47 £. S. KEY TO CARD No. 25. How many times 47 in 56?-1-place 47)566 7(12£.1 in the quotient for pounds--multiply 47 (12€.|| by 1-set the product under 56 subtract-the remainder is 9-bring down the other 6, makes 96. .96 94 £ 2 7s. 20 47)47(1s. .47 How many times 47 in 96?-2-set 2 in the quotient, makes £12-multiply 47 by 2-place the product under 96-subtract-the remainder is £2 and 7s. in the given sum, make £ 2 7s. or 47s. How many times 47 in 47? We know it can be contained 1 time and nothing remains; therefore the quotient in shillings is 1-The quotient in the pounds is £12, and in the shillings 1; consequently the answer is £12 18. LESSON 9, Eighty-nine industrious boys hoed garden and pruned fruit trees, till their wages amounted to £ 28 3 8-They wished to divide the sum and purchase quills, ink, and paper: : What was each one's share? £. S. d. 89)28 3 8 20 89)563(6s. 534 . 29 12 89)356(4d. 356 Pounds. As you cannot have 89 in 28, therefore multiply by 20 to reduce the pounds into shillings, and add the 3 shillings of the given sum, which makes 563s. How many times 89 in 563 ?-6-place 6 in the quotient for shillings-multiply 89 by 6; set the product under 563subtract-The remainder is 29s. Multiply 29 by 12 to reduce it into pence, and add the 8 pence of the given sum, which makes 356 pence. KEY TO CARD No. 25. How many times 89 in 356?-4; set 4 in the quotient for pence-multiply 89 by 4-place the product under 356-as the two numbers are equal, subtraction is needless. The answer is £0 6s. 4d. How to find the price of one pound, one yard, one bushel, &c., when fractions are contained in the whole quantity; as, 34 pounds, 56 yards, 77 bushels, &c. RULE. 1. Multiply the quantity by 4 for a divisor. 2. Multiply the price by 4 for a dividend. 3. The quotient will be the answer. LESSON 10. EXAMPLE. If 34 pounds of butter cost £ 2 19 11 1, what is that Now proceed and divide £11 19 9, by 137, the quotient will be the answer, or the price of one pound. £. S. d. As you cannot have 137 in 11£-reduce 137)11 199 it to shillings and add the 19s. which 20 137)239(1s. 137 102 12 137)1233(9d. makes 239s. One hundred and thirty-seven is contained 1 time in 239 and 102 remain. Reduce this remainder into pence, and add the 9d. which makes 1233d. One hundred and thirty-seven is CORtained exactly 9 times in 1233. KEY TO CARD No. 25. RECAPITULATION. The first quotient is 1 shilling and the second is 9 pence; which make the answer £0 1s. 9d. for the price of each pound. See remarks after Lesson 12. LESSON 11. Bought 56 yards of calico for £9 8 4, what is that a yard? In this case 561 is the quantity. 4 for a divisor. The dividend is £ 37 13 4 a quadruple sum from the first. Proceed and divide this sum by 226. The quotient will be the answer. £. S. d. 226)37 13 4 20 226)753(3s. 678 .75s. 4d. 226)904(4d. 904 ... In this Lesson I find that 226 cannot be contained in £37, therefore reduce the pounds to shillings and bring in the 13 shillings, which make 7538. Divide this sum by 226-the quotient is 3s. and there remain 75s. and 4d. over, to be reduced into pence, which makes 904d.-Divide this by 226-the quotient is 4d. RECAPITULATION. The first quotient is 3s.-the second, 4d-consequently the answer is £ 0 3. 4. LESSON 12. If 773 bushels of salt cost £34 0 3 3, what is that a bushel? The dividend is £ 136 1 3 0 a quadruple sum from the first price. £. Now proceed and divide this sum by 311, the quadruple sum of the quantity; the quotient will be the answer. s. d. Three hundred and eleven cannot be contained in 136, therefore reduce the pounds, 136, into shillings, and add the 1 shilling above, which makes 2721s. 311)136 1 3 20 311)2721(8s. 2488 .233 311)2799(9d. 2799 Divide this sum by 311, the quotient is 8s. and the remainder 233s. Reduce this remainder into pence, and add the 3d. above, which makes 2799d.Divide this number by 311-The quotient is 9d. The answer to the question is £0 8s. 9d. REMARKS. NOTE 1. When multiplying the 344 pounds by 4, in Lesson 10, I say 4 times 4 are 16 and the one fourth makes 17—7 and carry 1-then 4 times 3 are 12 and 1 is 13, which makes 137 for a divisor. This augments the quantity, and makes it 4 times greater than at first. 2. Then I multiply the price £2 19 11 1 by 4, as in Compound Multiplication, which multiplying makes a sum of £11 19 9. This also augments the price, and makes it 4 times greater than at first, or a quadruple sum from the first. 3. In multiplying 561 by 4 in Lesson 11, I say, 4 times 6 KEY TO CARD No. 25. are 24 and the two fourths in the fraction make 26-6 and carry 2, &c. 4. When multiplying 773 of Lesson 12, I say, 4 times 7 are 28, and the three fourths in the fraction make 31-1 and carry 3, &c. 5. Multiplying the quantity by 4, and multiplying the price by 4, keep the numbers in proportion; as in the following example. Suppose we divide 6 by 2, the quotient is 3. Now multiply the divisor 2, by 4, it makes 8; and multiply the dividend 6, by 4, it makes 24. Divide 24 by 8, the quotient is 3, the same as when dividing 6 by 2. How to find the price of one pound, when the price is given of one hundred weight or 112 pounds. RULE. Divide the price of 112 pounds by 8-divide that quotient by 7, which makes a second quotient; then divide this second quotient by 2, and the third quotient will be the answer. EXAMPLES. If 1 hundred of iron cost 79s. 4d. what is that a pound? First. Shillings. Seven in 7-1-7 in 9-1 and 2 remain I carry to the pence. Pence. Two shillings I carried make 24 pence and 4 are 28-7 in 28-4. Second. Shillings. Eight in 11-1 and 3 over I carry to the pence. Pence. Three shillings over I carried make 36 pence and 4 make 40--How many times 8 in 40 ?-5. |