The National Arithmetic, on the Inductive System

SECTION IX.

COMPOUND MULTIPLICATION.

CASE I.

per

1. If 1 quire of paper cost 8d., what will 2 quires cost? 3? 4? 2. If 1 bushel of corn cost 4s. 6d., what will 2 bushels cost? 3. What is the width of 2 boards, each of which is ift. 6in. wide: 4. What is the width of 3 boards ? 4 boards ? 5? 6? 7 ? 3?

5. If a man drink 2qt. 1pt. of water a day, how much will he drink in 2 days? In 3? În 4? In 5 ? In 6? In 7? In 8 ?

6. If 1 spoon weigh 2oz. 10dwt. what will 2 spoons weigh?

7. If a man walk 3m. 4fur. in an hour, how far will he walk in 2 hours? In 3? In 4? In 5 ? In 6? In 7 ? In 8? In 9 ? 8. What will 6 bales of cloth cost, at 7£. 12s. 7d. bale ?

In this question, we multiply 7d. by 6 and find £. 7 12 7

the product to be 42d. This we divide by 12, the 6

number of pence in a shilling, and find it contains

3s., and 6d. remaining, which we write under the 45 15 6 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

d.

RULE.

When the quantity is less than 12, multiply the price by the quantity, and carry as in Compound Addition.

Note.

- For the answers in Multiplication, see Section 10, in Division.

9. Multiply 18£. 16s. 7 d. by 4.

Ans. 75£. 6s. 6d. 10. Multiply 15£. 11s. 8 d. by 8. Ans. 124£. 13s. 10d. 11. Multiply 27£. 19s. 11 d. by 9. Ans. 251£. 19s. 7}d. 12. Multiply 19£. 5s. 74d. by 11. Ans. 212£. 1s. 7 d. 13. Multiply 81£. 14s. 9d. by 8.

Ans. 653£. 18s. Od. 14. Multiply 15£. 18s. 5d. by 7.

Ans. 111£. 8s. 11d. 15. Multiply 13£. 5s. 44d. by 12. Ans. 159£. 4s. 9d. 16. Multiply 171b. 7oz. 13dwt. 13gr. by 9. 17. Multiply 15lb. 11oz. 19dwt. 15gr. by 7. 18. Multiply 16T. 12cwt. Sqr. 131b. 12oz. by 11. 19. Multiply 13T. 3cwt. lqr. 141b. 13oz. by 8. 20. Multiply 21b. 53.53.17. 161gr. by 8.

21. Multiply 47yds. 3qr. Qna. 2in. by 7.
22. Multiply 17m. 7fur. 36rds. 13ft. 7in. by 12.
23. Multiply 16deg. 39m. 3fur. 39rds. Syds. 2ft. by 9.
24. Multiply 16deg. 20m. 7fur. 12rds. 8ft. 11in. libar. 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. Sgi. by 7.
28. Multiply 3Tun. Shhd. 56gal. 2qt. by 9.
29. Multiply 7hhd. 5gal. 2qt. 1 pt. by 8.
30 Multiply 19bu. 2pk. 7qt. 1 pt. by 6.
31. Multiply 36chald. 18bu. 3pk. 7qt. by 7.
32. Multiply 13y. 316da. 15h. 27m. 39sec. by 8.

33. If a man gives each of his 9 sons 23A. BR. 194p. what do they all receive ?

34. If 12 men perform a piece of labor in 7h. 24m. 30s. how long would it take 1 man to perform the same task ?

35. If 1 bag contain Sbu. 2pk. 4qt. what quantity does 8 bags contain ?

CASE II.

When the quantity 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.

d.

36. What will 42 yards of cloth cost at 6s. 9d. a yard ? £. S.

In this example, we find that 6 0 6 9

multiplied by 7 will produce the 6

quantity 42 yards. We therefore 2 0 6=price of 6 yds. multiply 6s. 9d. first by the 6, and 7

then its product by 7; and the last

product, 14£. 3s. 6d. is the answer 14 3 6 price of 42 yds. or price of the 42 yards.

The pupil will now see the propriety of the following

RULE.

Multiply the price by one of the factors of the composite number and the product 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. 9fd. a piece ?
42. What cost 21 yards of cloth at 95. 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. 91d. 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. SR. 17p. 30yd. 8ft. 100in. by 32.

49. If a man be 2da. 5h. 17m. 19sec. in walking 1 degree, how long would it take him to walk round the earth, allowing 3654 days to a year?

CASE III.

When the quantity required is such a number, as cannot be produced by the product of two or more numbers, we should proceed as in the following.

EXAMPLE.

s.

50. What is the value of 53 tons of iron at 13£. 175. 11d. a ton? £. d.

£.

d. 18 17 11

18 17 11 5

3 94 9 7= price of 5 tons. 56 13 9=price of 3 tons.

10 944 15 10=price of 50 tons.

Because 53 is a prime 56 13 9=price of 3 tons.

number, that is, it cannot

be produced by the product 1001 9 7=price of 53 tons. 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.

, as will be nearest the given quantity, and then find the value of the remainder by Case I., and the two products will be the

answer.

51. What will 57 gallons of wine cost at 8s. 31d. 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 S7yd. Sqr. 2na. 2in. ; what was the whole quantity ?

54. Bought 59 casks of wine, each containing 47gal. 3qt. 1 pt. ; what was the whole quantity ?

55. If a man travel 17m. Šfur. 13rd. 14ft. in one day, how far will he travel in a year?

56. If a man drink 3gal. 1qt. 1 pt. 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. lispt. by 39. 60. Multiply Sbu. 1pk. 4qt. 1pt. Odgi. by 53. 61. Multiply 16chal. 7bu. 1pk. Sqt. 01 pt. by 17.

336

BILLS.