To find the amount of any quantity of goods, or other mercantile articles, at any given price by the integer. CASE 1. When the number of integers in the given quantity does not exceed 12, multiply the price of an integer by the given number, and the product will be the answer required. EXAMPLES. 1. What will 5 gallons of molasses cost, at 7s. 6d. per gallon? Ans. 1£ 17s. 6d. 2. What will 6 lbs. of cinnamon cost, at 10s. 9d. per lb.? Ans. 3£ 4s. 6d. Ans. 0£ 5s. 71⁄2d. 3. What will 9 lbs. of iron cost, at 7d. per lb.? Ans. 11£2s. 6d. CASE 2. When the number of integers in the given quantity exceeds 12, and is the exact product of any two factors in the multiplication table. RULE. Multiply the price of an integer by one of the said factors, and the product thence arising by the other-the last product will be the answer required. 50 price of 14 yds. 2. What will 16 yards of cassinet cost, at 7s. 10d. per yard? Ans. 6£ 58. 4d. 3. What will 18 lbs. of sugar come to at 103d. per lb.? 4. What will 20 lbs. of tobacco come to at ls. 5. What will 21 lbs. of pepper come to at 4s. 6. What will 22 lbs. of butter come to at 74d. 7. What will 24 yards of scarlet come to at 23s. 6d. Ans. 13s. 9d. per yard? Ans. 28£ 4s. CASE 3. When the number of integers in the given quantity exceeds 12, and is not the exact product of some two factors in the multiplication table. RULE. 1. Choose two such factors as will produce the nearest product to the given number of integers and proceed with them as in the last case. 2. Multiply the given price of one integer by any number that will supply the deficit, and add the result to the amount produced by the last factor, and that sum will be the answer required. EXAMPLES. 1. What will 118 lbs. of bacon come to at 101d. per lb. ? The price of 1lb.=10d.x8 2. What will 13 yards of linen come to at 5s. 6d. per yard? Ans. 3£ 11s. 6d. per bushel? Ans. 3£ 3s. 9d. 3. What will 17 bushels of rye come to at 3s. 9d. 4. What will 19 bushels of wheat come to at 13s. 6d. per bushel ? Ans. 12 16s. 6d. 5. What will 23 lbs. of sugar come to at 103d. per lb.? Ans. 10s. 1d. 6. What will 26 bushels of corn come to at 2s. 6d. per bushel? Ans. 3£ 5s. CASE 4. When the number of integers in the given quantity is greater than the product of any two numbers in the Multiplication Table. RULE. Multiply continually by as many tens, less one, as there are figures in the given quantity; then multiply the last product by the left hand figure of the given quantity, (if it be more than one.) Again: multiply the units figure into the given price of one integer, and that in the ten's place into the price of 10, and that in the hun dred's place into the price of 100, &c. Place the several products as in Compound Addition, and their sum will be the answer required. EXAMPLES. 1. What will 7859 lbs. of tobacco come to, at 13 per lb.? £ s. d. 13 or 1 13×9=0 10 11 10 The price of 1 lb. is The price of 10 lbs. is 11 3.x5=2 16 3 10 The price of 100 lbs. is 5 12 6.x8=45 0 0 2. What will 352 lbs. of beef eome to, at 31d. per lb. ? Ans. 4£ 15s. 4ď. 3. What will 195 lbs. of loaf sugar come to, at 14d. per lb.? Ans. 11 4. What will 390 lbs. of bacon come to, at 7d. per lb. ? Ans. 11 7s. 6d. 7s. 6d. 5. What will 407 lbs. of Crawley steel cost, at ls. 7d. per lb.? Ans. 33 Is. 41d. MULTIPLICATION OF DUODECIMALS, COMMONLY CALLED CROSS MULTIPLICATION. Multiplication of Duodecimals is used for finding the superficial content of hewn timber, planks, boards, and scantling. It is also used for calculating the superficial content of carpenters', joiners', bricklayers', plasterers', painters', and glaziers' work; and, likewise, for ascertaining the solidity or superficial content of any thing else, when the dimensions are taken in feet, inches, and parts of an inch. GENERAL RULE. Feet multiplied by feet give feet. Multiply 7 3 3 9 By CASE 1.-Of feet and inches. 21 0 EXAMPLES. In this example, I say 3 times 7 are 21 feet, which I set down in the first line under feet, and place a cipher in the second, under inches. Next, I say 3 feet multiplied by 3 inches give 9 inches, which I set down in the second line under inches, and place a cipher in the first, under feet. Now, I begin with 9 inches, and say 9 inches multiplied by 7 feet give 63 inches, which are equal to 5 feet 3 inches; that I set down for the third line, under feet and inches. Lastly, I say 9 inches multiplied by 3 inches give 27 seconds, which make 2 inches and 3 seconds; that I set down for the last line, and then add them together, and the answer is 27 ft. 2 inches, and 3 seconds. Answer 27 2 3 Answer 25 58 6 64 0 7 8 11 7 9 11 6 13 10 10 4 8 APPLICATION OF DUODECIMALS. 1. If a plank be 18 feet long and 9 inches wide, how many square feet does it contain? Ans. 13 feet 6 inches. 2. If a plank be 22 feet long, and 11 inches wide, how many square feet does it contain? Ans. 21 feet 1 inch. 3. There is a piece of scantling that is 6 inches wide, 4 inches thick, and 24 feet long. How many square feet does it contain ? 4. There are 12 planks, each 17ft. 6 inches long and 8 inches 9 |