79. A farm consisting of 127 acres, was sold at auction for $37,565 an acre: what sum of money did it bring? 80. 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? 81. What will 75 firkins of butter cost, each firkin weighing 56 pounds, at 16 cents a pound? 82. A merchant bought a box of goods containing 37 pieces, each piece containing 46 yards, worth 7 dollars a yard: what did the box of goods cost? 83. 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? 84. What distance will a wheel 16 feet 8 inches in circumference measure on the ground, if rolled over 84 times? 85. What is the difference between twice eight and fifty, and twice fifty-eight? 86. How much wood in 4 piles, each containing 5 cords, 6 cord feet and 32 cubic feet? 87. 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? 88. If 12 men can build a wall in 16 days, how many men will be required to build a wall nine times as long in half the time? 89. A farmer sold 4 cows for $25,50 each; 12 sheep for $2,121 each; and 3 calves for $7,25 each; what was the amount of the sale? 90. 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? 91. A merchant bought 960 pounds of cheese at 9 cents a pound; 148 pounds of butter at 12 cents a pound. He gave in payment, 12 yards of cloth, at $4,75 a yard; 186 pounds of sugar at 7 cents a pound, and the remainder in cash: how much cash did he pay? 92. If a family consume 12gal. 2qt. 1pt. of ale in a week, how much will they consume in 14 weeks? 93. How much brandy will supply an army of 25,000 men for one month, if each man requires 1gal. 2qt. 1pt. 2gi. 94. 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 first cost of each horse to be $100, and the cost of transportation $95 per head, what was the value of the horses lost? 95. 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 nett profit of 45 cents a cord: how much did the profit on the wood fall short of paying for the land? 6 hogs. of molasses, each containing 63 gallons, GEO. BLISS & Co. $ 98. Gideon Jones, HARTFORD, November 21st, 1856. 78 chests of tea, at $55,65 per chest, 251 bags of coffee, 100 pounds each, at } 12 cts. per pound, 317 boxes of raisins, at $2,75 per box, 1049 barrels of shad, at $7,50 per barrel, 76 barrels of oil, 32 gallons each, at $1,08 per gal., DIVISION. 57. DIVISION is the operation of finding from two numbers a third, which multiplied by the first, will produce the second. The first number, or number by which we divide, is called the divisor. The second number, or number to be divided, is called the dividend. The third number, or result, is called the quotient. The quotient shows how many times the dividend contains the divisor. When the quotient is expressed by an integral number, the division is said to be exact. When it cannot be so expressed, the part of the dividend that is undivided, is called the remainder. 58. There are always three parts in every division, and sometimes four 1st. the dividend; 2d. the divisor; 3d. the quotient; and 4th. the remainder. There are three signs used to denote division; they are the following: 123 expresses that 12 is to be divided by 3. 3 128 expresses that 12 is to be divided by 3. expresses that 12 is to be divided by 3. When the last sign 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. 59. 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. 57. What is division? What is the number to be divided called? What is the number called by which we divide? What is the answer called? What is the number called which is left? 58. How many parts are there in division? Name them. How many signs are there in division? Make and name them. 59. What is short division? How is it generally performed? Where is the quotient written? To what cases is it limited? 1. Divide 456 by 4. OPERATION. 4)456 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. ANALYSIS.-Dividing £11 by 5, the quotient is £2 and £1 remainder. 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. 3. Divide £6 8s. 8d. by 8. Here we have to pass to shillings before making the first division. OPERATION. £ S. d. far. 5)₪1 8 7 3 2 5 8 3 OPERATION, d. 16 1 4. Divide 11772 by 327. 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, 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. the 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 quo |