OPERATION. In performing this question, we say 7 43 times 3 fifths are 21 fifths, and 21 fifths are equal to 41. We write down the } 324 Ans. and carry the 4 to the product of 7 times 4= 32. Hence the following 7 RULE. Multiply the numerator of the mixed number by the whole number, and divide the product by the denominator of the fraction; and, as many times as it contains the denominator, so many units must be carried to the product of the integers. If, after division, any thing remains, lei it be a numerator, and the divisor a denominator to a fraction to be affixed to the product. 14. Multiply 9by 5. Ans. 463. 15. Multiply 124 by 7. Ans. 881. 16. Multiply 813 by 9. Ans. 801. 17. Multiply 7} by 10. Ans. 715 18. Multiply 119 by 8. Ans. 949. 19. What cost 7&lbs. of beef at 5 cents per pound ? Ans. 37-11 20. What cost 237 bbs. flour at $6 per barrel ? Ans. $1411. 21. What cost yds. cloth at $5 per yard ? Ans. $ 417 22. What cost 9 barrels of vinegar at $6 per barrel ? Ans. $ 575. 23. What cost 12 cords of wood at $6.374 per cord ? Ans. $ 76,50. 24. What cost 11cwt. of sugar at $ 93 per cwt. ? Ans. $ 103} 25. What cost 43 bushels of rye at $ 1.75 per bushel ? Ans. $7.653. 26. What cost 7 tons of hay at $ 11% per ton ? Ans. $ 835 27. What cost 9 doz. of adzes at $ 10% per doz. ? Ans. $ 95%. 28. What cost 5 tons of lumber at $34 per ton ? Ans. $ 155. 29. What cost 15cwt. of rice at $ 7.62] per cwt. ? Ans. $ 114.371. 30. What cost 40 tons of coal at $ 8.374 per ton ? Ans. $ 335.00. Ans. To. III. To multiply simple fractions. 31. Multiply } by s. This question may be anal} x {=}=12 Ans. yzed in the same manner as in compound fractions. Hence the following OPERATION. RULE. Multiply the numerators together for a new numerator, and the denominators together for a new denominator ; then reduce the fraction to its lowest terms. 32. Multiply by it. Ans. It OPERATION. CANCELLED. 7 8 56 7 7 8 7 x Ans. Х Ans. 8 11 88 11 11 11 33. Multiply it by 11. Ans. 1 34. Multiply 13 by 11. Ans. . 35. Multiply is by 18. 36. Multiply 14 by 17. 37. Multiply by : 38. Multiply by . Ans.. 39. What cost of a bushel of corn at I of a dollar per bushel ? Ans. } of a dollar. 40. If a man travels & of a mile in an hour, how far would he travel in }} of an hour ? Ans. I of a mile. 41. If a bushel of corn will buy y of a bushel of salt, how much salt might be bought for # of a bushel of Ans. At of a bushel. Ans. } Ans. 1 corn ? Note. If there be mixed numbers in the question, they must be reduced to improper fractions, and compound fractions must be reduced to simple fractions. 1 43. Multiply 7} by 84. Ans. 6026 44. Multiply 47 by 91. Ans. 45;s: 45. Multiply 114 by 84. Ans. 99}}. 46. Multiply 123 by 11g. Ans. 147} 47. What cost 74 cords of wood at $ 5% per cord ? Ans. $ 4131. 48. What cost 7yds. of cloth at $34 per yard ? Ans. $ 2518 49. What cost 64 gallons molasses at 231 cents per gallon ? Ans. $ 15215 50. If a man travels 39 miles in one hour, how far will he travel in 97 hours ? Ans. 344.: 51. What cosť 3611 acres of land at $ 25% per acre ? Ans. $9167328 52. If sof of a dollar buy one bushel of corn, what will y of i of a bushel cost ? Ans. 11 of a dollar. 53. How many square rods of land in a garden, which is 9716 rods long, and 49: rods wide ? Ans. 48103 rods. 54. If z of 4 of ii of an acre of land cost one dollar, how much may be bought with of $ 18 ? Ans. 167 acres. Note. The following questions are to exercise the foregoing rules. 