46. It is 24899 miles around the world; how long would it take a man to make the trip traveling at the average daily rate of 39 miles? 47. The president of the United States receives $50000 annual salary; how much is that per day, counting 365 days in the year? 48. An army contractor paid $39865 for 2345 barrels of beef; how much did the beef cost him per barrel? 49. How many kettles, each weighing 348 pounds can be made from 20000 pounds of iron? 50. The earth moves around the sun at the rate of about 68000 miles per hour; what is its rate per minute? 51. How many bales will 281765 pounds of cotton make, allowing 517 pounds to the bale? 52. The Bible contains 31173 verses; how many must be read each day, that the book may be read through in a year of 365 days? 53. The annual cost of keeping a plank road in repair is $9264.92, at the rate of $28.42 per mile; how many miles long is the road? 54. If a pipe discharges 67 gallons in a minute, in what time will it empty a vat of 5484888 gallons? 55. How many hours will it take a person to count $212,492,745 at the rate of $1035 per hour. SPECIAL METHODS OF DIVISION. 84. PRINCIPLE.-Multiplying or dividing both dividend and divisor by the same integer, does not change the quotient. See Art. 124. 85. To divide by a divisor which can be separated into factors. 56. Divide 315 by 35. Explanation.-The factors of 35 are 5 and 7. I divide the dividend by one of the factors of the divisor, then divide the quotient by the other factor. Operation. 5 315 7163 9 Ans. Analysis: Dividing both dividend and divisor by the same number does not change the quotient. Hence, 315 35 = 5315 35 63 ÷ 7 = 9. = (61) Divide 893 by 30, using the factors 2, 3 and 5. Explanation.-Dividing by 2, I obtain 446 twos and 1 remainder; dividing 446 twos by 3, I have 148 sixes and 2 twos, or 4, remainder; again dividing 148 sixes by 5, I have 29 thirties and 3 sixes, or 18, remainder; hence, 18+4+1, or 23, is the true remainder. Operation. 21893 31446 1 18 5 148, 2 twos = 4 RULE. Find the product of each remainder by all the divisors preceding the one that produced it, and the sum of the products, with the first remainder, if any, will be the true remainder. 62. 4642 63 - ? 64. 3971 ÷ 108 = ? 63. 6573 ÷ 32 86. To divide by 10, 100, 1000, etc. (66) Divide 576 by 10. Explanation.-I cut off as many figures from the right of the dividend as there are Operation. 57,6 Os in the divisor, for the remainder (6); the remaining figures form the quotient (57). Analysis: 576 5 hunds. 7 tens 6 ones. ten 5 hunds. 7 tens 6 ones. 5 tens 7, and 6 ones remainder. 87. To divide by any multiple of 10, 100, 1000, etc. (71) Divide 3943 by 40. Explanation.-I cut off the ciphers at the right of the divisor, and as many figures from the right of the dividend. I then Operation. 4,0 394,3 98 quo. 23 rem. divide the remaining part of the dividend (394) by the remaining part of the divisor (4), and annex to the remainder (2) the figures cut off (3), and thus obtain the true remainder (23). Divide: Now dividing by 4 (Art. 85), we get 98 quo. 23 rem. 72. 576 by 80. 74. 63242 by 3500. 73. 71831 by 6400. 75. 893741 by 17000. 76. If 40 barrels of molasses cost $480, what is the price of 1 barrel? 77. A farmer sold 600 acres of land for $7800; how much was that per acre? 78. A merchant sold 800 yards of silk for 184,000 cents; how much was that per yard? 88. To divide by a divisor, which, by a simple multiplication, can be changed into a number with Os on the right. (79) Divide 1341 by 225. Explanation.I multiply both dividend and divisor by 4, which does not change the quotient; I then divide the new dividend (5364) by the new divisor (900), by Art. 87, and obtain 5 quo. and 864 rem. Operation. 225 1341 9,00 53,64 5, 864 rem. 216 true rem. The remainder being a part of the dividend has been made too large by the multiplication by 4, hence I divide it by the multiplier (4), to get the true remainder (216). NOTE.-Multiplying a divisor, which ends; With 5, by 2, will give one 0 on the right; With 25 or 75, by 4, will give two Os on the right. With 125, 375, 625 or 875, by 8, will give three Os on the right. A divisor, whose last significant figure is an even number, may be multiplied by 5 90. At 75 cents each, how many books can I buy for $14.25? 91. A lady bought a sewing machine for $36, and paid for it in monthly payments of $2.25 each. In how many months did she pay the debt? 92. A sugar planter packed 31500 pounds of sugar in hogsheads, putting 1125 pounds in each. How many hogsheads did he fill? 93. If the directors of a railroad company appropriate $402875 for the purchase of passenger cars, at $2750 each, how many cars can be bought with the appropriation? QUESTIONS. The quotient? What is division? The dividend? The divisor? Sign of division? Give the general rule. How is division proved? How do you divide when the divisor can be separated into factors? When the divisor is 10, 100, etc.? When the divisor has Os on the right? Mention the different ways of indicating division? What relation does division sustain to multiplication? the indicated operations may be performed in any order whatever, provided that any two of the numbers be added when their signs are alike (both or both —), subtracted when their signs are unlike (one + and the other —), and the sign of the greater, in each case, prefixed to the result. In this case, where no sign is written, + is understood. 1o. +24 6 = +18, 12 = + 6, 3 = +3, +18 2o. +18 - 3 = + 15, — 12 = : + 3, — 6 : = 3, +24 21; +42 = +21 = 21. = 4 = (8 + 9) +21 21. = 21. 21 (6+4). A parenthesis, preceded by the sign -, may be removed by changing the signs (+ to and to +) of all the terms within it. Conis placed before a parenthesis, the signs of all the (12-4)+(16-10-3)-(17-12-13 + 2). 90. To combine numbers connected by the signs X and ÷. The signs and ÷ also indicate opposite operations. Hence, wher several numbers are connected by these signs, as 24 ÷ 6 ÷ 12 ÷ 3 × 18, |