28. From a piece of cloth, containing 17yd. 3qr., there were taken two garments, the first measuring 3yd. 3qr. 2na., the second 4yd. 1qr. 3na.; how much remained?

Ans. 9yd. 1qr. 3na. 29. Venus is 3S. 18° 45′ 15′′ east of the Sun, Mars is 7S. 15° 36′ 18′′ east of Venus, and Jupiter is 5S. 21° 38′ 27′′ east of Mars; how far is Jupiter east of the Sun? Ans. 4S. 26°.

30. The longitude of a certain star is 3S. 18° 14′ 35′′, and the longitude of Jupiter is 11S. 25° 30′ 50′′; how far will Jupiter have to move in his orbit to be in the same longitude with the star? Ans. 3S. 22° 43′ 45′′.

§ XIV. MULTIPLICATION OF COMPOUND NUMBERS.

ART. 104. MULTIPLICATION of Compound Numbers is the process of taking a compound number any proposed number of

times.

ART. 105. To multiply when the multiplier is not more than 12.

Ex. 1. If an acre of land cost 14£. 5s. 8d. 2far., what will 9 acres cost? Ans. 128£. 11s. 4d. 2far.

Multiplicand 14 5
Multiplier
Product

8 2

We write the multiplier under the lowest denomination of the

multiplicand, and then say 9 9 times 2far. are 18far., equal to 4d. and 2far. We set down the

128 11 4 2

2far. under the number multiplied, reserving the 4d. to be added to the next product. We then say 9 times 8d. are 72d., and the 4d. make 76d., equal to 68. and 4d., and set the 4d. under the column of pence, reserving the 6s. to be added to the next product. Then, 9 times 5s. are 45s., and 6s. make 51s., equal to 2£. and 11s. We place the 11s. under the column of shillings, reserving the 2£. to be added to the next product. Again, 9 times 14£. are 126£., and 2£. make 128£. This, placed under the column of pounds, gives us 128£. 11s. 4d. 2far. for the answer.

QUESTIONS. Art. 104.

What is multiplication of compound numbers? - Art. 105. Explain the operation. By what do you divide the product of each denomination? What do you do with the quotient and remainders thus obtained?

RULE. Multiply each denomination of the compound number as in multiplication of simple numbers, and carry as in addition of compouna 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 that rule a better method of proving multiplication of compound numbers.

NOTE.The answers to the following questions are found in the corresponding questions in Division of Compound Numbers, p. 128.

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. 19lb. of hay, what will 8 acres produce?

QUESTIONS.—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 1 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?

ART. 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 yard? Ans. 57£. 10s. Od.

price of 1 yard.

We find the number 24 equal to the product of 4 and 6; we therefore multiply the

price of 4 yards. price first by 4, and then that product by 6, and the last product is the answer.

price of 24 yards.

Ex. 2. What cost 360 tons of iron at 17£. 16s. 1d. per ton?

· 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. 1na. ?

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.?

OPERATION.
£. S. d.

3 16

8 X 9 units.

10

38

6

8 X 7 tens.

10

383 6

8

1150 0 268 6

34 10

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 lcwt. by 9. Adding the several products, we obtain 1452£. 16s. 8d. for the answer.

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

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.

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 We write the quotient question, and divide tne amount, 51s., by 9. 58. 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?