46. A farm, consisting of 127 acres, was sold at auction for $37.565 an acre: what sum of money did it bring? 47. A drover bought 127 head of beef cattle, at an average of 39 dollars per head; he sold 86 of them for 43 dollars per head for how much per head must he sell the remainder, to clear on the first cost 1246 dollars? : 48. What will 75 firkins of butter cost, each firkin weighing 56 pounds, at 16 cents a pound? 49. A bond was given April 20th, 1850, and was paid Sept. 4th, 1856: what will be the product, if the time which elapsed from the date of the bond to the time it was paid be multiplied by 45? 50. What distance will a wheel, 16 feet 8 inches in circumference, measure on the ground, if rolled over 84 times? 51. What is the difference between twice eight and fifty, and twice fifty-eight? 52. How much wood in 4 piles, each containing 5 cords, 6 cord feet, and 32 cubic feet? 53. A man bought 56 acres of land for $25 an acre, and 94 acres for $32 an acre; if he sells the whole at $30 an acre, will he gain or lose, and how much? 54. If 12 men can build a wall in 16 days, how many men will build a wall nine times as long in half the time? 55. A farmer sold 4 cows for $25.50 each; 12 sheep for $2.12 each; and 3 calves for $7.25 each: what was the amount of the sale? 56. If it requires 116 tons of iron to construct one mile of railroad, how much would it require to construct a railroad from Albany to Buffalo, it being 326 miles ? 57. A merchant bought 960 lb. of cheese, at 9 cts. a pound; 148 lb. of butter, at 12 cts. a pound. He gave in payment, 12 yd. of cloth, at $4.75 a yard; 186 lb. of sugar, at 7 cts. a pound, and the remainder in cash: how much cash did he pay? 58. How much brandy will supply an army of 25,000 men for one month, if each man requires 1 gal. 2 qt. 1 pt. 2 gi.? 59. It is estimated that the French, during the years 1854 and 1855, transported to the Crimea 80000 horses, and that 70000 of them were lost in the same time. Supposing the firs cost of each horse to be $100, and the cost of transportation $95 per head, what was the value of the horses lost? 60. A man purchased a piece of woodland containing 27 acres, at 39 dollars per acre; each acre produced on an average 70 cords of wood, which, being sold, yielded a net profit of 45 cents a cord: how much did the profit on the wood fall short of paying for the land? 48 pounds of sugar, at 9 cents a pound, 6 hhds. of molasses, each containing 63 gallons, at 8 casks of rice, 285 lb. each, at 5 cts. a pound, Received payment, GEO. BLISS & Co. 68 Gideon Jones, HARTFORD, November 21, 1856. Bought of Jacob Thrifty. 78 chests of tea, at $55.65 per chest, . 251 bags of coffee, 100 lb. each, at 124 cts. per lb. 317 boxes of raisins, at $2.75 per box, 1049 barrels of shad, at $7.50 per bbl. 76 barrels of oil, 32 gal. each, at $1.08 per gal. DIVISION. 65. DIVISION is the operation of finding how many times one number is contained in another; or, of dividing a number into qual parts. 66. THE DIVIDEND is the number to be divided. It is 67. THE DIVISOR is the number by which we divide. the standard which measures the dividend; or, it shows into how many equal parts the dividend is to be divided. 68. THE QUOTIENT is the result of division. It shows how many times the divisor is contained in the dividend, or the value of one of the equal parts of the dividend. 69. THE REMAINDER is what is left after the operation. When it is 0, the quotient is a whole number, and the division is exact. Numbers in Division. 70. There are always three numbers in every division, and sometimes four: First, the dividend; second, the divisor; third, the quotient; fourth, the remainder. There are three methods of denoting division; they are the following: 12 12 ÷ 3 expresses that 12 is to be divided by 3 3) 12 When the last method is used, if the divisor does not exceed 12, we draw a line beneath the dividend, and set the quotient under it. If the divisor exceeds 12, we draw a curved line on the right of the dividend, and set the quotient at the right. Kinds of Division. 71. SHORT DIVISION is the operation of dividing when the work is performed mentally, and the results only written down It is limited to the cases in which the divisors do not exceed 12. 72 LONG DIVISION is the operation of dividing when all the work is expressed. It is used when the divisor exceeds 12. 73. Operations and Rule. 1. Divide 456 by 4. ANALYSIS.-The number 456 is made up of 4 hundreds, 5 tens, and 6 units, each of which is to be divided by 4. Dividing 4 hundreds by 4, we have the quotient, 1 hundred: 5 tens divided by 4, gives 1 ten, and 1 ten over: reducing this to units, and adding in the 6, we have 16 units, which contains 4, 4 times: hence, the quotient is 114: that is, the dividend contains the divisor 114 times. 2. Divide £11 8s. 7d. 3far. by 5. OPERATION. 4) 45 114 ANALYSIS.—Dividing £11 by 5, the quotient is £2, and £1 remaining. Reducing this to shillings, and adding in the 8, we have 28s., which, divided by 5, gives 5s., and 3s. over. This being reduced to pence, and 7d. added, gives 43d. Dividing by 5, we have 8d., and 3d. remainder. Reducing 3d. to farthings, adding 3 farthings, and again dividing by 5, gives the last quotient figure, 3far. Hence, £2 5s. 8d. 3far., is one of the five equal parts of the dividend. 3. Divide 11772 by 327. OPERATION. £ B. d. far. 5) 11 8 7 3 2 5 8 3 OPERATION. 327) 11772 (36 981 1962 1962 ANALYSIS.-Having set down the divisor on the left of the dividend, it is seen that 327 is not contained in the first three figures on the left, which are 117 hundreds. But by observing that 3 is contained in 11, 3 times, and something over, we conclude that the divisor is contained at least 3 times in the first four figures, 1177 tens, which is a partial dividend. Set down the quotient figure 3, and multiply the divisor by it: we thus get 981 tens, which being less than 1177, the quotient figure is not too great: we subtract the 981 tens from the first four figures of the dividend, and find a remainder 196 tens, which being less than the divisor, the quotient figure is not too small. Reduce this remainder to units, and add in the 2, and we have 1962. As 3 is contained in 19, 6 times, we conclude that the divisor is contained in 1962 as many as 6 times. Setting down 6 in the quotient, and multiplying the divisor by it, we find the product to be 1962. Hence, the entire quotient is 36, or the divisor is contained 36 times in the dividend, and 36 is also one of the 327 equal parts of the dividend |