Multiply by the factors of the composite number in succes

EXAMPLES FOR PRACTICE.

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

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

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

6. 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 3yd. 2qr. Ina. ?·

ART. 107. When the multiplier is not a composite number, and exceeds 12, or, if a composite number, and any of its factors exceed 12.

Ex. 1. What cost 379cwt. of iron at 3£. 16s. 8d. per cwt.?

383 6

8

1150 0 268 6 34 10

3 hundreds.
O cost of 300cwt.
8 cost of 70cwt.
O cost of 9cwt.

Ans. 1452£. 16s. 8d.

Since 379 is not a composite number, we cannot resolve it into factors; but we may separate it into parts, and find the value of each part separately; thus, 379=300+70

9. In the operation, we first multiply by 10, and then this product by 10, to get the cost of 100cwt. To find the cost of 300cwt., we multiply the last product by 3; and to find the cost of 70cwt., we multiply the cost of 10cwt. by 7; and then, to find the cost of 9cwt., we multiply the cost of lewt. by 9. Adding the several products, we obtain 1452£. 16s. 8d. for the answer.

1452 16 8 cost of 379cwt.

RULE. Having resolved the multiplier into any convenient parts, as of units, tens, &c., multiply by these several parts, adding together the products thus obtained for the required result.

QUESTIONS. Art. 106. What is the rule for multiplying by a composite number? Give the reason for the rule. Art. 107. How do you find the cost of 300cwt. in the example? Of 70cwt.? Of 9cwt.? What is the rule when the multiplier is large, and is not a composite number?

EXAMPLES FOR PRACTICE.

2. If 1 dollar will buy 171b. 10oz. 13dr. of beef, how much may be bought for 62 dollars?

3. What cost 97 tons of lead at 2£. 17s. 94d. per ton?

4. If a man travel 17m. 3fur. 19rd. 3yd. 2ft. 7in. in one day, how far would he travel in 38 days?

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

6. If it require 7yd. 3qr. 2na. to make 1 cloak, what quantity would it require to make 347 cloaks?

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

8. If 1 ton of copper ore will purchase 17T. 14cwt. 3qr. 18lb 14oz. of iron ore, how much can be purchased for 451 tons?

Ans. 8003T. 17cwt. 1qr. 12lb. 10oz.

§ XV. DIVISION OF COMPOUND NUMBERS.

ART. 108. DIVISION of Compound Numbers is the process of dividing compound numbers into any proposed number of parts.

ART. 109. To divide when the divisor does not exceed 12. Ex. 1. If 9 acres of land cost 128£. 11s. 4d. 2far., what is the value of 1 acre? Ans. 14£. 5s. 8d. 2far.

£.

OPERATION.

8. d. far.

9)128 11 4 2

14 5 8 2

Having divided the 128£. by 9, we find the quotient to be 14£. and 2£. remaining. We place the quotient 14£. under the 128£., and to the remainder 2£., equal to 40s., we add the 11s. in the question, and divide the amount, 51s., by 9. We write the quotient 5s. under the 11s., and to the remainder 6s., equal to 72d., we add the 4d., making 76d., which we divide by 9, and write the quotient 8d. under the 4d. To the remainder 4d., equal to 16far., we add

QUESTIONS.

Art. 108. What is division of compound numbers? - Art. 109. Where do you begin to divide? Why? When there is a remainder after dividing any one denomination, what must be done with it?

the 2far., and divide the amount, 18far., by 9, and obtain 2far. for a quotient, which we place under the 2far. in the dividend. Thus we find the answer to be 14£. 5s. 8d. 2far.

RULE. — Divide as in division of simple numbers, each denomination in its order, beginning with the highest.

If there be a remainder, reduce it to the next lower denomination, adding in the number already of this denomination, if any, and divide as before.

PROOF. - The same as in simple numbers.

NOTE. When the divisor and dividend are both compound numbers, they must be reduced to the same denomination, and the division then is that of simple numbers.

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

14. What costs 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. 2qr. 2lb. of hay, what will 1 acre produce?

QUESTION. What is the rule for division of compound numbers?

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

18. John Smith has 12 silver spoons, weighing 3lb. 10oz. 11pwt.; 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 24

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?

ART. 110. When the divisor is a composite number, and none of its factors exceed 12.

RULE.-Divide by the factors of the composite number in succession.

EXAMPLES FOR PRACTICE.

2. If 360 tons of iron cost 6409£. 10s. Od., what is the cost of 1 ton?

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

4. If 84 loads of hay weigh 201 tons 6cwt. Oqr. 12lb., what will 1 load weigh?

5. When 72 ladies require 567yd. Oqr. Ona. for their dresses, how many yards will be necessary for one lady?

QUESTIONS. Art. 110. How does it appear that dividing by 6 in Ex. 1 gives the price of 4 yards? How do you divide by a composite number?

6. When 132 sailors require 470yd. 1qr. of cloth to make their garments, how many yards will be necessary for 1 sailor?

ART. 111. When the divisor is not a composite number, and exceeds 12, or, if a composite number, and any of its factors exceed 12, the whole operation can be written down, as in the following example:

Ex. 1. If 23cwt. of iron cost 171£. 1s. 3d., what cost 1cwt.? Ans. 7£. 8s. 9d.

We divide the pounds by 23, and obtain 7 for the quotient, and 10£. remaining, which we reduce to shillings, and add the 1s., and again divide by 23, and obtain 8s. for the quotient. The remainder, 178., we reduce to pence, and add the 3d., and again divide by 23, and obtain 9d. for the quotient. Thus, the method of operation is the same as by the general rule (Art. 109), excepting more of the work is written down; and, by uniting the several quotients, we find the answer to be 7£. 8s. 9d.

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

3. Paid 280£. 5s. 91d. for 97 tons of lead; what did it cost per ton?

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

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

6. A tailor made 347 garments from 2732yd. 2qr. 2na. of cloth; what quantity did it take to make 1 garment?

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

8. If 451 tons of copper ore will purchase 8003T. 17cwt. 1qr. 12lb. 10oz. of iron ore, how much will 1 ton purchase?

Ans. 17T. 14cwt. 3qr. 18lb. 14oz.

QUESTION. Art. 111. When the divisor is large, and not a composite num ber, how is the division performed?