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In this question, we find the quantity 24 equal to the product of 4 and 6, we therefore multiply the price first by 4, and then that product by 6, and the last product is the answer. Or we

might have multiplied first by 6 and then by 4, and the answer would have been the same.

26. What cost 360 tons of iron at £17. 16s. 1d. per

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In this question, we find the factors of 360 to be 6 and 6 and 10, that is, 6 multiplied by 6 are 36, and 36 multiplied by 10 make 360. We then first multiply by 6, and then that product by 6, and then again the last product by 10. The result wolud have been the same, if we had multiplied by 10 first.

27. If a man travel 3m. 7fur. 18rds. in one day, how far would he travel in 30 days?

28. If a load of hay weigh 2 tons 7cwt. 3qrs. 18lb., what would be the weight of 84 similar loads ?

29. When it requires 7yds. 3qr. 2na. of silk to make a lady's dress, what quantity would be sufficient to make 72 similar dresses ?

30. A tailor has an order from the navy agent to make 132 garments for seamen ; how much cloth will it take, supposing each garment to require 3yds. 2qr. Ina. ?

III. When the quantity is more than 12, and the number is such, that it cannot be resolved into two or more factors, the better method is to find the factors of a number nearest the given number, and having multiplied the compound number by one of these factors, and the product by the other factor, then find the value of the remaining quantity and add it to the last product.

31. If 1 dollar will buy 17lbs. 10oz. 13dr. of beef, how much may be bought for 62 dollars?

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This we resolve

As 62 is not the product of any two numbers in the multiplication table, we take some convenithan 62, viz. 60. into two factors 5

12 8 12 35 5 10 and 12, and having found the amount 14 6 of 60 dollars, we then find the quantity 2 dollars will buy, and add this amount to the former, and the sum is the quantity 62 dollars will buy.

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32. What cost 97 tons of lead at £2. 17s. 9 d. per ton? 33. If a man travel 17m. 3fur. 19r. 3yd. 2ft. 7in. in one day, how far would he travel in 38 days?

34. If 1 acre will produce 27bu. 3pk. 6qt. 1pt. of corn, what will 98 acres produce?

35. If it require 7yd. 3qr. 2na. to make 1 cloak, what quantity would it require to make 48 cloaks ?

36. One ton of iron will buy 13A. 3R. 14p. 18yd. 7ft. 76in. of land; how many acres will 19 tons buy?

Section 17.

COMPOUND DIVISION.

MENTAL OPERATIONS.

1. If 2 yards of cloth cost 3s., what will 1 yard cost? 2. If 3 barrels of apples cost 5s., what cost 1 barrel? 3. If 4hhds. of lime cost 15s., what cost 1hhd. ? 4. Divide 9s. equally among 9 boys. 5. Divide 10d. equally among 3 girls. 6. What is a fourth part of 5 gallons; 7. What is a seventh part of 7 gallons? 8. What is a sixth part of 9 gallons?

FOR THE SLATE.

1. If 9 acres of land cost £128. 11s. 8d. 2qr., what is

the value of 1 acre?

Ans. £14. 5s. 8d. 2qr.

£.

OPERATION.

8. d.

qr.

2

2

Having divided the pounds by 9, we find the quotient to be £ 14, which we write under

9) 128 11 4 14 5 8 £ 128, and to the £2. remaining (40s.) we add the 11s. in question, and their amount is 51s.; and these 51s. we again divide by 9, and the quotient is 5s., which we write under the 11s. in the question; and to the remainder, 6s., which are 72d., we add the 4d. in the question, and the sum is 76d.; having again divided these by 9, we write the quotient, 8, under the 4d. in the question; and to the remainder, 4d., which is 16qr., we add the 2qr. in the question, and the amount is 18qr., which we again divide by 9, and find the quotient to be 2qr., which we write under the 2qr. in the question. Thus we find our answer to the question to be £14. 5s. 8d. 2qr. Hence the following

RULE.

I. Divide the highest denomination by the quantity; and if any thing remains, reduce it to the next lower denomination, and continue to divide until it is reduced to the lowest denomination.

