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17. Divide by and by

18. Divide 3- by and 4- by 2. Quot. 5

19. Divide 25- by of 4. Quot. 31

206. To divide a whole number by a fraction.

RULE. Invert the fraction, and multiply the numerator of the inverted fraction by the whole number, under the product place the denominator, and reduce this fraction (if necessary) for the answer i

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quotient required.

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i If I be put for a denominator to the whole number, it will become a fraction, and the divisor being inverted, this rule will coincide with the first rule in Division of Fractions, and is consequently founded on the same principles.

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207. To divide a fraction by a whole number.

RULE. Multiply the denominator of the fraction by the whole number, and over it set the numerator.

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208. When the whole number will divide the numerator of the fraction without remainder, then divide the numerator by it, and under the quotient set the denominator'.

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k Place 1 as a denominator to the whole number, and this rule will coincide with the first, in the same manner as the preceding rule has been shewn to coincide with it.

1 The truth of this rule is evident from ex. 30; for the one fourth part of twelve thirteenths is evidently three thirteenths: and the like will appear from other examples.

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1. What is the sum and the difference of and ?

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3. Which is greatest, the sum of

of 1

2. Required the product and quotient of 3

Answer, prod. 10 quot. 1

7 by 1

of 3.

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and or the difference 7 12'

7 29
and and how much? Answer, the sum, by
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quotient, and how much? Answer, the quotient, by

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by and how much? Answer, the latter, by

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est, the product or the quotient, and how much? Answer, the

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8. If 2If 27

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be added to and also divided by it, which is

greatest, the sum or the quotient, and how much? Answer, the

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9. What sum will arise by adding the sum and difference of

2 3

of 3 guineas and of 4 pounds together? Ans. 5l. 6s. 8d.

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10. If the quotient of 2- by of 2 be multiplied by the

sum, what is the product?

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210. PROPORTION, OR, THE RULE OF THREE
IN VULGAR FRACTIONS.

RULE I. Examine the question so as to be able to determine how the stating is to be made, then reduce the first and third terms to fractions of the same denomination, if they are not so already, and the second to a fraction of the greatest denomination contained in it, or of a greater denomination if convenient.

II. With the fractions to which the given numbers are reduced state the question, and examine whether the answer will be greater or less than the second term; if greater, mark the less extreme for a divisor, but if less, mark the greater.

III. Invert the marked term, and then multiply the three terms continually together; the product will be a fraction of the same denomination with that which the second term was reduced to, and must be reduced to its proper quantity for the

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This rule is founded on the same principles with the Rule of Three in whole numbers, (Art. 126,) and under it are included both the direct and inverse rules, which in effect are only branches of one and the same general rule.

EXAMPLES.

1. If 2-cwt. of cheese cost 10l. 2s. 6d. what cost lcwt. 1qr.

14lb.?

Reduction of the terms.

2-cwt.= cwt. 10l. 2s. 6d. = 10-L. =

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5

1

10 L. = SL.

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5

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of which I find that the answer ought to be less than the second term; I there

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three terms down with signs of multiplication between, and multiply them to

gether; the product is next reduced to its proper terms, which gives the

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answer. In the multiplication, the elevens cancel each other.

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Here as the terms require no reducing, I first state the question, and find that the answer will be less than the second term; I therefore mark the greater

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term for a divisor, which being inverted, and multiplied by the two other

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