PRACTICE. PRACTICE is a short method of calculating the value of goods, &c., by means of fractional or aliquot parts of the price. One number is said to be an aliquot part of another, when it is contained in it an exact number of times: thus 4 is an aliquot part of 16-namely, as it is contained in it exactly 4 times. The calculations in Practice are performed by means of such tables of aliquot parts as the following, which should be carefully committed to memory. The Rules of Practice are generally employed instead of those of Compound Multiplication, for calculating the prices of goods, &c., as the working is in many cases easier and shorter. The same principle of aliquot parts can be applied to any other weights or measures. I. WHEN THE GIVEN QUANTITY IS A SIMPLE NUMBER, AND THE PRICE IS AN ALIQUOT PART OF £1, OR ls., OR 1d. RULE.-Consider the quantity as so many pounds, shillings, or pence, according to the aliquot part used: that is, if the price be an aliquot part of a pound, consider the quantity as so many pounds; if part of a shilling, consider the quantity as so many shillings, &c.: then divide the sum as in Compound Division, by 2, if the aliquot part is ; by 3, if it is }; by 4, if it is ; and so on; converting the quotient, when necessary, into its highest denomination. Example 1.-What is the price of 713 yards of silk, at 3s. 4d. a yard? Here the quantity is considered as £713, and is divided as in Compound Division, by 6, because 3s. 4d. is the th of £1. Example 2.-What is the price of 1256 yards of cotton, at 4d. a yard? Here the quantity is considered as 1256s., and is divided by 3, as 4d. is of a shilling: the quotient is 418s. 8d., which being converted into its highest denomination, gives £20, 18s. 8d. for the answer. II. WHEN THE QUANTITY IS A SIMPLE NUMBER, BUT THE PRICE IS not AN ALIQUOT PART OF £1, OR 1s., OR ld. RULE. Find the nearest or most convenient aliquot part of the price, and divide the quantity as in Rule I.; then take such other parts as will make up the rest of the price, and divide in each case, that sum of which the aliquot part is taken; then add all the quotients together for the answer. When there are pounds in the price, multiply the quantity by the pounds, and add to the product the value of the aliquot parts. When the price is near a pound, and the difference is an aliquot part of a pound, the given quantity may be reckoned as so many pounds, and the aliquot part for the difference subtracted from the amount; the result is the answer. NOTE.-Before beginning to divide, the sums represented by the different aliquot parts to be used, should be written opposite the parts, and then added together, that it may be seen if the whole of the price has been taken into account. Example 1.-What is the price of 360 yards at 15s.? £360 10/of £1, 180 " 5/ = 10/ 90 15/ £270 Ans. Here we reckon the quantity as £360, and divide it by 2, as 10s. is the of £1; and then the quotient by 2, as 5s. is the of 10s. The answer is £270. Example 2.-What is the price of 549 yards at 18s. 9 d. a yard. Here we take the various sums that make up 18s. 94d. (adding them together to see that the sum is correct), and write opposite them the respective aliquot parts that they represent. We then divide the given quantity, which is considered as £549, by 2 for the first aliquot part; the quotient by 2 for the next; and so on; always dividing that sum of which the aliquot part is taken. In the present example, it will be noticed that 3s. 4d., which is of 10s., divides the quotient of 10s., and not that which immediately precedes it, because it is of 10s. that is taken. When all the aliquot parts have been used for division, the quotients are added together for the answer. Example 3.-What is the price of 1546 yards at 18s. 4d. £ yds. 1/8)1546 128 16 8 £1417 3 4 Ans. Here if the price were £1 per yard, the answer, it is evident, would be just as many pounds as yards; but as the price is 1s. 8d. less than a pound-that is,th part less-1-12th of the number, considered as pounds, is subtracted from it, and the difference is the price of so many yards at 18s. 4d. III. WHEN THE QUANTITY CONTAINS A FRACTION. RULE.-Calculate the value of the integer by either of the preceding rules; then multiply the given price by the fraction,* and add the whole for the answer. *See Compound Multiplication, Rule V. page 48. Example.-What is the value of 32763 yards at 5s.? IV. WHEN THE QUANTITY CONSISTS OF SEVERAL DENOMINATIONS. RULE.-Multiply the price by the highest denomination of the quantity, and for the other denominations take aliquot parts of the quantity, and proportionate aliquot parts of the price. Example.- What is the value of 7 cwts. 3 qrs. 7 lbs. at £5, 12s. 6d. per cwt.? |