OPERATION. 7 In performing this question, we say 7 times 3 fifths are 21 fifths, and 21 fifths are equal to 4. We write down the 32 Ans. and carry the 4 to the product of 7 times 432. Hence the following 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, let it be a numerator, and the divisor a denominator to a fraction to be affixed to the product. 19. What cost 7lbs. of beef at 5 cents per pound? Ans. 37. 20. What cost 23-7bbs. flour at $6 per barrel ? Ans. $141. 21. What cost 8 yds. cloth at $5 per yard? Ans. $417. 22. What cost 9 barrels of vinegar at $63 per barrel ? Ans. $57. 23. What cost 12 cords of wood at $6.37 per cord? Ans. $76.50. 24. What cost 11cwt. of sugar at $93 per cwt.? Ans. $103. 25. What cost 4g bushels of rye at $1.75 per bushel? Ans. $7.65ğ. 26. What cost 7 tons of hay at $117 per ton? 27. What cost 9 doz. of adzes at $10 Ans. $831. per doz. ? Ans. $95. 28. What cost 5 tons of lumber at $3 per ton? Ans. $15. 29. What cost 15cwt. of rice at $7.62 per cwt.? Ans. $114.371. 30. What cost 40 tons of coal at $ 8.37 per ton ? Ans. $335.00. Multiply the numerators together for a new numerator, and the denominators together for a new denominator; then reduce the fraction to its lowest terms. 39. What cost of a bushel of corn at of a dollar per bushel ? 40. If a man travels Ans. of a dollar. of a mile in an hour, how far would he travel in 1⁄2 of an hour? 41. If a bushel of corn will buy how much salt might be bought for corn? Ans. † of a mile. Ans. of a bushel of salt, of a bushel of of a bushel. 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. 42. Multiply 43 by 63. OPERATION. 47=28,63 = 20, 23 × 20=48030 Ans. 43. Multiply 7 by 84. 44. Multiply 47 by 91. 45. Multiply 114 by 84. Ans. 60%. Ans. 45. 46. Multiply 122 by 11§. 47. What cost 74 cords of wood at $ 48. What cost 7 yds. of cloth at $3 49. What cost 63 gallons molasses at lon ? Ans. 99 Ans. 1473. 53 per cord? 50. If a man travels 34 miles in one hour, how far will Ans. 34. per acre ? Ans. $9167118. 52. If of of a dollar buy one bushel of corn, what will of of a bushel cost? Ans. of a dollar. 53. How many square rods of land in a garden, which is 97 rods long, and 493 rods wide ? Ans. 4810 rods. 54. If of of of an acre of land cost one dollar, how much may be bought with of $18? Ans. 197 acres. NOTE. The following questions are to exercise the foregoing rules. 55. What are the contents of a field 767 rods in length and 18 rods in breadth ? Ans. 8A. 3R. 30 p. 56. What are the contents of 10 boxes which are 72 feet long, 1 wide, and 14 feet in height? Ans. 1697 cubic feet. 57. From 58. What cost of an acre at $1.75 per square rod ? 59. What cost of a ton at $15 Ans. 2R. 1p. 223ft. Ans. $236.9213. per cwt.? Ans. $49.7313. 60. What is the continued product of the following num bers 143, 11, 5, and 104 ? Ans. 9184. of it; 61. From of a cwt. of sugar there was sold Ans. $3.57. 62. What cost 194 barrels of flour at $73 per barrel ? Ans. $ 1434. 63. What cost 13 quintals of fish at $32 per quintal? Ans $5127. 64. I have two parcels of land, one containing 7 acres, and the other 911 acres. What is their value at $783 per acre? Ans. $1380.70§. 65. From a quarter of beef weighing 1753 lbs. I gave John Snow of it; of the remainder I sold to John Cloon. What is the value of the remainder at 82 cents per lb. ? Ans. $2.0413. 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 lb. What is the value of what still remains at 12 cents per lb., and what does Green make on his bargain? 67. What cost Ans. {Value of what remains $13.194. Ans. $2.00. 68. D. Sanborn's garden is 234 rods long and 134 rods wide, and is surrounded by a good fence 74 feet high. Now if he shall make a walk around his garden within the fence 75 feet wide, how much will remain for cultivation? Ans. 1A. 3R. 7p. 851981ft. 69. On of my field, I plant corn; on of the remainder I sow wheat; potatoes are planted on 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 of of by of 17 of 1. Ans.. Section 24. DIVISION OF VULGAR FRACTIONS. I. To divide a fraction by a whole number. 1. How many times will OPERATION. Ans. contain 9 ? To understand this question, we will suppose of an apple were to be divided equally among 9 persons. Now, if we divide of an apple into 9 equal parts, there would be 63 parts, and each person would receive; but there being, each man will receive 5 times = Ans. Hence we see the propriety of the following RULE. Multiply the whole number by the denominator of the fraction, and write the product under the numerator. 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? 6. Divide by 15. 7. Divide by 28. Ans. 4. Ans. T Ans. 8. James Page's estate is valued at $10,000, and he has given 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. $680 II. To divide a whole number by a fraction. 9. How many times will 13 contain ? OPERATION. 4X3=4=30 Ans. Ans. 30. It is evident, that 13 will contain, as many times as there are sevenths in 13, which are 7 X 1391 times. Again, if 13 contain 1 seventh 91 times, it will contain 3 sevenths as many times as 91 will contain 3= 30 Ans. Hence the following RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 10. Divide 18 by 7. 11. Divide 27 by ††. Ans. 204. Ans. 29T |