38. What number is that from which if of of itself be subtracted, the remainder will be 25? Ans. 50. 39. A father bequeathed to his eldest son $12000, which was of his estate; what was the value of his estate? Ans. $20000. 40. A, B, and C owned a section of land (640 acres); A owned of it, which was of what B owned, and C the remainder; how many acres did each own? Ans. A owned 256 A., B 288 A., and C 96 A. 41. The part of a pole above the water was of the part under the water; what part of the pole was above the water and what part under the water? 42. Find the sum, difference, and product of § and ; also the quotient, making the larger fraction the divisor? Ans. Sum 1, diff., prod. 4, and quo. . 43. What number must be divided by duce 4 times 61? of 36 to pro Ans. 183. 44. What is the least common multiple of 7 and 9 ? Ans. 435. Ans. 2. 45. What is the greatest common divisor of 242 and 273? 46. A farmer has three separate parcels of land which he wishes to divide into lots of equal size and as large as possible; the first parcel has 5 acres, the 2d 4 acres, and the 3d 2 acres. What will be the size of each lot? Ans. acre. 47. A can mow 3 acres of grass in 4 days, and B can mow 4 acres of grass in 5 days; how long will it take both to mow 12 acres? Ans. 7 days. 48. A and B together can perform a piece of work in 9 days; A alone can do it in 15 days? How long would it take B to do it? Ans. 224 days. 49. A and B can do a piece of work in 5 days, A and C in 6 days, and B and C in 8 days; in what time will each one alone do it? Ans. A in 8 days, B in 121 days, and C in 21 days. 50. A merchant bought goods at less than cost, and sold them at first cost; what part of the money he paid was his profit? Ans. 51. A and B bought 1000 acres of land, of which A is to have 11 acres as often as B 9 acres; how much does each get? Ans. A 550 acres, B 450 acres. 52. A merchant sold of his stock for what the whole cost; what was the rate of profit? Ans. 1. 53. A, B, and C engage in business; A puts in $9, to B $8 and C $7; what is each one's part of the stock? Ans. A, B, C. 54. The profits of a firm this year is $4875%, which is one-fourth more than last year; what were they last year? Ans. $3900. 55. If of a cord of wood cost $5, what will be the cost of 255 cords? Ans. $155. 56. If 25 cords of wood cost $155, what will of a cord cost?. 57. Reduce × 1 × 11 × 1÷÷ 4 × 14 × 13×18 to a simple fraction. Ans. $4. Ans. . 60. What is the value of 8 x 12 x 16 x 18 x 24÷ 4 x 6 x 32 × 9 × 48? Ans. 2. 61. The difference between and of & number is 21; what is the number? 62. is of what number? Ans. 90. Ans. 1. 63. If a pole 6 ft. long cast a shadow 9 ft., what is the height of a tree that casts a shadow 90% ft.? Ans. 60% ft. Ans. 30. 64. What is the least common multiple of 1,,, and ? 65. What is the greatest common divisor of, I, I, and ? Ans. 4. 66. A and B bought goods for $1200; A paid as much as B; what did each pay? Ans. A $450, B $750. 67. Divide $12000 among 4 persons; the first to have $as often as the second $, the third $1, and the fourth $; what part does each get? 1, 1, 1, 1 = 18, 88, 15, 18; 30+20 + 15 + 12 = 77. The first to have, the second 44, the third 4, and the fourth 44. 68. A, B, and C traded together. A put in $61 as often as B $83 and C $91; the amount of their stock was $2890; what was each one's share? Ans. A $750, B $1000, C $1140. 69. The sum of two fractions is, their difference is * 1. In Addition and Subtraction, how do you place the figures as regards the orders? Ans. Like orders must be placed in the same column; that is, directly under each other. 2. Does the relation of the orders in decimals correspond to that of abstract numbers? Ans. The relation of any two orders in the same direction is the same. 3. How much greater is the value of the same figure in each consecutive column or order going to the left? Ans. Ten times. 4. Do the names of the orders taken in the same direction correspond? Ans. No, but in opposite directions. 5. From what order, going in opposite directions, do the names of the other orders correspond? Ans. From the order of units, going to the left in the Integral numbers, and to the right in the decimals. 6. What are Decimal Fractions? Ans. Fractions whose denominators are 10, 100, 1000, etc. 7. Express the decimal fraction in the common form; thus,,, etc., and decimally, .1, .01, etc.; and these expressions are respectively of the same value. 8. Which do you generally use? Why? Ans. The common fraction. Because it is more easily understood than the decimal, and is so convenient for cancellation. |