(b.) Perform the following examples : 2. 239 · 43? 12. 3817 • 617 7 3. 627 • 81 ? 13. 1358 • 421 ? 4. 518 • 647 14. 3157 · 835? 5. 697 • 79 ? 15. 3773 = 937 ? 6. 416 • 68 ? 16. 6179 · 875 ? 7. 213 · 47 ? 17. 3579 • 498 ? 8. 438 ; 75 ? 18. 3163 • 369 ? 9. 216 = 45 ? 19. 43796 · 8236 ? 10. 715 • 92? 20. 25794 · 7167 ? 11. 317 • 53 ? 21. 36854 – 5947 ? 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. NOTE. - 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. 225 171 tens = 1710 units, to which adding the 6 units 1. 2375 · 52 ? 2. 3796 • 43? 3. 4986 · 72 ? 4. 5389 · 91 ? 5. 2456 • 33? 6. 4795 · 49? 7. 1396 · 37 ? 8. 4258 • 46 ? 9. 2397 • 68? 10. 675.4 • 83? 11. 3586 • 412? 12. 38.47 • 212? 13. 5978 · 613? 14. 2974 – 391 ? 15. .6137 : 196 ? 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 6327 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. 994 In tho written work opposite, we have carried out the quotient to 4 places of decimal fractions, .3560 thus obtaining 763.4527 for the quotient, and 3479 .0081 for the remainder, or 763.4527,81 for the .0081 complete quotient. 57. Examples and Practical Problems. 16. 87943 • 45? 17. .62379 · 83? 18. 25978 · 127 ? 19. 36594 • 41 ? 20. 63974 • 25 ? 21. 39547 · 62? 22. 542.96 • 83? 23. 47698 • 45 ? 24. 63897 328? 25. 1.59468 • 1274 ? 26. 294875 • 3079 ? 27. 205879 • 4983 ? 28. 62574 • 99 ? 29. 37.9856 • 5387 ? 30. 6257.94 · 8215 ? 31. lIow 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.? 39. 623458 grains equal how many lb. oz. dwt. and gr. ? 40. 3517965 sq. in. equal how many sq. yd. sq. ft. and sq. in. ? 41. 527943 cu. in. equal how many cu. ft. and cu. in.? 42. 379421 farthings equal how many £ s. d. and far. ? 43. How many straw hats, at $.97 each, can be bought for $53.68? (See 53, note after 6lst 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 ? 49. If 17 pounds of Young Hyson tea cost $10.20, how much will 83 pounds cost ? 50. I bought 38 cows at $22 each, and sold one of them for $35 and another for $43. For how many dollars each must I sell the rest, to gain $196 by the transaction ? SECTION XI. 58. COMPOUND DIVISION. (a.) COMPOUND Division is the division of Compound Numbers. (b.) It is performed in accordance with the principles illustrated in Simple Division. Note. - All questions in Compound Division are included in the second part of the definition of Division in 52, A. 1. What is ! of £53 178. ? £ d. far. But £5 5 times 20s. 100s., to which adding the 8)53 17 0 0 178. gives 1178. of 117s. 14s., with 5s. remain 6 14 7 2 ing. But 58. 5 times 12d. 60d., and } of 60d. 7d., with 4d. remaining. But 4d. 16 far., and $ of 16 far. 2 far. Hence, of £53 178. £6 14s. 7d. 2 far. 2. What is f of 34 rd. 4 yd. 2 ft. 8 in.? Solution.- of 34 rd. 3 rd., with 7 rd. remain rd. yd. ft. in. ing. But 7 rd. = 7 times 54 yd. *38ļ yd. 38 9)34 4 8 gd. 1 ft. 6 in., to which adding the 4 yd. 2 ft. 8 in. 3 4 gives 42 yd. 3 ft. 14 in. $ of 42 yd. 4 yd., with 6 yd. remaining. But 6 yd. 6 times 3 ft. 18 ft., to which adding the 3 ft. gives 21 ft. f of 21 ft. 2 ft., with 3 ft. remaining. But 3 ft. = 36 in., to which adding the 14 in. gives 50 in. f of 50 in. 5 in., with 5 in. remainder, or 5.5 in. Hence, 5 of 34 rd. 4 yd. 2 ft. 8 in. 3 rd. 4 yd. 2 ft. 55 in. * For 7 times 5 yd. = 35 yd., and 7 times ļ yd. = 1 yd. = 34 yd., which, added to 35 yd., gives 384 yd. 2 2 55 8. What is } of £16 17s. 5d. 1 far. ? 4. What is $ of 14 T. 5 cwt. 2 qr. 20 lb. 6 oz. 11 dr. ? 5. What is of 51 T. 3 gr. 9 oz. ? 6. What is $ of 64 lb. 11 oz. 15 dwt. 21 gr. ? 7. What is $ of 5 lb 83 53 29 17 gr. ? 8. What is it of 437 bu. 3 pk. 5 qt. 1 pt.? 9. What is 1 of 63 bu. 1 pk. 1 pt. ? 10. What is ķ of 33 gal. 2 qt. 1 pt. 3 gi. ? 11. What is £ of 94 yd. 3 qr. 3 pa. ? 12. What is } of 83 yd. 1 qr. 3 na.? 13. What is 4 of 33 rd. 1 yd. 2 ft. 2 in. ? 14. What is t'of 49 rd. 5 yd. 2 ft. 11 in. ? 15. What is } of 17 A. 1 R. 28 rd.? 16. What is thy of 17 sq. rd. 8 sq. yd. 137 sq. in. ? 17. What is as of 49 C. 3 cd. ft. 15 cu. ft. 813 cu. in. ? 18. What is į of 213 C. 5 cd. ft. 13 cu. ft. 1315 cu. in. ? 19. What is It of 75 wk. 3 da. 27 min. 18 sec. ? 20. What is $ of £48 11d.? 21. What is of £87 138. 5 d. 2 far. ? 22. What is of 1 T. 1 cwt. 1 qr. 1 lb. ? 23. What is 1 of 27 T. ? 24. What is t'y of 121b 73? 25. What is zb of 38 m. 7 fur. 20 rd. 1 in. ? 26. What is t'a of 8 m.? 27. What is I of 1 C. 4 cd. ft. ? What is 4 of 48 rd. 3 yd. 7 in. ? 29. What is t of 11 A. 1 R. 29 sq. rd. 11 sq. in. ? 30. What is of 39 m. ? |