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CASE IV.

To reduce a whole number to an equivalent fraction, hav ing a given denominator.

RULE.-Multiply the whole number by the given denominator' place the product over the said denominator, and it will form the traction required.

12.

EXAMPLES.

1. Reduce 7 to a fraction whose denominator will be 9. Thus, 7×9-63, and 3 the Ans. 2. Reduce 18 to a fraction whose denominator shall be Ans. 18

3. Reduce 100 to its equivalent fraction, having 90 for a denominator. Ans. 90-900-100

CASE V.

To reduce a compound fraction to a simple one of equal value.

RULE.-1. Reduce all whole and mixed numbers to their equiva lent fractions.

2. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator; and they will form the fraction required.

EXAMPLES.

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

1×2×3×4

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4. Reduce of of 8 to a simple fraction.

60

Ans. 836

1500

Ans. =31

5. Reduce of 1 of 42 to a simple fraction.

Ans. 1800-217

NOTE. If the denominator of any member of a com pound fraction be equal to the numerator of another mem

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

6. Reduce of 2 of to a simple fraction.

Thus 2×5

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7. Reduce of of of to a simple fraction.

CASE VI.

Ans.

To reduce fractions of different denominations to equiva lent fractions having a common denominator.

RULE I.

1. Reduce all fractions to simple terms.

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

EXAMPLES.

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

1 + 2 + 2 =24 common denominator.

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24 24 24 denominators.

2. Reduce, f, and 11, to a common denominator.

Ans. f, ft, and ff.

3. Reduce,, f, and 7, to a common denominator.

Ans, 111, 11}, {1}, and fff.

4. Reduce,, and, to a common denominator.

800

300 400

-and

and 1 Ans.

1000 1000 1000

5. Reduce 3, 3, and 121, to a common denominator.

60 888

Ans. 11, W.

6. Reduce, 2, and § of 11, to a common denominator. Ans. 768 2592 1980

34569 34561 3456

The foregoing is a general rule for reducing fractions to a common denominator; but as it will save much labour to keep the fractions in the lowest terms possible, the following Rule is much preferable.

RULE II..

For reducing fractions to the least common denominator. (By Rule, page 143) find the least common multiple of all the denominators of the given fractions, and it will he the common denominator required, in which divide each particular denominator, and multiply the quotient by its own numerator, for a new numerator, and the new nume rators being placed over the common denominator, will ex press the fractions required in their lowest terms.

EXAMPLES.

1. Reduce 1, 2, and 3, to their least common denominator. 4)2 4 8

2)2 1 2

N

1 1

1 4×28 the least com. denominator.

8÷2x1=4 the 1st numerator.

8 4×3-6 the 2d numerator.

8÷8x55 the 3d numerator.

These numbers placed over the denominator, give the answer 1, §, §, equal in value, and in much lower terms

than the general Rule would produce 2. Reduce, f, and, to their least

tor.

48

34, 11, 11. common denomina Ans. 47, 41, 44.

3. Reduce and to their least common denominator. Ans. 1!

24

4. Reduce and to their least common denomi nator.

CASE VII.

Ans. H

To Reduce the fraction of one denomination to the fraction of another, retaining the same value.

RULE.

Reduce the given fraction to such a compound one, as will express the value of the given fraction, by comparing it with all the denominations between it and that denomination you would reduce it to; lastly, reduce this com. pound fraction to a single one, by Case V.

EXAMPLES.

1. Reduce of a penny to the fraction of a pound. By comparing it, it becomes of

5 x 1 x 1

of

of a pound.

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3. Reduce of a farthing to the fraction of a snilling.

Ans.

4. Reduce of a shilling to the fraction of a pouna. Ans. T

5. Reduce of a pwt. to the fraction of a pound troy. Ans. T

6. Reduce of a pound avoirdupois to the fraction of

ewt.

Ans.

cut.

7. What part of a pound avoirdupois is T of a cwt. Compounded thus T off of = }}? -j Ans.

8. What part of an hour is

of a week.

Ans.

nee

9. Reduce of a pint to the fraction of a hhd, Ans. ła
}
10. Reduce of a pound to the fraction of a guinea.
Compounded thus, of 2 of

4 Ans. 11. Express 5 furlongs in the fraction of a mile. Thus 5 of 1=1} Ans.

12. Reduce of an English crown, at 6s. 8d. to the frac Ans. of a guinea.

tion of a guinea at 28s.

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 de nomination, 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 70 and 71; but for the scho lar's exercise, I shall give a few more examples in each.

EXAMPLES.

1 What is the value of 1 of a pound? Ans. 8s. (Id.

2. Find the value of 3 of a cwt. Ans. 3 qrs.3 ‚ò, 1oz.124 dı 8. Find the value of 4 of 3s. Jd. Ans. 3s. 08d.

4. How much is

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of a pound avoirdupois?

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6. What is the value of 1 of a dollar?

Ans. 7 oz. 10 dr.

Ans. 45 gals.

7 What is the value of of a guinea?

Ans. 5s. Vid.

Ans. 18s

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