LONG DIVISION. 84. 1. Divide 3653 by 24. SOLUTION.-24 is not contained in 3 thousands, so we change 3 thousands to hundreds, and add to it 6 hundreds, making 36 hundreds. 24 is contained in 36 hundreds, 1 hundred times. We 15224 write the quotient 1 hundred over the hundreds of the 24)3653 24 125 120 53 48 This gives a dividend, and multiply the divisor by it. 24 is contained in 125 tens, 5 tens times. We write the quotient, 5 tens over the tens of the dividend and multiply the divisor by it. This gives a product of 120 tens, which we place under the 125 tens and subtract. The remainder is 5 tens, to which we unite the 3 units, making 53 units. 5 24 is contained in 53 units, 2 units times. We write the quotient 2 units over the units of the dividend, and multiply the divisor by it. This gives a product of 48 units, which we write under the 53 units and subtract. The remainder is 5, which we write over the divisor as part of the quotient. Hence the quotient is 1524. We prove by multiplying the divisor, 24, by the quotient, 152, and adding the remainder to the product. The sum is the dividend, which proves the work to be correct. 85. Rule.- Write the divisor at the left of the dividend, with a curved line between. Find how many times the divisor is contained in the fewest figures on the left of the dividend, and write the result over the right-hand figure of this partial dividend, as the first quotient figure. Multiply the divisor by this quotient figure, subtract the product from the partial dividend, and to the remainder unite the next figure of the dividend, for the second partial dividend. Proceed as before until all the figures of the dividend have been united to the remainder. If any partial dividend does not contain the divisor, place a naught in the quotient, bring down the next figure of the dividend, and proceed as before. If there is a remainder after dividing the last partial dividend, write it over the divisor at the right of the quotient. PROOF. Find the product of the divisor and quotient, add the remainder, if any, and if the sum equals the dividend, the work will be right. 39. If a carriage costs $74, how many such carriages can De purchased for $62826? 40. What number multiplied by 351 will give a product of 347,692 ? 41. In a dollar there are 1000 mills. How many dollars in 968,000 mills? 42. There are 8 quarts in a peck. How many pecks are there in 1032 quarts? 43. How many bushels are there in 24064 quarts, there being 32 quarts in a bushel? 44. How many barrels in 8232 pounds of flour, there being 196 pounds in a barrel? 45. If 165 acres of land yield 5280 bushels of wheat, what is the average yield for an acre? 46. If a railway train travels at the rate of 54 miles an hour, how many hours will it require to travel 1944 miles? 47. The product of two numbers is 72924, and one of the numbers is 354. What is the other number? 48. A man, dying, left property to the amount of $425000, of which he gave $28350 for a public library, three times as much to charitable institutions, and the remainder he divided equally among 100 persons. How many dollars did each person receive? 49. I bought 27 tons of coal for $148.50. What was the price of a ton? 50. A landlord has provisions sufficient to last 1 person 391 days. How long would they last 17 persons? 51. What is the value of a single share of bank stock if 500 shares are worth $ 63500 ? 52. There are 1728 cubic inches in one cubic foot. How many cubic feet are there in 93312 cubic inches? 53. Which is cheaper, and how much per yard, thirteen yards of cloth for $48.75, or 65 yards for $211.25? 54. A drover sold 135 head of cattle at $38 a head, and with the proceeds bought horses at $114 a head. How many horses did he buy? 55. At what rate per hour should a railway train run in order to travel 1944 miles in 36 hours? 56. If I save out of my salary $432 each year, in how many years can I save enough to buy a home for $6480 ? 57. The dividend is 287609, the quotient 904, and the remainder 137. What is the divisor? 58. A farmer has fodder enough to last 1 cow 224 days. How many days will the same fodder last 9 cows and 28 sheep, if 4 sheep eat as much as 1 cow? 59. If it costs $9687.50 a year to board 62 persons, how much will it cost to board 1 person for the same time? 60. A grocer buys 520 barrels of flour at $5.25 a barrel. If 100 barrels become damaged and worthless, for how much a barrel must he sell the remainder in order to get back the cost? 61. A merchant buys 324 yards of cloth at $2.25 a yard. For how much per yard must he sell it in order to gain $165.24? 62. Which costs the more per bushel, 228 bushels of wheat for $207.48 or 12 bushels for $10.80 ? 63. The product of three numbers is 43200. them are 32 and 50. What is the third ? Two of INDICATED OPERATIONS. 86. The Parenthesis, ( ), indicates that all the numbers contained therein are to be taken together. 87. Brackets, [], Braces, {}, and the Vinculum, have the same use as the parenthesis. These are called Signs of Aggregation. 88. When the parenthesis is not used, operations indicated by or must be performed first. Thus, 1. 12 ÷ 4 × 2 + 36 ÷ 4 − 2 x 4 = ? SOLUTION. NOTE. 12 ÷ 4 x 2 = 6. 36-49. 2 x 4 = 8. 2. 4+3x2 =? 3. (43) x 2 = ? 4. 4×3+2= ? 69-87. Ans. 5. 4 × (3+2)=? 6. 842 = ? 7. (8+4)÷ 2 =? When one of the signs of aggregation includes another, the operations indicated within the one included should be performed first, and the sign removed. 89. Find the value of: 90. 5. 11+43 + 6 × 4. 6. 34x6÷(15+9 ÷ 3). 7. 1641625010+ 16 x 3. 8. 17+ 3 × 4 × 6+3 ÷ 3 + 3. 9. [39+82 +7] × 6. 10. [6+15 × 3-6 +16÷8+4]÷8+5. If I divide the dividend by twice the divisor, or 12, the quotient will be how many times smaller? 24 ÷ (2 × 6) = ? If I divide twice the dividend, or 48, by the divisor, the quotient will be how many times as great? (2 × 24) ÷ 6 = ? |