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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".

20. Divide 12 by #. The divisor inverted is #. then 12 x #= so - 18; the

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* If 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.

23. Divide 9 by # and 10 by 4. Quot 13+ and 11%. - - 4 , aw 24. Divide by +, and 3 by ... out 2 and 4%. 2 13 13 35. Divide 9 by #, and 11 by # out 10 and 374. 10 5 - 2

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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4 I 4 I 28. Divide 5 by 3, and 3 by 4. Quot IE * 15

11 40 11 . Divide — — by 4. t. d 2. 29. Divide 12 by 10, and 5 by Quo 120 * 208. When the whole number will divide the numerator of the jraction without remainder, then divide the numerator by it,

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* Place l 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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4 11 . 1. What is the sum and the difference of - and is’ AnM 8 swer, sum 138. diff. 25. 91 9 |

2. Required the product and quotient of 3; by ; of 3.

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3. Which is greatest, the sum of # and

29 of *% and 30’ and how much Answer, the sum, by

4. Which is the greater, the product of # by #. or their

quotient, and how much Answer, the quotient, by #.

... 10 9 19 5. How much is + greater than –? —. ; greater than IO Answer 90

6. Which is greatest, the quotient of # by #. or that of #

3 l by T” and how nuch Answer, the latter, by ;

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

- 27 quotient, by TT2" 7. 4 - - 8. If 2. be added to +, and also divided by it, which is 8 5 greatest, the sum or the quotient, and how much Answer, the sum. b 13_ sum, by 160

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

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3 10. If the quotient of 2+ by + of 2 be multiplied by the

- - 61 sum, what is the product? Answer 7 128

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 anSWel" m.

* 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.

l 1. If 25 cwt. of cheese cost 10l. 2s. 6d. what cost lcut. 1gr. 14 lb. ? Reduction of the terms. 1

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Erplanation. I first reduce the terms which will be the first and third to fractions of an

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10l. 2s. 6d., the second, to *L.; I then state the question, from the nature of which I find that the * ought to be less than the second term; I therefore mark the greater extreme ll for a divisor; having inverted 4. I put the three terms down with signs of * between, and multiply them together; the product # is next reduced to its proper terms, which gives the

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

- 4 3 2. If 9 of a yard of lace cost T; of a pound, what cost i. of

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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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