56. Long Division. (a.) When, in performing the division, we write only the divisor, dividend, quotient, and final remainder, the process is called Short Division; but when, in addition to these, we write the products of the divisor by the successive figures of the quotient, and also the remainder of each subtraction, the process is called LONG Division. Nore. --Short Division was illustrated in the articles from 52 to 54, and Long Division was in part illustrated in 55. (b.) Long Division differs from Short Division in these respects, viz.: First. That having obtained a quotient figure, we multiply the divisor by it, writing the product under the part of the dividend considered. Second. That we subtract this product from the part of the dividend considered, writing the remainder. Third. That we write the next figure of the dividend after the remainder, to form the next partial dividend. (c.) The essential difference, then, is that in Long Division more of the work is written than in Short Division. What is the quotient of 31536 • 497 ? Solution. — 497 is so near 500, that we make 5 the 497)31536(63 trial divisor. Since 5 is contained 6 times in 31, wo 2982 make 6 the first figure of the quotient, and infer that 1716 497 is contained 6 tens times in 3153 tens. Multiply1491 ing 497 by 6 tens gives 2982 tens, which, subtracted from 3153 tens, leaves 171 tens. 171 tens = 1710 units, to which adding the 6 units 225 gives 1716 units to be next divided. Since 5 is contained 3 times in 17, we make 3 the next figure of the quotient, and infer that 497 is contained 3 units times in 1491 units. Multiplying 497 by 3 units gives 1491 units, which, subtracted from 1716 units leaves 225 units. This gives 63 for the quotient and 225 for the remainder, or 63225 for the complete quotient. NOTE.- If it should be desirable to carry the 497)31536.(63.4527 quotient out in decimal fractions, we should reduce 2982 the 225 units to tenths thus : 1716. 225 units = 2250 tenths to be divided. Since 1491 5 is contained 4 times in 22, we make 4 the next figure of the quotient, and infer that 497 is con 225.0 tained 4 tenths times in 2250 tenths. Multiply 1988 ing 497 by 4 tenths gives 1988 tenths, which, 26.20 subtracted from 2250 tenths, leaves 262 tenths. 24 85 262 tenths = 2260 hundredths, to be divided as 1.350 before. In the written work opposite, we have carried 994 out the quotient to 4 places of decimal fractions, .3560 thus obtaining 763.4527 for the quotient, and 3479 .0081 for the remainder, or 763.452728.1, for the 0081 complete quotient. 31. IIow many months will it take a man who earns $97 per month, to earn $2425 ? 32. A drover received $1363 for cattle, at $29 per head. How many cattle did he sell? 33. How many suits of clothes, at $32 each, can be bought for $1024? 34. If one acre will produce 19 bushels of wheat, how many acres will produce 1294 bushels ? 35. A person bought 1224 yards of cloth, in pieces each containing 34 yards. How many pieces did he buy? 36. In how many hours will a cistern, capable of containing 32571 gallons, be filled through a pipe which discharges 185 gallons per hour ? 37. How many barrels, each containing 196 pounds, can be filled from 23741 pounds of flour? 38. 937467 drams equal how many T. cwt. gr. lb. oz. and dr.? 43. How many straw hats, at $.97 each, can be bought for.. $53.68? (See 53, note after 61st problem.) 44. If one passenger can be carried on a railroad for $1.41, how many can be carried for $31.02? 45. A man paid $28.625 for eggs, at $.125 per dozen. How many dozen did he buy? 46. How much will one horse cost if 14 horses cost $2534, the horses being of equal value ? 47. A flour dealer exchanged 358 barrels of flour, worth $6.37 per bbl., for flour worth $7.83 per bbl. How many barrels did he receive? 48. I sold my house for $2846, receiving in payment a lot of land containing 37 acres, and $1378 in cash. How much ought the land to be worth per acre ? |