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CASE IV.

To reduce a whole number to an equivalent fraction, bav

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 fraction required.

EXAMPLES.

1. Reduce 7 to a fraction whose denominator will be 9.

Thus, 7x9=63, and y the Ans. 2. Reduce 18 to a fraction whose denominator shall be 12.

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

Ans. 88°="='

Ans. 1

CASE V.

To reduce a compound fraction to a simple one of equal

valu

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

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

EXAMPLES.

Ans. as

1. Reduce of of off to a simple fraction,

1 X2 X3 X4

==ió Ans.

2x3x4x10 2. Reduce of off to a single fraction. 3. Reduce of ij of to a single fraction.

Ans. 836 A. Reduce of of 8 to a simple fraction.

Ans. W=33 5. Reduce of jf of 42} to a simple fraction.

Ans. 1344°=2175 Note. If the denominator of any member of a com. pound fraktion be equal to the numerator of another mem

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ber thereof, they may both be expunged, and the other members continually multiplied (as by the rule) will pro. duce the fraction required in lower terms. 6. Reduce fofof{to a simple fraction.

Thus 2 x 5

==í Ans. 4x7

7. Reduce of off of it to a simple fraction.

Ans. if}
CASE VI.

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 each 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.

+ t =24 common denominator.

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2. Reduce }, to, and ií, to a common denominator.

Ans. Hi, ift, and if. 3. Reduce , , k, and 7, to a common denominator.

Ans. Han 1:1, 314, and jl.

si

4. Reduce , on, and to, to a common denominator 800

300 400

-and- =it is and 1=11 Ans. 1000 1000 1000 5. Reduce , 5, and 12, to a common denominator.

Ans.49, 41, 42 8. Reduce , 1, and of 11, to a common denominatoz.

Ans. 2008, 19, 1988. 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.

I'or reducing fractions to the least common denominatnr.

(By Rule, page 143) find the least common multiple of all the denominators of the given fractions, and it wili he the common denominator required, in which divide each partioular denominator, and multiply the quotient by its own numerator, for a new numerator, and the new numerators being placed over the common denominator, will express the fractions required in their lowest terms.

EXAMPLES

1. Reduce }, , and f, to their least common denominator

4)2 48

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I 1 1 4x2=8 the least com. denominator:

8+2x1=4 the 1st numerator.
8+4x3–6 the 2d numerator.

8:8x575 the 3d numerator. These numbers placed over the denominator, give the answer , , , equal in value, and in much lower terms than the general Rule would produce

2. Reduce , s, and ja, to their least common denomina for.

Ans. 31, 3, 4

8

Dator.

3. Reduce } i and to their least common denomi

Ans. ita 4. Reduce } } and is to their least common denomi

Ans. 1' 18 18

Dator.

CASE VII.

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To Reduce the fraction of one denomination to the fracation 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 coms. 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 i of g of at of a pound.

Ans. 6x 12 x 20

1440
2. Reduce tako of a pound to the fraction of a penny.

Compared thus Tit of Y of Yd.
Then 5 X 20 X 12

1440

1440 1 1 3. Reduce of a farthing to the fraction of a snilling.

Ans. of

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

Ans. Tho=d. 5. Reduce of a pwt. to the fraction of a pound troy.

Ans. Tror 6. Reduce $ of a pound avoirdupois to the fraction of swt.

Ans. cwt. 7. What part of a pound avoirdupois is to of a cwt.

Compounded thus to off of =+= As. *8. What part of an hour is of a week.

Ans. H=

127

9. Reduce of a pint to the fraction of a hhd. Ans. ati 10. Reduce şof a pound to the fraction of a guinea.

Compounded thus, f of 2 of 's=Ans. 11. Express 5furlongs in the fraction of a mile.

Thus 5=of}=Ans. 12. Reduce of an English crown, at 6s. Sd. to the frac tion of a guinea at 288.

Ans. fi 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 inferie ienomination, 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.

Nore. This and the following Case are the same with Problems II. and III. pages 70 and 71 ; but for the scholar's exercise, I shall give a few more examples in enclr.

EXAMPLES.

1. What is the value of a lt of a pound? Ans. 8s. gold. 2. Find the value of 7 of a cwt. Ans. 3 qrs. 3 lb. 1 oz.124 de 3. Find the value of of 3s. 6d. Ans. 3s. 03d. 4. How much is of a pound avoirdupois ?

Ans. 7 oz. 10 dr. 5. How much is of a hhd. of wine? Ans. 45 gals. 6. What is the value of 1 of a dollar ? Ans. 58.71d. 7. What is the value of i'r of a guinea?

Ans. 185.

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