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IV. TO MULTIPLY A COMPOUND QUANTITY BY A DECIMAL FRACTION.

Rule. Convert the compound quantity into a decimal of one of its denominations, multiply by the multiplier, and express the result in positive terms.

If the multiplier be a recurring decimal, it must be reduced to a vulgar fraction, and the operation performed by the last case.

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V. TO DIVIDE A COMPOUND QUANTITY BY A VULGAR FRACTION.

Rule. If the divisor be a mixed number, reduce it to an improper fraction. Invert the divisor, and multiply by the resulting fraction.

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5

217

= 3-

qrs.

920

139

6 lbs.

230

139

2

3

.. 13 cwt. 3 qrs. 11-lbs.—7—1 cwt. 3 qrs. 6- lbs.

230

VI. Rule. Convert the compound quantity into a decimal of one of its denominations; divide by the divisor, and express the result in positive terms. If the divisor be a recurring decimal, it must be reduced to a vulgar fraction, and the division performed by the last case.

TO DIVIDE A COMPOUND QUANTITY BY A DECIMAL FRACTION.

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Def. 1. A quantity which is contained an exact number of times in another, and which is therefore expressible in terms of it by a fraction with numerator 1, is called an aliquot part of it.

Def. 2. Practice is a Rule, which by a combination of Multiplication and Division of compound quantities, enables us to find the cost of a quantity of goods in the most expeditious manner.

1. WHEN THE QUANTITY OF GOODS IS EXPRESSED BY A SIMPLE NUMBER,

THE PRICE OF ONE BEING GIVEN.

Rule-I. If the price be an aliquot part of £1, or 1s. take the same part of the number of articles, the quotient will be pounds or shillings as the aliquot part may be, which, if possible, must be expressed in higher terms.

2. If the price be not an aliquot part of any denomination, and less than £1, divide it into parts, each of which is an aliquot part of £1, or 1s. or of any of those which have preceded it; find the value of the goods on the supposition of each of these being the price, and add the several results.

3. If the price be greater than £1, multiply by the number of pounds, and divide the lower denominations into parts as in the last case.

II. WHEN THE QUANTITY OF GOODS IS NOT EXPRESSED BY A SIMPLE NUMBER.

Rule-1. If the quantity of the goods be expressed by a mixed number, calculate for the whole number as before, and for the fraction by the Rule for multiplying a compound quantity by a fraction.

2. If the quantity of goods be expressed by a compound number, multiply the price of one of the highest denomination by the number in the highest denomination, and find the prices of the lower denominations by means of aliquot parts. The sum of these several results will be the price required.

EXAMPLES.

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5. Find the cost of 8 cwt. 2 qrs. 6lbs. at £5: 12: 8 per cwt.

£. s. d.

5 12 8 cost of

cwt. qrs. lbs.

0 0

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6. Find the rent of 1 acre 1 ro. 25 po. at 7s. 6d. per rood.

£. S. d.

ac. ro. po.

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9. Find the rent of 38 ac. 3 ro. 35 po. at £1: 11: 8 per acre.

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Note. Sometimes it may shorten the process to calculate as for a greater price than that given, and to subtract the cost at the difference of price as in Example 8; or to calculate for a greater amount, and to subtract the cost of the difference in amount, as in Example 9. Thus it is easier, in calculating the cost of goods at 11d. to find the cost at 1s. and subtract the cost at d. than to find the cost at 11 d. directly: and it is easier to find the cost of 14lbs. and subtract that of loz. than to find the cost of 13lbs. 15oz.

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