72. Division is indicated not only by the sign÷, given in Art. 70, but also by the colon, thus, 8:2; also, by writing the divisor before the dividend, with a curved line between them, thus, 2) 8; also, by writing the divisor under the dividend, with a line between them, thus, §; each of which expressions means that 8 is to be divided by 2. 73. The last mode of indicating division, sometimes called the fractional sign, gives the following compact 7=1 16 186 =7 | 21 8 24 =832=8 8 40 9 27 = 9 36 945 31 18 = =22 182 28 =222=2 23 243 273 246 3,0 = 7 287 7 35 || || || || 36 6 689 7 4.2 7 8 || || || || 23 6 co 497 567 7 63 872 8 888 3=9729 81 72. Second sign of Division, what is it? Third mode of indicating Division, what is it? Fourth method, what? 73. How are the dividend and divisor written in the second Division Table? 18 7|1=7 8 88 19 9 289 £f=9 4089 789 Ans. 4. 32, or 328? Ex. 31. How many are 24, or 246? 32. 33. 34. 35. 28, or 287? How many are 42, or 426? 42, or 497 ? WRITTEN EXERCISES. 74. To perform Short Division. Ex. 1. If 7 days make a week, how many weeks are there then imagine the remainder, 1, placed before the 4, and say, 7 in 14, 2 times; set the 2 under the 4, and thus we find the quotient to be, 52. 75. This process, called Short Division, usually employed when the divisor is small, may be performed by the following RULE. Having set the divisor at the left of the dividend with a line between them, divide the fewest figures in the left of the dividend that will contain the divisor, and set the quotient under the right hand figure taken in the dividend; if anything remains, prefix it MENTALLY to the next figure in the dividend, and divide the number thus formed as before, and so proceed till all the figures of the dividend have been employed. 75. When is Short Division usually employed? Rule? How are divisor and dividend written? Which figures of the dividend are used first? How many? Quotient, where set? Remainder, to what is it prefixed? How? What is done with the number so formed? How far is the process carried? By 8. 76. When there is no remainder, as in the first nine examples, the division is complete. The dividend is then said to be divisible by the divisor, and the divisor is called an exact divisor. When there is a remainder, as in Ex. 10, the division is incomplete, and the dividend is said to be indivisible by the divisor. 10. Divide 325 by 7. Ans. 463. NOTE 1. The remainder is often written over the divisor in the fractional form (Art. 73), and the fraction is annexed to the quotient; thus, the answer in Ex. 10 is written 46% which, expressed in words, is forty-six and three-sevenths. Other fractions are read in a similar manner; thus, means one-half; thirds; five-ninths; etc. one-third; two NOTE 2. The remainder, when written in a fractional form as a part of the quotient, becomes like the quotient. 11. Divide 6276 by 5. 12. Divide 8765 by 5. 13. Divide 4823 by 8. Ans. 1255, and 1 remainder. 76. When is the division complete? When is one number divisible by another? What is an exact divisor? When is one number indivisible by another? How is the remainder often written? The fraction where placed? 24. How many pounds of sugar, at 9 cents per pound, can be bought for $35.64? Ans. 396. 25. How many barrels of flour, at $8 a barrel, can be bought for $5368 ? 26. If 6 shillings make a dollar, how many dollars are there in 7416 shillings? Ans. 1236. 27. If 4 weeks make a month, how many months are there in 3716 weeks? 28. How many oranges, at 6 cents apiece, can you buy for $35.64? Ans. 594. 29. If 7328 marbles are divided equally among 8 boys, how many marbles will cach boy receive? 31. Ans. 916. 30. If an estate, worth $16,492 dollars, is divided equally among 7 children, how many dollars does each child receive? Divide two thousand one hundred and forty-two by six. 32. A mile is equal to 5280 feet; how many steps of 3 fect each will a man take in walking a mile? 77. To perform Long Division : 33. Divide 4654 by 13. OPERATION. 13) 4 6 5 4 (3 58 39 75 6 5 Ans. 358. Having set the divisor and dividend as in Short Division, draw a curve at the right of the dividend, and then say, 13 in 46, 3 times, and set the 3 at the right of the dividend. Then multiply the divisor by the quotient, 3, and set the product, 39, under the 46 of the dividend, and subtract the 39 from the 46. To the remainder, 7, annex 5, the next figure of the dividend, so forming a new partial dividend, 75, and then say, 13 in 75, 5 times, and set the 5 as the next figure of the quoticnt. Multiply the divisor by 104 0 77. Explain Ex. 33. Of what order is any quotient figure? Illustrate. |