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NOTE. The answers to the following questions are found in the corresponding numbers in Compound Multiplication.

14. What cost 1 yard of cloth, when 7yd. can be bought for £6. 11s. 3d. ?

15. If a man, in 9 days, travel 112m. 1fur. 21rd., how far will he travel in 1 day?

16. If 8 acres produce 21T. 5cwt. 1qr. 12lb. of hay, what will 1 acre produce?

-+17. If a family consume in 1 year 598gal. 2qt. of molasses, how much may be necessary for 1 month?

18. John Smith has 12 silver spoons, weighing 3lb. 10oz. 11dwt.; what is the weight of each spoon?

19. Samuel Johnson bought 7 loads of timber, measuring 55T. 19ft.; what was the quantity in each load? 20. If the moon, in 10 days, move in her orbit 4S. 11°. 55'. 50"., how far does she move in 1 day?

21. If $9 will buy 24lb. 83. 33. 19. 10gr. of ipecacuanha, how large a quantity will $1 purchase?

22. When $12 will buy 34A. OR. 32p. 8yd. 5ft. 48in. of wild land; how much will $1 buy?

23. Joseph Doe will cut 24 cords 105 feet of wood in 9 days; how much will he cut in 1 day?

24. When 8 acres of land produce 25Ch. 17bu. 3pk. 4qt. of grain; what will 1 acre produce?

When the quantity is a composite number, that is, one which is composed of the product of two or more numbers, we proceed as in the following question.

25. When 24 yards of broadcloth are sold for £57. 10s. Od., what is the price of 1 yard? Ans. £2. 7s. 11d.

£.

8.

d.

0

6)57 10

4)9 11

8

£2 7 1 1

In this question, we find the component parts, or factors, of 24 are 6 and 4; that is, 6 multiplied by 4 produces 24. We therefore first divide the price by one of these numbers, and then divide the quotient by the other. From the above process we deduce the following

RULE.

II. 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.

When the quantity is such, that it cannot be resolved

into two or more factors, the question must be performed by Long Division, as in the following question.

OPERATION.

26. If 23cwt. of iron cost £171. 1s. 3d. what cost 1cwt. ? Ans. £7. 8s. 9d. In this question we first divide 23) 171 1 3(£7. the pounds by 23, and obtain 7 for

£. 8. d.

161

10
20

23) 201(8s. 184

17

12

23) 207 (9d. 207

the quotient, and £10 remaining, we reduce to shillings and annex the 1s. and again divide by 23 and obtain 8s. for the quotient. The remainder, 17s., we reduce to pence and annex the 3d. and again divide by 23, and obtain 9d. for the quotient. Thus we find the answer to be £7. 8s. 9d.

So in similar cases we should divide the highest denomination by the quantity, and if any thing remains, reduce it to the next lower denomination and continue to divide until it is reduced to the lowest denomination.

27. If a man travel 117m. 7fur. 20rd. in 30 days, how far will he travel in 1 day?

28. If 84 loads of hay weigh 201 Tons 4cwt. 2qr. Olb., what will 1 load weigh?

29. When 72 ladies require 567yd. Oqr. Ona. for their dresses, how many yards will be necessary for 1 lady? 30. When 132 sailors require 470yd. 1qr. of cloth to make their garments, how many yards will be necessary for 1 sailor?

31. If $62 will buy 1095lb. 14oz. 6dr. of beef, how much may be obtained for $1?

32. Paid £280. 5s. 94d. for 97 tons of lead; what did it cost per ton?

33. If a man travel 662m. 4fur. 28rd. 3yd. 2ft. 2in. in 38 days, how far will he travel in 1 day?

34. When 98 acres produce 2739bu. 1pk. 5qt. of grain, what will 1 acre produce?

35. A tailor made 48 garments from 378 yards of cloth; what quantity would it take to make 1 garment?

36. When 19 tons of iron will purchase 262A. 3R. 37p. 25yd. 1ft. 40in. of land, how much may be obtained for 1 ton?

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