SECTION XV. COMPOUND DIVISION. COMPOUND DIVISION is when the dividend consists of several denominations. EXAMPLES. 1. Divide 598£. 8s. 9d. equally among 5 persons. £. 8. d. 5)598 8 9 119 13 9 Having divided the pounds by 5, we find 3£. remaining, which are 60s.; to these we add the 8s. in the question, and again divide by 5 and find 3s. remaining, which are 36d. to these we add the 9d. in the question, and divide their sum by 5. The several quotients we write under their respective denominations. 2. Divide 168£. 15s. Od. equally among 36 men. )168 15 144 24 20 36)495(13s. 36 135 108 27 12 36)324(9d. d. (4£. When the divisor is more than 12, we usually perform the operation by Long Division. In the present example, we first divide the pounds by 36, and obtain 4£. for the quotient and 24£. remaining, which we reduce to shillings and annex the 15s., and again divide by 36, and obtain 13s. for the quotient. The remainder we reduce to pence, and again divide, and obtain 9d. for the quotient. 324 From the above examples and illustrations we deduce the following RULE. Divide the highest denomination of the dividend by the divisor, and, if there be a remainder, reduce it to the next lower denomination, adding to the number thus found the number in the dividend of the same denomination. Divide the result thus obtained by the divisor; and, if there be a remainder, proceed as before, till all the denominations of the dividend are taken, or till the work is finished. The successive quotients will be of the same denominations with the successive numbers divided, or will correspond with the several denominations of the dividend. NOTE. When the operation is performed by Short Division, the several quotients must be placed under their respective denominations. 2. When 10£. 13s. Od. are paid for 9 barrels of flour, what is the cost of one barrel ? 3. If 7bbls. of flour cost 10£. Os. 44d., what cost one barrel ? 4. Paid 3£. 2s. 4d. for 8lbs. of Cayenne pepper; what was the cost of one pound? 5. Divide 54yd. 2qr. 3na. equally among 5 persons. 6. Divide 29cwt. 3qr. 161b. equally among 9 persons. 7. If 5 pair of oxen in one year consume 37 tons 17cwt. Oqr. 16lb. of hay, what quantity would be sufficient for one pair? 8. If one man could perform a piece of labor in 76 days 11h. 53m., how long would it take 10 men to perform the same labor? 9. Divide 151£. 19s. 114d. by 9. 10. Divide 350£. 17s. 32d. by 519. 11. Divide 225£. 1s. 104d. by 63. 12. Divide 159 £. 4s. 9d. by 12. 13. Divide 75£. 6s. 6d. by 4. 14. Divide 111£. 8s. 11d. by 7. 15. Divide 159£. 4s. 9d. by 12. Ans. 16£. 17s. 91d. Ans. 13s. 6d. Ans. 3£. 11s. 5d. Ans. 13£. 5s. 4 d. Ans. 18£. 16s. 74d. 16. Divide 158lb. 9oz. 1dwt. 21gr. by 9. 17. Divide 111lb. 11oz. 17dwt. 9gr. by 7. 18. Divide 183 tons lcwt. 2qr. 11lb. 4oz. by 11. 19. Divide 105 tons 7cwt. Oqr. 6lb. 8oz. by 8. 20. Divide 19 93 43, 29 9gr. by 8. 21. Divide 335yd. 2qr. Ona. 0 in. by 7. 22. Divide 215m. 7fur. 1rd. 14ft. 6in. by 12. 23. Divide 149deg. 8m. Ofur. Ord. lyd. 1ft. 6in. by 9. 24. Divide 97deg. 55m. 7fur. 35rd. 4ft. 2in. 1bar. by 6. 25. Divide 181A. 3R. 11p. 6yd. 4ft. 41in. by 11. 26. Divide 31 cords 83ft. 1332in. by 4. 27. Divide 209hhd. 55gal. 3qt. Opt. 1gi. by 7. 28. Divide 35 tuns 3hhd. 4gal. 2qt. by 9. 29. Divide 56hhd. 45gal. by 8. 30. Divide 118bu. 1pk. 5qt. by 6. 31. Divide 255ch. 24bu. 3pk. 1qt. by 7. 32. Divide 110y. 343d. 3h. 41m. 12sec. by 8. 33. A man divides his farm of 214A. 3R. 12p. equally among his 9 sons; how much does each receive? 34. If one man perform a certain piece of labor in 3da. 16h. 54m., how long would it take 12 men to perform the same work? 35. A farmer has 29 bushels of rye, which he wishes to put into 8 bags; how much must each bag contain ? CASE II. When the divisor is a composite number, proceed as in the following EXAMPLE. 36. If 42 yards of cloth cost 14£. 3s. 6d., what is the value of 1 yard? Ans. 6s. 9d. £. 8. d. 7)14 3 6 6)2 0 6 0 6 9 In this question, we find the component parts of 42 are 6 and 7; we therefore first divide the price by 7, and then divide the quotient by 6. From the above, we deduce the following RULE. Divide the dividend by one of the component parts, and the quotient thence arising by the other, and the last quotient will be the answer. NOTE. To find the true remainder; multiply the last remainder by the first divisor, and to the product add the first remainder. 