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17. A merehant bought 29 pieces of cloth, each piece containing 47 yards, at $8 a yard. What was the cost of the whole?

18. What will be the cost of 45 sets of Cyclopædias, each set containing 16 volumes, at $7 a volume?

19. How many yards of sheeting in 57 bales, each bale containing 26 pieces, and each piece 44 yards?

20. What is the cost of 128 barrels of beef, each containing 216 pounds, worth 13 cents a pound?

21. Three schooners ship 239 cords of wood each, and a fourth ships 248 cords. What is the value of the whole at $4.25 a cord?

58. When there are ciphers at the right of one, or of both factors.

1. Multiply 236 by 100.

EXPLANATION.-Since removing a figure one place to

the left increases its representative value ten times

236

100

23600

(17-II), annexing a cipher to a number multiplies it by 10; annexing two ciphers multiplies it by 100, etc.

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252000

First multiply together the two factors 84 and 3, and then multiply their product 252 by 10 × 100, or 1000, by annexing three ciphers, which gives 252000, the required product.

RULE.-To the product of the significant figures annex as many ciphers as there are on the right of both factors.

1. For an occasional exercise, require the pupil to give at sight the products of each number in columns of Drill Table No. 1 multiplied by 10, 20, 30, to 90; then by 100, 200, 300, etc., and then by 1000, 2000, 3000, etc. See pages 16 and 24.

2. These combinations should be made from dictation as well as at sight.

What is the product

3. Of 436 by 10? by 100? by 1000? by 10000?

4. Of 2340 by 60? by 500? by 3200? by 25000 ?
5. At $160 an acre, what will 500 acres of land cost?

6. At $9 a barrel, what is the cost of 1200 barrels of flour? 7. A merchant bought 240 barrels of flour for $1920, and sold it at $10.50 a barrel. What did he gain?

8. What is the difference in the cost of 48 horses, at $184.50 each, and 130 sheep at $4.80 a head?

9. If a man buys 40 acres of land at $35 an acre, and 56 acres at $29 an acre, and sells the whole at $32 an acre, what does he gain or lose?

10. If my income is $3000 a year, and my expenses $40 a week, what do I save in a year

?

11. From 207300
12. Multiply 675 (77 +56) by 3 x 155

236 × 48 take 976 × 98 + 10050.

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(214 — 28). 13. Bought 150 barrels of flour for $1050, and finding 25 barrels worthless, sold the remainder at $8,50 a barrel. What was gained or lost?

Find the amount of each of the following bills:

14. M. H. DECKER,

Bought of WM. C. DRYER.

136 bushels of oats, at $.37 a bushel.
56 barrels of potatoes, at $2.50 a barrel.

17 tons of hay, at $16.75 a ton.

42 cords of wood, at $3.125 a cord.

15. GEO. MCDOUGAL,

Bought of JOHN CLARK & Co.

128 tons of coal, at $5.25 a ton.

1600 pounds of bar lead, at 6¢ a pound.

750 pounds of printing paper, at 12¢ a pound.

16. THOS. MCMILLAN.

Bought of SAMUEL STONE & Co.

25 barrels of mess pork, at $16.25 a barrel.

14 tubs of butter, of 64 pounds each, at 28¢ a pound.
36 barrels of winter apples, at $4.18 a barrel.

16 barrels of flour, at $7.84 a barrel.

17. A flour merchant bought 1500 barrels of flour, at $7 a barrel; he sold 800 barrels at $10 a barrel, and the remainder at $6 a barrel. What was his gain?

18. A farmer exchanged 584 bushels of wheat at $2 a bushel, for 78 barrels of flour at $9 a barrel, and received the balance in money. How much money did he receive?

19. Two persons start from the same point and travel in opposite directions; one travels at the rate of 32 miles a day, the other at the rate of 39 miles a day. How far apart will they be in 14 days?

20. A planter sold 209 bales of cotton at $76 a bale, and from the proceeds he bought 107 acres of land, at $60 an acre, 18 mules at $75 each, and 4 pairs of horses at $218 a pair. How much money had he left?

21. A man bought 45 acres of land at $38 an acre, and 76 acres at $47 an acre, and sold the whole at $45 an acre. Did he gain or lose, and how much?

22. A man owing $15760, gave in payment 5 lots of land worth $730 each, 6 horses valued at $226.50 each, an interest he owned in a coal mine, worth $2000, and $1589.80 in money. How much did he still owe?

Complete the following equations :

23. (142+405) × (1000—850)—5000 = ?
24. 97×1000—(75 × 500—420)+1500 = ?
25. $73.46-($.94+$3.02)+$47 × 35 = ?
26. $246.08 × 104+ ($2000–$240.50) × 10 = ?

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59. 1. How many 4's are 12? Are 16? Are 24? 2. How many men are 12 men less 6 men, less 6 men? 3. How many feet are 16 feet 4 feet 4 feet 4 feet 4 feet?

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4. How many times can 6 men be taken from 12 men? 4 feet from 16 feet?

5. How many 6's in 12? 4's in 16? 5's in 20?

6. How many times can 6 yards of cloth be cut from a piece containing 24 yards?

7. How many 6's in 24? 4's? 8's? 2's? 3's? 12's? 8. How many times can 5 gallons be taken from a cask containing 30 gallons? How many 5's in 30?

9. Can we say 5 gallons are contained in 30 gallons 6 times? Why?

10. Into how many equal parts are 30 gallons separated? 11. What is the size of each part? How many 6's in 30? 12. Distribute 20 cents equally among 4 boys? How many cents will each receive?

13. Can we say, 4 boys are contained in 20 cents 5 times? Why not?

14. Can we subtract 4 boys from 20 cents, 5 times? Why not?

15. When we find how many times 6 cents is contained in 60 cents, what kind of a number is the result?

16. When we find one of the 6 equal parts of 60 cents, what kind of a number is the result?

DEFINITIONS.

60. Division is the process of finding how many times one number is contained in another of the same kind. Or, it is finding one of the equal parts of a number.

1. The dividend is the number to be divided.

2. The divisor is the number by which to divide.

3. The quotient is the result of the division.

4. The remainder is the part of the dividend remaining when the division is not exact, and must always be less than the divisor.

61. The Sign of division is, or :. It is read divided by.

Thus, 369, or 36 : 9, is read, 36 divided by 9.

Division is also indicated by writing the dividend over the divisor, with a line between them; or, by writing the divisor at the left of the dividend, with a curved line between them. Thus, 24, or 6)24, is read, 24 divided by 6.

Division may also be regarded as a short method of performing several subtractions of a number.

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Thus, 15-5-5-5 10. Since 5 can be taken from 15 three times, there are three 5's in 15, or 5 is contained in 15, 3 times.

62. Since one number is contained in another as many times as it is a factor of the other, division may be regarded as the reverse of multiplication.

In multiplication, both factors are given to find the product ; in division, one factor and the product (answering to the dividend) are given to find the other factor, which answers to the quotient.

Thus, 6×424, the factor 6 being taken 4 times; hence, there are four 6's in 24, or 6 is contained in 24, 4 times.

The divisor and quotient are the factors of the dividend.

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