DIVISION. 64. Division is the process of finding how many times one number is contained in another of the same kind. 65. The Quotient is the result obtained, and shows how many times the divisor is contained in the dividend. MENTAL EXERCISES. 1. How many barrels of flour, at 6 dollars a barrel, can be bought for 30 dollars? ANALYSIS. Since 6 dollars will buy 1 barrel of flour, 30 dollars will buy as many barrels as 6 dollars is contained times in 30 dollars, which is 5 times. Therefore, at 6 dollars a barrel, 5 barrels of flour can be bought for 30 dollars. 2. How many oranges, at 4 cents apiece, can be bought for 28 cents? 3. How many tons of coal, at 5 dollars a ton, can be bought for 35 dollars ? 4. When lard is 7 cents. a pound, how many pounds can be bought for 49 cents? For 63 cents? For 84 cents? 5. If a man travel 48 miles in 6 hours, how far does he travel in one hour? 6. At 3 cents apiece, how many lemons can be bought for 24 cents? For 30 cents? For 36 cents? 7. If you give 55 cents to 5 beggars, how many cents do you give to each? 8. If a man builds 42 rods of wall in 7 days, how many rods can he build in 1 day? 9. At 4 dollars a cord, how many cords of wood can be bought for 20 dollars? For 28 dollars? For 32 dollars? 10. A farmer paid 33 dollars for some sheep, at 3 dollars a head; how many did he buy? 11. At 7 cents a pound, how many pounds of sugar can be bought for 63 cents? For 84 cents? 12. If a man spends 5 cents a day for cigars, how many days will 50 cents last him? 60 cents? 13. At 12 cents a pound, how many pounds of coffee can be bought for 48 cents? For 72 cents? For 96 cents? For 120 cents? PROMISCUOUS DIVISION TABLE. 6 in 36, how many times? 9 in 63, how many times? 4 in 28, how many times? 66. The Dividend is the number to be divided. 67. the Divisor is the number by which to divide. 68. The Sign of Division is a short horizontal line, with a point above and one below, ÷. It shows that the number before it is to be divided by the number after it. Thus, 20÷4-5, is read, 20 divided by 4 is equal to 5. Division is also expressed by writing the dividend above, and the divisor below, a short horizontal line; 12 Thus, 4, shows that 12 divided by 3 equals 4. CASE I. 69. When the divisor consists of but one figure. 1. How many times is 4 contained in 848? OPERATION. Divisor, 4) 848 212 ANALYSIS. After writing the divisor on the left of the dividend, with a line between them, begin at the left hand and say: 4 is contained in 8, 2 times, and as 8 in the dividend is hundreds, the 2 in the quotient must be hundreds; therefore write 2 in hundreds' place under the figure divided. 4 is contained in 4, 1 time, and since 4 denotes tens, write 1 under it in tens' place. 4 in 8, 2 times, and since 8 is units, write 2 in units' place under it, and we have 212 for the entire quotient. When the divisor is not contained in the first figure of the dividend, find how many times it is contained in the first two figures. 9. How many times is 4 contained in 2884 ? OPERATION. 4) 2884 721 ANALYSIS. As we cannot divide 2 by 4, say 4 is contained in 28, 7 times, and write the 7 in hundreds' place; then 4 is contained in 8, 2 times, which write in tens' place under the figure divided and 4 is contained in 4, 1 time, which write in units' place in the quotient, and we have the entire quotient, 721. After obtaining the first figure of the quotient, if the divisor is not contained in any figure of the dividend, place a cipher in the quotient, and prefix this figure to the next one of the dividend. OPERATION. 6) 1824 times is 6 contained in 1824 ? ANALYSIS. Beginning as in the last examples, say, 6 is contained in 18, 3 times, which write in hundreds' place in the quotient; then 6 is contained in 2 no times, and write a cipher (0) in tens' place in the quotient, and prefixing the 2 to the 4, say 6 is contained in 24, 4 times, which write in units' place, and we have 304 for the entire quotient. |