55. What are the contents of a field 7625 rods in length and 184 rods in breadth ? Ans. 8A. 3R. 304p. 56. What are the contents of 10 boxes which are 7 feet long, 14 wide, and 14 feet in height? Ans. 16917 cubic feet. 57. From 11 of an acre of land there were sold 20 poles and 200 square feet. What quantity remained ? Ans. 2R. 1p. 227ft. 58. What cost of an acre at $ 1.75 per square rod ? Ans. $ 236.9245. 59. What cost is of a ton at $ 15% per cwt. ? Ans. $ 49.7315. 60. What is the continued product of the following numbers 143, 114, 5%, and 101 ? Ans. 9184. 61. From iz of a cwt. of sugar there was sold # of it; what is the value of the remainder at $0.12 per lb.? Ans. $ 3,57. * per acre ? per lb. ? 62. What cost 194 barrels of flour at $7% per barrel ? Ans. $ 1434. 63. What cost 130 quintals of fish at $37 per quintal? Ans. $ 51 64. I have two parcels of land, one containing 77, acres, and the other 911 acres. What is their value at $ 783 Ans. $ 1380.70%. 65. From a quarter of beef weighing 1752 lbs. I gave John Snow of it ; of the remainder I sold to John Cloon. What is the value of the remainder at 8fcents Ans. $2.0415 66. Alexander Green bought of John Fortune a box of sugar containing 475 lbs. for $ 30.00. He sold of it at 8 cents per lb., and of the remainder at 10 cents per 1b. What is the value of what still remains at 124 cents per lb., and what does Green make on his bargain ? Value of what remains $ 13.194. . 67. What cost 11 of an acre at $ 14+ per acre ? Ans. $2.00. 68. D. Sanborn's garden is 234 rods long and 134 rods wide, and is surrounded by a good fence 7 feet high. Now if he shall make a walk around his garden within the fence 7 feet wide, how much will remain for cultivation ? Ans. 1A. 3R. 7p. 85138_ft. 69. One of my field, I plant corn ; one of the remainder I sow wheat ; potatoes are planted on 4 of what still remains, and I have left two small pieces, one of which is 3 rods square, and the other contains 3 square rods. How large is my field ? Ans. 1A. OR. 29p. 70. Multiply 3 of 4 of 11 by 1 of 1 of 18. Ans. to. Ans. Green's bargain, $ 16.973 Section 24. DIVISION OF VULGAR FRACTIONS. I. To divide a fraction by a whole number. 1. How many times will contain 9 ? To understand this question, x= Ans. we will suppose 4 of an apple OPERATION. were to be divided equally among 9 persons. Now, if we divide 4 of an apple into 9 equal parts, there would be 63 parts, and each person would receive o's; but there being , each man will receive 5 times 63 = Ans. Hence we see the propriety of the following RULE. Ans. zis: Multiply the whole number by the denominator of the fraction, and write the product under the numerator. 2. Divide 11 by 12. Ans. 15z 3. Divide 11 by 8. Ans. 4. Divide / by 12. Ans. The 5. John Jones owns of a share in a railroad valued at $117 ; this he bequeaths to his five children. What part of a share will each receive ? Ans. 1. 6. Divide by 15. Ans. Tis: 7. Divide by 28. 8. James Page's estate is valued at $ 10,000, and he has given 4 of it to the Seamen's Society ; { of the remainder he gave to his good minister ; and the remainder he divided equally among his 4 sons and 3 daughters. What sum will each of his children receive ? Ans. $ 68047 II. To divide a whole number by a fraction. 9. How many times will 13 contain ? Ans. 301. It is evident, that 13 X == 30° Ans. will contain , as many times as there are sevenths in 13, which are 7 x 13=91 times. Again, if 13 contain 1 seventh 91 times, it will contain 3 sevenths as many times as 91 will contain 3 = 301 Ans. Hence the following OPERATION. RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 10. Divide 18 by . 11. Divide 27 by it. Ans. 204. Ans. 295 |