KEY TO CARD No. 25. £. s. How many times 47 in 56 ?-1-place 47)566 7(12£.||1 in the quotient for pounds--multiply 47 47 by 1-set the product under 56-sub. 96 tract--the remainder is 9—bring down the 94 other 6, makes 96. How many times 47 in 96 ?42—set 2 £275. in the quotient, makes £12—multiply 47 20 by 2–place the product under 96-sub47)47(1s. tract-the remainder is £2 and 78. in the .47 Ilgiven 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 ls. 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 per: What was each one's share ? £. d. Pounds. 89)28 3 As you cannot have 89 in 28, therefore 20 multiply by 20 to reduce the pounds into 89)563(6s. shillings, and add the 3 shillings of the 534 given sum, which makes 563s. times 89 in 563?-6-place . 29 6 in the quotient for shillings-multiply 12 |89 by 6; set the product under 563— 89)356(4d. subtract-The remainder is 29s. Multi356 ply 29 bý 12 to reduce it into and jadd the 8 pence of the given sum, which makes 356 pence. pence, pa 8 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 £o 6s. 4d. How to find the price of one pound, one yard, one bushel, &c., when fractions are contained in the whole quantity; as; 341 pounds, 561 yards, 773 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 341 pounds of butter cost £ 2 19 11 1, what is that a pound? Here the quantity is 341 pounds, 4 The divisor is 137 quarters of pounds. £2 19 11 1 4 The dividend is £11 19 9 0 Now proceed and divide £11 19 9, by 137, the quotient will be the answer, or the price of one pound. £. d. As you cannot have 137 in 11£-reduce 137)11 19. 9 it to shillings and add the 198. which 20 makes 239s. 137)239(1s. One hundred and thirty-seven is con137 tained i time in 239 and 102 remain. Reduce this remainder into pence, and 102 12 add the 9d. which makes 1233d. One hundred and thirty-seven is con137)1233(9d. tained exactly 9 times in 1233. 1233 KEY TO CARD No. 25. RECAPITULATION. The first quotient is 1 shilling and the second is 9 pence; which make the answer £0 ls. 9d. for the price of each pound. See remarks after Lesson 12. LESSON 11. In this case 564 is the quantity. a: The divisor is 226 quarters of yards. £9 8 4 4 for a dividend. for S. The dividend is £ 37 13 4 a quadruple sum fron. the first. Proceed and divide this sum by 226. The quotient will be the answer. d. In this Lesson I find that 226 cannot 226)37 13 4 be contained in £37, therefore reduce 20 the pounds to shillings and bring in the 226)753(38. 13 shillings, which make 7538. 678 Divide this sum by 226—the quotient is 3s. and there remain 75s. and 4d. .758. 4d. 12 over, to be reduced into pence, which makes 904d.- Divide this by 226_the 226)904(4d. quotient is 4d. 904 RECAPITULATION. The first quotient is 3s.--the second, 4d.—consequently the answer is £o LESSON 12. If 77 bushels of salt cost £ 34 0 3 3, what is that a bushel ? KEY TO CARD No. 25. 4 The quantity is 77 bushels. Multiplied by 4 311 quarters of bushels. The dividend is £ 136 13 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.ll Three hundred and eleven cannot be con311)136 1 31 tained in 136, therefore reduce the pounds, 20 136, into shillings, and add the 1 shilling 311)2721(8s. above, which makes 2721s. 2488 Divide this sum by 311, the quotient is 8s. and the remainder 233s. ,233 Reduce this remainder into pence, and 12 add the 3d. above, which makes 2799d. 311)2799(9d. Divide this number by 311—The quotient 2799 is 9d. The answer to the question is £0 8s. 9d. REMARKS. Note 1. When multiplying the 34 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 777 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. LESSON 13. If i hundred of iron.cost 79s. 4d. what is that a pound? NOTE.-It will make no difference to divide by 7 first and then by 8. First. Shillings. Seven in 7-1-7 in 9-1 and 2 remain I 8)11 4 carry to the pence. Pence. Second. Shillings. Pence. Three shillings over I carried make 36 pence and 4 make 40_How many times 8 in 40?_5. d. q. 7)794 2) 1 5 |