CASE IV. When the quantity is any number above the Multiplication Table. Multiply the price of 1 yard by 10, which will produce the price of 10 yards: This product, multiplied by 10, will give the price of 100 yards; then you must multiply the price of 100 by the number of hundreds in your question; the price of ten by the number of tens; and the price of unity, or 1, by the number of units lastly, add these several products together, and the sum will be the answer. EXAMPLES. 1. What will 359 yards of cloth, at 4s. 74d. per yard, amount to? To find the value of a hundred weight or 112 pounds, having the price of one pound given. Multiply the price of 1 pound by 7, the product will be the price of 7 pounds; multiply the price of 7 pounds by 4, the pro 190. When the quantity is a number above the multiplication table, how do you proceed?-191. What is the method of finding the value of a cut. or 112 lbs. the price of 1 pound being given? duct will be the price of 28 pounds or 1 qr. of a cwt.; then multiply the price of 28 pounds by 4, and the product will be the price of 112 pounds, or a cwt. EXAMPLES. 1. What will 1 cwt. of lead come to, at 64d. per pound? 1. What is the weight of 4 hogsheads of sugar, each weighing 7 cwt. 3qrs. 19lb. ? Ans. 31cwt. 2qrs. 20lb. 2. What is the weight of 6 chests of tea, each weighing 3cwt. 2 qrs. 9lb.? Ans. 21cwt. 1qr. 26lb. 3. If I am possessed of 12 dozen of silver spoons, each weighing 3oz. 5pwt.-2 dozen of tea spoons, each weighing 15pwt. 14gr.-3 silver cans, each 9oz. 7pwt.-2 silver tankards, each 21oz. 15pwt.and 6 silver porringers, each 11oz. 18pwt.; what is the weight of the whole? Ans. 18lb. 4oz. 3pwt, 4. In 35 pieces of cloth, each measuring 27 yards, how many yards? Ans. 971 yards. 5. How much brandy in 9 casks, each containing 45 gallons, 3qt. Ans. 412gal. 3qt. 1pt. 1pt.? 6. If I have 9 fields, each of which contains 12 acres, 2 roods, and 25 poles; how many acres are there in the whole? Ans. 113ac. 3r. 25p. COMPOUND DIVISION. COMPOUND DIVISION is the dividing of numbers of different denominations in doing which, always begin at the highest, and when you have divided that, if any thing remain, reduce it to the next lower denomination, and so on, till you have divided the whole, taking care to set down your quotient figures under their respective denominations.* INTRODUCTORY EXAMPLES. 1. Divide 549 £ 3. £109 19 6 In this example, having divided the pounds, the 4 which remains is £4, which are equal to 80s. and 17 in the shillings, make 978.; we then find that 5 is contained 19 times in 97, and 2 over: we set down the 19 under the shillings, and reduce the 2s. that remain into pence, and they make 24, which, added to the 9d. in the question, make 33d.;-then how often 5 in 33? 6 times, and 3 over. We set down 6 under the pence, and reduce the 3d. which remain to farthings-they make 12: 5 is contained in 12 twice; we therefore set down d. and the 2 which remains, being of a farthing, is disregarded. *To divide a number, consisting of several denominations by a simple number, is, evi: dently, the same as dividing all the parts of which it is composed by the same simple number. And this will be true, when any of the parts are not an exact multiple of the divisor; for if the excess of that multiple has its proper value in the next less denomination, the dividend will still be divided into parts, and the true quotient will be found as before. Thus, 81. 1s. 104d. divided by 5, will be the same as 51. 60s. 20d. 10qr. divid. ed by 5, which is equal to 11. 12s. 44d. as by the rute. 192. What is Compound Division? CASE I.* Having the price of any number of yards, &c. within the pence table, to find the price of 1 yard, &c. If the quantity do not exceed 12, proceed by setting down the price, and dividing it by the quantity; which quotient will be the price of one yard, required; but if the quantity exceed 12, then divide by two such numbers as, when multiplied together, will produce the quantity, and the last quotient will be the value of 1 yard, required. NOTE. If there be a remainder after the division by one of the parts of a composite number before the last, that remainder must be divided according to the rule for division of fractions. Thus, If 35 yards cost £37 11s. what is the price of 1 yard? Having the price of 1cut. or 112lbs. to find the price of one pound. Divide the price of 1 cwt. by 8, that quotient by 7, and this *This case proves the 1st and 2d cases in Compound Multiplication. 193. Having the price of several yards, how do you find the price of one?-194. In case of a remainder, how do you proceed?-195. Having the price of lcwt. or more, how do you find that of a pound? quotient by 2, and the last quotient will be the price of one pound, required. The reason is, 8 x 7 x 2 = 112 lbs. or 1 cwt. EXAMPLES. 1. If 1 cwt. of flax cost £2 7s, 8d. what is that £ 8. d. 2. At $156 per cwt. what is the price per lb.? Ans. $1 394c. 3. At $3 33c. 3m. per cwt. what is the cost of 1 lb. ? Ans. 2c. 9m. 4. If 1 cwt. of sugar cost £3 7s. 6d. what is that CASE III.* Having the price of several hundred weight, to find the price per pound. Divide the whole price by the number of hundreds, which will give the price per cwt. and then proceed as in the last case. EXAMPLES. 1. If 5 cwt. sugar cost £13 8s. 4d. what is that per lb. ? |