37. If 16 yards of velvet cost 2£. 18s. 8d., what will 1 yard cost? 38. If 72 yards of broadcloth cost 71£. 14s. Od., what is the value of 1 yard? 39. If 84 yards of cotton cost 8£. 1s. Od., what will 1 yard cost? 40. If 90 hogsheads of sugar weigh 56T. 13cwt. 3qr. 10lb., what is the weight of 1 hogshead ? 41. What will be the price of 1 sheep, if 18 cost 5£. 4s. 3d. ? 42. If 21 yards of cloth cost 10£. 8s. 3d., what is the price of 1 yard? 43. What is the value of 1 hat, when 22 cost 12£. 13s. Od. ? 44. When 96 shares of a certain stock are valued at 1290£. 4s. Od., what would be the cost of 1 share? 45. If 120 spoons weigh 32lb. 9oz. 15dwt., what does 1 weigh? 46. If a man in 1 month travel 746m. 5fur. Ord., how far does he go in 1 day? 47. If the earth revolve 15° on its axis in 1 hour, how far does it revolve in 1 minute ? 48. Divide 1275A. 2R. 16p. 22yd. 8ft. 32in. equally among 32 men. 49. If a man walk round the earth in 2y. 68d. 19h. 54m., how long would it take him to walk 1 degree, allowing 365 days to a year ? The following questions are to be performed as the second example of this section. 50. If 53 tons of iron cost 1001£. 9s. 7d., what is the value of 1 ton? 51. If 57 gallons of wine cost 23£. 11s. 51d., what cost 1 gallon? 52. Divide 3419A. 2R. 23p. by 29. 53. If 89 pieces of cloth contain 3375yds. 3qr. Ina. Oțin., how much does 1 piece contain? 54. If 59 casks contain 44hhd. 52gal. 2qt. 1pt. of wine, what are the contents of 1 cask? 55. If a man travel in 1 year (365 days) 6357m. 5fur. 14rd. 11 ft., how far is that per day? 56. When 175gal. 2qt. of beer are drunk in 52 weeks, how much is consumed in 1 week? 57. When 17 sticks of timber measure 15T. 38ft. 1074in., how many feet does 1 contain? 58. Divide 132 cords 2ft. by 17. 59. Divide 89hhd. 52gal. 3qt. 1pt. by 39. 60. Divide 179bu. 3pk. 5qt. Opt. 1gi. by 53. Ans. 2£. 1s. 3 d. 61. Divide 275ch. 19bu. 2pk. equally among 17 men. Ans. 4T. 15cwt. 2qr. 122 lb. 66. Divide 916m. 3fur. 30rd. 10ft. 6in. by 47. Ans. 19m. 3fur. 39rd. 13ft. 22 in. 67. Divide 718A. 3R. 37p. by 29. Ans. 9A. 1R. 19p. 1398ft. 69. Divide 144A. 3R. 18p. 3yd. 1ft. 36in. by 11. Ans. 13A. OR. 27p. 3yd. Oft. 45in. 70. Divide 6718£. 19s. 11d. by 47. Ans. 142£. 19s. 13 d. 71. Divide 1237£. 17s. 4d. by 86. Ans. 14€. 7s. 1044d. 72. Purchased 18T. 17cwt. 3qr. 20lb. of copperas, at 4 cents per pound. I sold 4T. 6cwt. 1qr. 14lb. at 5 cents per pound, and 7T. lcwt. 3qr. 10lb. at 6 cents per pound. Moses Atwood purchased one fourth of the remainder at 6 cents per pound. One half of what then remained I sold to J. Gale at 10 cents per pound. The remaining quantity I sold to J. Smith at 12 cents per pound; but he has become a bankrupt, and I lose half my debt. What have I gained by my purchase? Ans. $1001.34. QUESTIONS TO BE PERFORMED BY ANALYSIS. 1. If 7 pair of shoes cost $8.75, what will one pair cost? what will 20 pairs cost? Ans. $25.00. 2. If 5 tons of hay cost $85, what will 1 ton cost? what will 17 tons cost? Ans. $289.00. 3. When $0.75 are paid for 3gal. of molasses, what is the value of 1gal.? What cost 37gal. ? Ans. $9.25. 4. Gave $1.92 for 4lbs. of tea; what cost 1lb. ? what cost 37lbs. ? Ans. $17.76. 5. For 12lbs. of rice I paid $ 1.08; what was paid for 1lb.; and what must I give for 25lbs. ? 6. Gave S. Smith $ 63.00 for 9 tubs of butter; what was the cost of 1 tub? What cost 27 tubs ? Ans. $189.00. Ans. $2.25. 7. T. Swan can walk 20 miles in 5 hours; how far can he walk in 1 hour? How long would it take him to walk from Bradford to Boston, the distance being in a straight line 28 miles? Ans. 7 hours. 8. If a hungry boy would eat 49 crackers in 1 week, how many would he eat in 1 day? how many would be sufficient to last him 19 days? Ans. 133 crackers. 9. Gave $20 for 5 barrels of flour; what cost 1 barrel? what cost 40 barrels ? 10. For 3lbs. of lard there were paid 36 cents; what was the cost of 37lbs. ? Ans. $160.00. Ans. $4.44. how many cents charged for 37 Ans. $2.96. what cost 1lb.? Ans. 11. Paid F. Johnson 72 cents for 9 nutmegs; were paid for 1 nutmeg; and what should be nutmegs ? 12. Paid 2€. 17s. 5d. for 52lbs. of sugar; what cost 76lbs. ? 13. Paid 4£. 3s. 11d. for 76 pounds of sugar; what cost 52lbs. ? Ans. Ans. 14. If 52lbs. of sugar cost 2£. 17s. 5d., how many pounds can be purchased for 4£. 3s. 11d. ? 15. When 4£. 3s. 11d. are paid for 76lbs. of sugar, how many pounds can be obtained for 2£. 17s. 5d. ? Ans. |