52. What is the value of and 53. 24 54. 23 34 22 9 21 33 = 3 22 9 2 62. †, f. 63., 4. 64. f, f. 65. 11, f. 66., 3. 67. f. ૐ. The above is only an expression of division, and simply means, divide 2 by 3. Such expressions are sometimes called Complex Fractions. Find the value of 7 or of ÷ 2. or of 21 38. 28? 3 63. 1, f. 69. 1, 24. 70. 48, . 71. 31, 72. 31, 21. 73. 44, 22. 3 Or, 11 3 74. 5, 21. 57. 59. If a horse eat of a bushel of oats a day, in how many days will he eat 12 bushels? 60. At $6 a bushel, how many bushels of clover seed can be bought for $403 ? 61. At of $3 a yard, how many yards of muslin can be bought for of $? 76. 21, f. 77. 241, J. 78. 28, 1. 79. 621, 36. 58. For further exercise upon fractional numbers, use the following, thus: take the first set of numbers, & and ; find, in the simplest form, their sum, difference, product, and, lastly, the quotient of the first divided by the second. In like manner, treat each set in the double columns. 32= 3 of 11 18 of 5 of 2 1% RELATION OF NUMBERS. 125. To find what fractional part one number is of another. 1. What part of 5 is 3? ANALYSIS. Since 1 is of 5, 3 is 3 times or of 5. 2. What part of 9 is 5? Of 12 is 7? Of 24 is 18? 3. Ten yards are what part of 25 yards? 8 pounds, of 20 pounds? 9 eggs, of a dozen? 10 ounces, of a pound? 4. What part of 3 is? ANALYSIS.-1 is of 3, and § of 1 is § of, or of 3; or, §÷3 = §• 5. What part of 9 is ? Of 8 is? 6. What part of 15 is 14? 7. What part of is? Of 18 is 24? ANALYSIS.-1 is of , and of 1 is of Or,=, and, and the relation of 10 to 12. 19 = 5. to 8. What part of 9. What part of Of 20 is ? Of 25 is 61? of. of, or 19 of is? Of is ? Of is ? RULE.-Divide the number denoting the part by the number denoting the whole. = 126. To find a number when a fractional part of it is given. 1. 15 is of what number? ANALYSIS.-15 is of 4 times of 15, which is 20. 2. 16 is of what number? 3. 31 is of what number? 4. 1s of what number? of what number? of what number? ANALYSIS.- is of 5 times of, which is 1. 5. 18 of what number? 6. 1 is of what number? of what number? 7. 36 is ANALYSIS. in 32, 8 times. 8. 28 is 9. 35 is 10. of how many times 4 ? 36 is g of 8 times of 36, which is 32, and 4 is contained of how many times 8? 12? of how many times of 28? # of 56 is of what number? 13. 54 is 14. 45 is ANALYSIS. of 56 is 3 times of 56, which is 21; and 21 is of 10 times of 21, which is 30. 11. of 27 is of what number? of what number? of 64 is of what number? of what number? 12. of of how many times 5? of how many times 8? 9? 16? 6? 8? 9? 12? 9? REVIEW. WRITTEN EXERCISES. 127. 1. Change 21 to a fraction having 25 for its denominator; 34 to 50ths, 75 to 18ths. 2. Reduceof,, and 14 to equivalent fractions having the least common denominator. 3. The difference between two numbers is 13, and the smaller 94; what is the greater? 4. The product of two numbers is 50%, and one of the numbers is 12; what is the other? 5. What number divided by will give a quotient of ? 6. Find the value of 3×××4 33 × ×4×8. 4 21/ 7. Reduce the fractions and $ 11 8. A farmer put of his corn in one bin, in another, and 77 bushels in a third. How much corn had he? to their simplest form. 9. If 3 pounds of sugar cost $.33, what will be the cost of 65 pounds? 10. A man owning of an iron foundry, sold of his share for $5402. What was the value of the foundry? 11. 1f of a farm is valued at $17294, what is the value of the whole? 12. A man having $150, gave $25 for a robe, and of the remainder for a harness. What part of $150 had he left? 13. Bought a horse for $275, and sold him for $160. For what part of the cost was he sold? 14. A pole stands & in the mud, in the water, and 35 feet above the water. What is the length of the pole? 15. At $ a pound, how many pounds of coffee can be bought for $61? 16. If from 18 yards of cloth 23 yards are cut, what part of the whole is taken? 17. If 48 is § of some number, what is of the same number? 18. If 7 tons of hay cost $120, how many tons can be bought for $78? 19. Gave 6 gallons of oil. 20. If worth? pounds of butter, at 36 cents a pound, for 31 What was the oil worth a gallon? of an acre of land is worth $791, what is 1 acre 21. What number taken from 2 times 124 will leave 20? 22. At $3 a yard, how many yards of silk can be bought for $10% ? 23. What is the sum, the difference, and the product of and its reciprocal ? 24. How many pounds of tea, at $3 a pound, will pay for 101 baskets of peaches, at $ a basket? 25. A can do a certain piece of work in 8 days, and B can do the same piece of work in 6 days. In what time can both together do it? 26. A horse and wagon cost $270; the horse cost 11 times as much as the wagon. What was the cost of the wagon? 27. If 7 barrels of pork cost $60, how many barrels can be bought for $156, at the same rate? 28. What is the quotient of 13 divided by its reciprocal? 29. A certain sum of money is divided among 4 persons; A has, B, C, and D has the remainder, which is $30. What is the whole sum divided? 30. How many times can a bottle, holding of of a gallon, be filled from a demijohn containing of 1 gallons? 31. If 5 be added to both terms of the fraction, will its value be increased or diminished? 32. If 5 be added to both terms of the fraction, will its value be increased or diminished? 33. If 235 acres of land cost $47253, what will 628 acres cost? 34. From 100 tons of iron were sold 40 tons at $42 a ton, and the remainder at $401. What was received for all? 35. A gentleman owning of an iron foundry, sold of his ₤ share for $25703; how much was the whole foundry worth? per head; afterward bought of the whole number at $13 $23. Did I gain or lose, and 36. Bought 320 sheep at $2 435 at $13 per head; then sold per head, and the remainder at how much? What is the value of 37. (of of 3+83))÷(103-752)? 38. ( of f÷15) × (15÷₹ of §) ? 39. (123÷11-15§ × 3) × 4 ? 40. ( of 81-3×1%)× (3÷1+5})? 41. (14 of 15) × 371 ? 42. of (24÷6§) × (95÷48) ? 43. 44. 2 of 4 64 of fr 11 9 |