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 £l, 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 ls 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 £!, 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 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. 1. Find the cost of 2066 at 14d. d. 2066 0 = cost of goods at 1s. 1ļd. =s. - 25,8 3 = 11d. 2,0 £12 18s. 3d. Ans. 2. Find the cost of 9709 at 15s. 6ů. £. £. $. d. 9709 0 0= cost at 1 0 0 8. 108. = 1£. 4854 10 0= 0 10 0 15 0 0 0 6 Ans. £7524 9 6 = 0 15 6 3. Find the cost of 2864 at £4: 13 : 103. $. d. £. $. d. 2864 0 0 = cost at 1 0 0 4 108.= i£ 20 of 10s. 3d. = 1 of 6d. 11456 0 4 0 0 £13439 11 4 = 4 13 10 4. Find the cost of 2515,93 at £3 : 16 : 41. £. 8. d. d. 2515 0 0= cost of 2515 at 1 0 0 £ 8. 5. Find the cost of 8cwt. 2 qrs. 6 lbs. at £j: 12:8 per cwt. £. $. d. cwt. qrs. Ibs. 5 12 8 = cost of ! 0 0 8 2 qrs. 45 1 4 8 0 0 cwt. 2 16 4 0 0 4 lbs. 14 of 2 qrs ( 4 Ozd. 0 0 4 of 4 lbs. 0 2 04d.=. 0 0 2 8 2 6 6. Find the rent of lącre 1 ro. 25 po. al 78. 6d. per rood. £. ac. ro. po. 0 7 6.3 = rent of 0 1 0 4 I 10 2 0 7 6 20 po. = 0 3 91 5 po. = 1 of 20 po. To 011 1 0 0 0 0 0 1 0 0 20 0 5 ro. £2 2 516=......1 1 25 7. Find the cost of 5416 at £7:4:98. £. $. d. £. 8. d. 5416 0 0 = cost at 100 7 8. Find the cost of 4216 at £3:3:11). £. $. d. £. $. d. 4216 0 0= cost at 1 0 0 3 9. Find the rent of 38 ac. 3 ro. 35 po. at £1:11 : 8) per acre. £. 8, d. 9 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 amonnt, 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 111d. to find the cost at ls. 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. VII. SIMPLE PROPORTION OR RULE OF THREE. In questions of Simple Proportion, quantities of two different kinds are involved, which vary either directly or inversely, as each other. Corresponding values (one of each) of these quantities are given, and a second value of one of them; and it is required to find the corresponding value of the other. This is effected by the Rule of Three, so called, because three quantities are given to find a fourth. Rule-1. Put that quantity for the third term, which is of the same kind with the answer. 2. Put that quantity, which is connected with the third term, as being the value corresponding to the value of the third term, for the first or second term, according as the quantities vary directly or inversely as each other. 3. Put the remaining quantity for the other term. 4. Reduce the first and second terms to the same denomination, and the third to any denomination, or not at all, as may be most convenient. 5. If the first and second, or the first and third, terms have any common divisor, divide them by it. 6. Multiply the second and third terms together, and divide the product by the first. 7. The quotient will be the answer required, in the denomination to which the third terni was recluced, and must be expressed, if possible, in higher terms. EXAMPLES. 1. What cost 39 yards of silk at £3: 16 : 7 for 13 yards. yds. £. d. 3 16 7 : Ans. 3 yds. 39 :: 2. If 173 lbs. of sugar cost 6s. 64d. what cost 13 cwt. Iqr. 11 lbs. ? lbs. lbs. d. 12 cwt. qr. : : 4. The expenses of a parish are £251:10: 103 and the rental is £3054: 10:6, how much in the pound must be levied to pay it ? s. d. £. d. 1 254 10 10.: Ans. 20 : 4. If 8 men occupy 9 days in mowing 24 acres, how many days will 18 men occupy in doing the same work ? men days 8 Ans. 1 4 days = Ans. men : or 5. If the penny loaf weighs 6 oz. 15 drs. when wheat is at 7s.6d,, what ought it to weigh when wheat is at 5s. 3d. per bushel ? d. oz. drs. 7 6 Ans. 4 : : 7)696 9 145. Ans. |