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to a common denominator; then subtracting 7 from 108, the

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remainder is 101. Lastly, I reduce

101 252

L. to its proper quantity, which is

shill.

63

34. From of a hhd. of wine take 3 gallons.

3

11.

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5

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5 x 63 315

945Į new numerators.

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MULTIPLICATION OF VULGAR FRACTIONS.

198. To multiply fractions together.

RULE I. Multiply the numerators together for a numerator, and the denominators together for a denominator.

II. If the new fraction be a proper fraction, reduce it to its lowest terms; if an improper one, reduce it to its equivalent whole or mixed number".

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I first multiply the numerators 3, 2, and 7 together, and the product is 42.

a To multiply a fraction by a whole number, we must evidently multiply the numerator by the whole number; but to divide it, we must multiply the denominator by the whole number: thus, if be multiplied by 2, the pro

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1

4

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for two fourths are double of one fourth, and one eighth is the half of one

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fourth this being premised, let it be required to multiply by 3 5 now 2 multiplied by 4 equals 8; but it is not 2, but a third part of 2, which

to be

8

3

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multiplied, and therefore the product will be the third part of 8 only, or but the multiplier is not 4, but the fifth part of 4 only, wherefore the product

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will be the fifth part only of

that is,

15

; wherefore X

3

4
5 15'

8

; or

3' the numerators multiplied together give the numerators of the product, and

the denominators multiplied give the denominators; which is the rule.

Then I multiply the denominators 4, 3, and 8 together, and the product is 96.

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199. When mixed numbers or complex fractions are to be

multiplied.

RULE. Reduce the mixed numbers to improper fractions, and the complex fractions to simple ones, and proceed as before.

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The reason of this process evidently follows from the preceding note.

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together, and reduce the product to its equivalent mixed num

30

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200. To multiply a whole number and fraction together.

RULE. Multiply the numerator of the fraction by the whole number, and under the product set the denominator; then reduce this fraction to its lowest or proper terms, as the case requires, and it will be the answer°.

< Whatever parts a fraction consists of, its product when multiplied by any whole number will consist of like parts; thus two sevenths multiplied by three

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201. When the whole number will divide the denominator of the fraction without remainder, divide by it, and set the quotient under the given numerator; this fraction reduced as before will give the answer.

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To divide the denominator by any number is the same as to multiply the

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the same holds true in every other instance: wherefore the truth of the rule is manifest.

1

and the quotient will be

4÷2

the same as by the former method; and

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