6. From of an acre take of a rod. Ans. 1R. 17p. 22yd. 2ft. 108in. 7. From of a cord take of a cord. Ans. 91ft. 16021 in. 8. From of a hhd. of wine there leaked out of it; what remained? Ans. 6gal. 3qt. Opt. 17gi. 9. From Boston to Concord, N. H., the distance is 72 miles; having travelled of this distance, how much remains? Ans. 30m. 6fur. 34rd. 4ft. 8in. 14bar. 10. From of a year take § of a week. Ans. 101da. 5h. 54m. 174sec. of a foot. Ans. 1R. 18p. 5yd. 4ft. Oin. SECTION XIX. MULTIPLICATION OF VULGAR FRACTIONS. CASE I. To multiply a simple fraction by a simple fraction. 1. Multiply by §. OPERATION. This process may be understood by sup × Ans. posing a man to have found of a dollar, and that he gave of it to his wife, and that he wished to ascertain what part of a dollar his wife received. If of a dollar be divided into 5 equal parts, one of these parts will be of a dollar. And, ifofof a dollar be of a dollar, ofwill be 7 times as much, and 7 times are. If then, of be, of will be 3 times as much, and 3 times are. The wife will therefore receive of a dollar. RULE. Multiply the numerators together for a new numerator, and the denominators for a new denominator. The fraction should then be reduced to its lowest terms. 2. Multiply by . 3. Multiply by 18. 4. Multiply by Fr. 5. Multiply 6. Multiply by by 4. by 11. 7. Multiply by 18. 8. Multiply The operation of the following questions may be abridged by To multiply a whole number by a fraction, or a fraction by a whole number. 1. If a man earn of a dollar in one day, how much will he earn in 9 days? OPERATION. To analyze this question, we say, }X÷==$73 Ans. if he earn 7 eighths of a dollar in 1 much, and 9 times 7 eighths day, in 9 days he will earn 9 times as are 63 eighths = 63=$77 Ans. RULE. Multiply the whole number by the numerator of the frac tion, and divide the product by the denominator, and the quotient is the answer required. NOTE. If any of the fractions are compound, they must be reduced to simple fractions by Case VI., Sect. XVI.* 11. Multiply of 7 of by 12. Ans. 24. Ans. $91. 15. What cost of a ton of hay, at $ 17 per ton? of an acre of land, at $ 37 per acre? Ans. $1613. 16. At § of a dollar per foot, what cost 7 cords of wood? CASE III. Ans. $35. To multiply a mixed number by a whole number, or a whole number by a mixed number. 1. Multiply 7 by 9. 7 OPERATION. In performing this question, we say 9 times 5 eighths are 45 eighths, and 45 eighths are equal to 5g. We write down the and carry the 5 to the product of 9 times 7 = 68. 9 684 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. 2. Multiply 8g by 7. 9. Multiply 37 by 18. 10. Multiply 67811 by 24. 11. What will 237 pounds of lead cost, at 8 cents a pound? 12. What will 15 pound? 13. What will 29 Ans. $1.91. pounds of sugar cost, at 12 cents a Ans. $1.881. cwt. of hay cost, at $1.12 per cwt.? Ans. $32.943. 14. What will 97 yards of broadcloth cost, at $8 per yard? Ans. $79.00. 15. What will 17 tons of potash cost, at $97 per ton? Ans. $1703.561. 16. What will 3 per ton? 17. What will 17 18. What will 273 pound? 19. What will 29 dozen ? dozen of axes cost, at $11.62 per Ans. $343.75%. 20. Bought 28 bales of cotton cloth, each bale containing 31 yards; what will be the cost, at 16 cents per yard? Ans. $140.56. NOTE. If both numbers be mixed, or either of them be a complex fraction, they must first be reduced to simple ones. 21. Multiply 8 by 11%. OPERATION. 87; 11 = 4. 왕. 71 × 21 = 44211008 Ans. 22. Multiply 16111 by 1911. 23. Multiply by 8. 24. Multiply by 17. 25. Multiply by 714. 26. Multiply of 94 by 4 of 17. 27. Multiply of 7 by 1 of 87. 28. Multiply 7 by 33. 29. Multiply 8 by 7. 30. Multiply 12 by §. 31. Multiply 15 by fr 32. A merchant owns of a ship, he sells A. What part is that of the whole ship? 33. Multiply 37 by 104. 34. Multiply of 74 by 7 of 11, 35. Multiply of 9 by of 17. 36. Multiply of 83 by 4 of 94. 37. Multiply 188 by 159. Ans. 313648. 38. Multiply of by 114 71 53 590 of 81 39. What cost 7 40. What cost 9 barrels of flour, at $5 acres of land, at $273 41. What cost 83 bushels of apples, at $14 per bushel? Ans. $11. 42. Bought 117 bushels of corn, at $13 per bushel, and sold of it for $1 per bushel, and the remainder at $17 per bushel; what is gained on the sale of the corn? Ans. $33. 43. What is the continued product of the following numbers: 27 873 Ans. and 374 981 2 128 SECTION XX. DIVISION OF VULGAR FRACTIONS. CASE I. To divide a fraction by an integer or whole number. 1. How many times will contain 8? OPERATION. To illustrate this question we will supAns. pose of an orange to be divided equally among 8 persons. Now, if we divide of an orange into 8 equal parts, one of these parts will be equal to of a whole orange, but as there are to be divided among 8 persons, each person will receive 5 times Ans. RULE. Multiply the whole number by the denominator of the fraction, and write the product under the numerator. Or, divide the numerator of the fraction by the whole number, if it can be done without a remainder, and write the quotient over the denominator. To divide a whole number by a fraction. 1. How many times will 17 contain ? |