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RULE. - Multiply each denomination of the compound number as in multiplication of simple numbers, and carry as in addition of compound numbers.
Note. — Going a second time carefully over the work is a good way of testing its accuracy. On learning Division of Compound Numbers, the pupil will find by that rule a better method of proving multiplication of compound numbers.
EXAMPLES FOR PRACTICE.
Note. - The answers to the following questions are found in the corresponding questions in Division of Compound Numbers, p. 126.
14. What cost 7 yards of cloth at 18s. 9d. per yard ?
15. If a man travel 12m. 3fur. 29rd. in one day, how far will he travel in 9 days?
16. If 1 acre produce 2 tons 13cwt. 191b. of hay, what will 8 acres produce ?
104. What is the rule? How may the work be tested ?
17. If a family consume 49gal. 3qt. 1pt. of molasses in one month, what quantity will be sufficient for one year?
18. John Smith has 12 silver spoons, each weighing 3oz. 17pwt. 14gr. ; what is the weight of all ?
19. Samuel Johnson bought 7 loads of timber, each measuring 7 tons 37ft. ; what was the whole quantity ?
20. If the moon move in her orbit 13° 11' 35" in 1 day, how far will she move in 10 days?
21. If 1 dollar will purchase 2b 83 73 19 10gr. of ipecacuanha, what quantity would 9 dollars buy ?
22. If i dollar will buy 2A. 3R. 15p. 30yd. 8ft. 100in. of wild land, what quantity may be purchased for 12 dollars?
23. Joseph Doe will cut 2 cords 97ft. of wood in 1 day; how much will he cut in 9 days ?
24. If 1 acre of land produce 3ch. 6bu. 2pk. 7qt. 1pt. of corn, what will 8 acres produce?
106. When the multiplier is a composite number, and none of its factors exceed 12. Ex. 1. What cost 24 yards of broadcloth at 2£ 7s. 11d. per
Ans. 57£ 10s. Od.
Ex. 2. What cost 360 tons of iron at 17£ 16s. 1d. per ton ?
Ans. 6409£ 103. Od.
price of 1 ton. 360 is equal to 6 X 6 X
10. We therefore multiply
the price of 1 ton by 6, and price of 6 tons.
obtain the price of 6 tons,
which multiplied by 6 gives price of 36 tons. that by 10 gives the price
the price of 36 tons, and
of 360 tons. price of 360 tons.
Rcle. – Multiply by the factors of the composite number in succes sion.
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. 181b., 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.?
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. ?
Ans. 1452£ 16s. 8d. OPERATION.
Since 379 is not a com£ 8. d.
posite number, we cannot 3 16 8 = cost of lcwt. resolve it into factors; but 10
may separate it into
parts ; thus, 379 = 300 + 38 6 8 cost of 10cwt.
70+ 9. In the operation 10
we first multiply by 10, and
then by 10, to get the cost 3 83 6 8 cost of 100cwt.
of 100cwt. To find the cost 3
of 300cwt., we multiply the 1150 0 0 cost of 300cwt.
cost of 100cwt. by 3; and to
find the cost of 70cwt., we 2 68 6 8 cost of 70cwt.
multiply the cost of 10cwt. 34 10 cost of 9cwt.
by 7; and then, to find the 14 5 2 1 6 8 cost of 379cwt. cost of 9cwt., we multiply the
cost of lcwt. by 9. Adding the several products, we obtain 1452£ 16s. 8d. for the answer.
RULE. Having resolved the multiplier into any convenient parts, as of units, tens, etc., multiply by these several parts, adding together the products thus obtained for the required result.
106. What is the rule for multiplying hy a composite number? Reason for the rule? - 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 nuinber?
EXAMPLES FOR PRACTICE.
2. If 1 dollar will buy 17lb. 10oz. 13dr. of beef, how much may be bought for 62 dollars ?
3. What cost 97 tons of lead at 2£ 17s. 9 d. 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
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. lqr. 121b. 10oz.
108. Division of Compound Numbers is the process of dividing a compound number into any proposed number of equal parts.
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£ 53. 8d. 2far.
Having divided the 128£ by 9, we find
the quotient to be 14£ and 2£ remaining. 9) 128 11
We place the 14£ under the 128£, and 14 5 8 2
reduce 2£ to shillings, making 40s., and adding the 11s. in the dividend, we have
51s We next divide the 51s. by 9, and write the quotient 58. under the 11s., and to the remainder 6s., equal to 72d., add the 4d., making 76d. The 76d. we divide by 9, and write the quotient 8d. under the 4d., and to the remainder 4d., equal to
108. What is division of compound numbers ? — 109. Where do you begin to divide ? Why? When there is a remainder after dividing any one do nomination, what must be done with it?
16far., we add the 2far., making 18far. The 18far. we divide by 9, and obtain 2far. for a quotient, which we place under the 2far. in the dividend; and thus find the answer to be 11£ 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 dividle as before.
Proof. — The same as in simple numbers.
Note. — When the divisor and dividend are denominate numbers, and one or both are compound, reduce them to the same denomination, and then proceed as with simple numbers. 2. 3.
Ib. 6)11 2 14 4 2 6)113 2 5 12 7) 103 11 0 9 18 15 8 3
18 3 17 10 14 15 3 1 2
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. lfur. 21rd., how far will he travel in 1 day ?
16. If 8 acres produce 21T. 5cwt. 2qr. 21b. of hay, what will 1 acre produce ?
109. What is the rule for division of compound numbers ?