SECTION XIV. COMPOUND MULTIPLICATION. CASE I. COMPOUND MULTIPLICATION consists in multiplying numbers of different denominations by simple numbers. £. 8. d. 7 12 7 6 45 15 6 1. What will 6 bales of cloth cost, at 7£. 12s. 7d. per bale ? In this question, we multiply 7d. by 6, and find the product to be 42d. This we divide by 12, the number of pence in a shilling, and find it contains 3s. and 6d. We write the 6d. under the pence, and carry 3 to the product of 6 times 12, and find the amount to be 75s., which we reduce to pounds by dividing them by 20, and find them to be 3£. 15s. We write down the shillings under the shillings, and carry 3 to the product of 6 times 7£.; and we thus find the answer to be 45£. 15s. 6d. From the above illustration we deduce the following RULE. When the multiplier is less than 12, multiply by the multiplier and carry as in Compound Addition. NOTE. For the answers in Multiplication, see Section XV., in Division. 2. What cost 9yds. of cloth, at 1£. 3. What cost 7bbls. of flour, at 1£. 3s. 8d. per yard? Ans. 10£. 13s. Od. 8s. 71d. per barrel ? 4. What cost 8lbs. of Cayenne pepper, at 7s. 94d. per lb. ? 5. Multiply 10yd. 3qr. 3na. by 5. 6. Multiply 3cwt. 1qr. 8lb. by 9. 7. Multiply 7T. 11cwt. 1qr. 20lb. by 5. 8. Multiply 7 days 15h. 35m. 18sec. by 10. 9. Multiply 18. 16s. 71⁄2d. by 4. 10. Multiply 15. 11s. 8 d. by 8. 11. Multiply 27£. 19s. 11 d. by 9. 12. Multiply 19£. 5s. 74d. by 11. 13. Multiply 81£. 14s. 9d. by 8. 14. Multiply 15£. 18s. 5d. by 7. 15. Multiply 13£. 5s. 4 d. by 12. 16. Multiply 17lb. 7oz. 13dwt. 13gr. by 9. 17. Multiply 15lb. 11oz. 19dwt. 15gr. by 7. Ans. 75£. 6s. 6d. Ans. 124£. 13s. 10d. Ans. 251£. 19s. 7±d. Ans. 212£. Is. 7 d. Ans. 653£. 18s. Od. Ans. 111£. 8s. 11d. Ans. 159£. 4s. 9d. 18. Multiply 16T. 12cwt. 3qr. 13lb. 12oz. by 11. 22. Multiply 17m. 7fur. 36rd. 13ft. 7in. by 12. 23. Multiply 16deg. 39m. 3fur. 39rd. 5yd. 2ft. by 9. 24. Multiply 16deg. 20m. 7fur. 12rd. 8ft. 11in. 11bar. by 6. 25. Multiply 16A. 2R. 4p. 19yd. 7ft. 79in. by 11. 26. Multiply 7 cords 116ft. 1629in. by 4. 27. Multiply 29hhd. 61gal. 3qt. 1pt. 3gi. by 7. 33. If a man gives each of his 9 sons 23A. 3R. 19p., what do they all receive? 34. If 12 men perform a piece of labor in 7h. 24m. 30sec., how long would it take 1 man to perform the same task? 35. If 1 bag contain 3bu. 2pk. 4qt., what quantity do 8 bags contain ? CASE II. When the multiplier is more than 12, and is a composite number, that is, a number which is the product of two or more numbers, the question is performed as in the following EXAMPLE. 36. What will 42 yards of cloth cost, at 6s. 9d. a yard ? £. 8. d. 0 6 9 2 0 6 price of 6 yds. 7 14 3 6=price of 42 yds. In this example, we find that 6 multiplied by 7 will produce the quantity 42 yards. We therefore multiply 6s. 9d. first by the 6, and then its product by 7; and the last or price of the 42 yards. product, 14€. 3s. 6d. is the answer The pupil will now see the propriety of the following RULE. Multiply by one of the factors of the composite number, and the product thus obtained by the other. 37. What will 16 yards of velvet cost, at 3s. 8d. per yard? 38. What will 72 yards of broadcloth cost, at 19s. 11d. per yard ? 39. What will 84 yards of cotton cost, at 1s. 11d. per yard ? 40. Bought 90 hogsheads of sugar, each weighing 12cwt. 2qr. 11lb.; what was the weight of the whole? 41. What cost 18 sheep, at 5s. 91d. a piece? 42. What cost 21 yards of cloth, at 9s. 11d. per yard ? 43. What cost 22 hats, at 11s. 6d. each? 44. If 1 share in a certain stock be valued at 13£. 8s. 91⁄2d., what is the value of 96 shares? 45. If 1 spoon weigh 3oz. 5dwt. 15gr., what is the weight of 120 spoons? 46. If a man travel 24m. 7fur. 4rd. in 1 day, how far will he go in 1 month? 47. If the earth revolve 0° 15′ per minute, how far per hour? 48. Multiply 39A. 3R. 17p. 30yd. 8ft. 100in. by 32. 49. If a man be 2d. 5h. 17m. 19sec. in walking 1 degree, how long would it take him to walk round the earth, allowing 365 days to a year? CASE III. When the multiplier is such a number as cannot be produced by the product of two or more numbers, we should proceed as in the following EXAMPLE. 50. What is the value of 53 tons of iron, at 18£. 17s. 11d. a 944 15 10 price of 50 tons. 56 13 9= price of 3 tons. 1001 9 7= price of 53 tons. 3 price of 3 tons. Because 53 is a prime number, that is, it cannot be produced by the product of any two numbers; we therefore find a convenient composite number less than the given number, viz. 50, which may be produced by multiplying 5 by 10. Having found the price of 50 tons by the last Case, we then find the price of the 3 remaining tons by Case I., and add it to the former, making the value of the whole quantity 1001£. 9s. 7d. The pupil will hence perceive the propriety of the following RULE. Take for successive multipliers two or more numbers, whose continued product will be nearest the proper multiplier, and then find the value of the remainder by Case I., and the sum of the last two products will be the answer. 51. What will 57 gallons of wine cost, at 8s. 34d. per gallon? 52. Bought 29 lots of wild land, each containing 117A. 3R. 27p.; what were the contents of the whole ? 53. Bought 89 pieces of cloth, each containing 37yd. 3qr. 2na. 2in.; what was the whole quantity ? 54. Bought 59 casks of wine, each containing 47gal. 3qt. 1pt.; what was the whole quantity? 55. If a man travel 17m. 3fur. 13rd. 14ft. in one day, how far will he travel in a year? 56. If a man drink 3gal. 1qt. 1pt. of beer in a week, how much will he drink in 52 weeks? 57. There are 17 sticks of timber, each containing 37ft. 978in.; what is the whole quantity? 58. There are 17 piles of wood, each containing 7 cords 98 cubic feet; what is the whole quantity? 59. Multiply 2hhd. 19gal. Oqt. 1pt. by 39. 60. Multiply 3bu. 1pk. 4qt. 1pt. 1gi. by 53. 61. Multiply 16ch. 7bu. 2pk. Oqt. Opt. by 17. |