. 17lb. Boz.

Ans.

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.

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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 numbers of the given mixed numbers.

6. Find the sum of 53 74 and 15.
I find the sum of 3 and 4 to be 21-111
Then 1+5+7+15-2811 Ans.
Ans. 17

7. Add and 17 together.

8. Add 25, 81 and 2 of 3 of 150

Ans. SS

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.

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10. Add b Troy, to of a pwt.

11. Add of a ton, to fo

Ans. 7oz. 4pwt. 133gr

of a cwt.

Ans. 12cwt. 1gr. Slb. 120.

12. Add 2 of a mile to 7 of a furlong.

Ans. 6fur. 28po. 13. Add of a yard, of a foot, and of a mile toAns. 1540yds. 2ft. 9in.

gether.

14

14. Add of a week, 4 of day, of an hour, and of Ans. 2da. 2ho. 30min. 45sec

a minute together.

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.

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7. From 14 take of 19

8. From 3 take

24

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17

172

O remains.

9. From of a pound, take of a shilling.

42

4 of 26=150%. Then from 11. takeof. Ans. £. 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 pro

per terms.

10. From

take 37 shilling. Ans. 5s. 6d. 23grs. 11. From of an oz. take of a pwt.

Ans. 11pwt. 3gr.

12. From of a cwt. take of a lb.

Ans. 1gr. 27lb. 6oz. 10 3dr. 13. From 52 weeks, take of a day, and 4 of 3 of of an hour. Ans. Sw. 4da. 12ho. 19min. 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 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 over the denominator, then taking one from the whole number.

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