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CASE III.

63. When there are ciphers at the right hand of one or both of the factors.

1. Multiply 7200 by 40.

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OPERATION.

Multiplicand, 7200

Multiplier,

Product,

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40

288000

ANALYSIS. The multiplicand, factored, is equal to 72 × 100; the multiplier, factored, is equal to 4 x 10 and as these factors taken in any order will give the same product,

we first multiply 72 by 4, then this product by 100 by annexing two ciphers, and this product by 10 by annexing one o pher. Hence, the following

RULE. Multiply the significant figures of the multiplioand by those of the multiplier, and to the product annex as many ciphers as there are ciphers on the right of either or both factors.

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Ans. 12191740000.

6. Multiply 403700 by 30200.

7. At 150 dollars an acre, what will be the cost of 500 acres of land?

Ans. 75000 dollars.

8. What will be the freight on 4000 barrels of flour, at 50 cents a barrel ? Ans. 200000 cents.

9. If there are 560 shingles in a bunch, how many shingles in 260 0 bunches? Ans. 14560000.

EXAMPLES COMBINING ADDITION, SUBTRACTION, AND MULTIPLICATION.

1. Bought 9 cords of wood at 3 dollars a cord, and 15 tons of coal at 5 dollars a ton; what was the cost of the wood and coal? Ans. 102 dollars.

2. A grocer bought 6 tubs of butter, each containing 64 pounds, at 14 cents a pound; and 4 cheeses, each weighing 42 pounds, at 8 cents a pound; how much was the cost of the butter and cheese? Ans. 6720 cents.

3. If a clerk receive 540 dollars a year salary, and pay 180 dollars for board, 116 dollars for clothing, 58 dollars for books, and 75 dollars for other expenses, how much will he have left at the close of the year? Ans. 111 dollars.

4. A farmer having 2150 dollars, bought 536 sheep at 2 dollars a head, and 26 cows at 23 dollars a head; how much money had he left? Ans. 480 dollars.

5. A man sold three horses; for the first he received 275 dollars, for the second 87 dollars less than for the first, and for the third as much as for the other two; how much did he receive for the third ? Ans. 463 dollars.

6. Bought 76 hogs, each weighing 416 pounds, at 7 cents a pound, and sold the same at 9 cents a pound; how much was gained? Ans. 63232 cents.

7. A man bought 14 cows at 26 dollars each, 4 horses at 112 dollars each, and 125 sheep at 3 dollars each; he sold the whole for 1237 dollars; did he gain or lose, and how much? Ans. Gained 50 dollars. 8. B has 174 sheep, C has three times as many lacking 98, and D has as many as B and C together; how many sheep has D? Ans. 598.

9. There are 36 tubs of butter, each weighing 108 pounds; the tubs which contain the butter, each weigh 19

pounds; how much is the weight of the butter without the tubs ? Ans. 3204 pounds.

10 A man paid for building a house 2376 dollars, and for his farm 4 times as much lacking 970 dollars; how much did he pay for both?

11. A merchant bought 9 hogsheads of sugar at 32 dollars a hogshead, and sold it for 40 dollars a hogshead; how much did he gain? Ans. 72 dollars.

12. Bought 360 barrels of flour for 2340 dollars, and sold the same at 8 dollars a barrel; how much was gained by the bargain? Ans. 540 dollars.

13. A farmer sold 462 bushels of wheat at 2 dollars a bushel, for which he received 75 barrels of flour at 9 dollars a barrel, and the balance in money; how much money did he receive? Ans. 249 dollars.

14. Two persons start from the same point, and travel in opposite directions; one travels at the rate of 28 miles a day, the other at the rate of 37 miles a day; how far apart will they be in 6 days? Ans. 390 miles. 15. If a man buy 40 acres of land at 35 dollars an acre, and 56 acres at 29 dollars an acre, and sell the whole for 32 dollars an acre, how much does he gain or lose?

Ans. Gains 48 dollars.

16. In an orchard, 76 apple trees yield 18 bushels of apples each, and 27 others yield 21 bushels each; how much would the apples be worth, at 30 cents a bushel?

Ans. 58050 cents.

17. A man bought two farms, one of 136 acres at 28 dollars an acre, and another of 140 acres at 33 dollars an acre; he paid at one time 4000 dollars, and at another time 1875 dollars; how much remained unpaid?

Ans. 2553 dollars.

DIVISION.

64. Division is the process of finding how many times one number is contained in another.

65. The Quotient is the result obtained, and shows how many times the divisor is contained in the dividend.

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MENTAL EXERCISES.

1. How many barrels of flour, at 6 dollars a barrel can be bought for 30 dollars?

ANALYSIS. Since 6 dollars will buy one barrel of flour, 30 dollars will buy as many barrels as 6 dollars, the price of one barrel, is contained times in 30 dollars, which is 5 times. Therefore, at dollars a barrel, 5 barrels of flour can be bought for 30 dollars.

2. How many oranges, at 4 cents apiece, can be bought for 28 cents?

3. How many tons of coal, at 5 dollars a ton, can be bought for 35 dollars?

4. When lard is 7 cents a pound, how many pounds can be bought for 49 cents? for 63 cents? for 84 cents ?

5. If a man travel 48 miles in 6 hou how far does he travel in one hour?

6. At 3 cents apiece, how many lemons can be bought for 24 cents? for 30 cents? for 36 cents.?

7. If you give 55 cents to 5 beggars, how many cents do you give to each ?

8. If a man build 42 rods of wall in 7 days, how many rods can he build in 1 day?

9. At 4 dollars a cord, how many cords of wood can be bought for 20 dollars? for 28 dollars? for 32 dollars?

10. A farmer paid 33 dollars for some sheep, at 3 dollars apiece; how many did he buy?

11. At 7 cents a pound, how many pounds of sugar can be bought for 63 cents? for 84 cents?

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12. If a man spend 5 cents a day for cigars, how many days will 50 cents last him? 60 cents?

13. At 12 cents a pound, how many pounds of coffee can be bought for 48 cents? for 72 cents? for 96 cents? for 120 cents?

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