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MULTIPLICATION.

11. 7 times 5 are how many? This is called a question in multiplication. To obtain the answer we repeat or multiply the number 5, 7 times; thus, 7 times 5 are 35.

Ex. 1. Multiply 564 by 7,

Hundreds.

Tens.

Units.

5 6 4

7 3948

Writing the numbers thus, the 7 under the units, we say, 7 times 4 (units) are 28 (units), or 2 tens and 8 units. We write down the 8 (units) and reserve the 2 (tens); then, 7 times 6 (tens) are 42 (tens) and the 2 (tens) which we reserved are 44 (tens) or 4 hundreds and 4 tens. write the 4 (tens) and reserve the 4 (hundreds); then, 7 times 5 (hundreds) are 35 (hundreds), which, with the 4 (hundreds) we reserved are 39 (hundreds) or 3 thousands and 9 hundreds. This we write down, and the answer is 3948.

3.

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23. Multiply 129 by 35.

Thousands.
Hundreds.
Tens.

Units

129

35

Writing the numbers in order, units under units, and tens under tens, we multiply, first, by the 5 units, and write the result in its proper place, as when we multiplied by one figure. We multiply next by the 3 (tens) and write the first figure of the result in the place of tens, because units multiplied by tens ought to produce tens. Then adding together the results obtained by multiplying by the 5 (units) and 3 (tens), heir sum will be 4515, which is the answer.

645

387

4515

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46. How much will 48 barrels of flour cost at 8 dollars a barrel?

47. In a room there are 9 windows with 16 panes of glass in each. How many panes of glass in all the windows?

48. If a man receive 47 dollars a month, how much will he receive in twelve months?

49. In a certain regiment there are 13 companies, and 126 men in each company. How many men in the regiment?

50. There are 365 days in a year. How many days in 19 years?

12.

DIVISION.

24 are how many times 8? This is called a question in division, because we divide or separate the larger number into as many equal parts as there are units in the smaller number.

13. The number to be divided is called the dividend; the number by which we divide, the divisor; and the result, the quotient. If anything is left after the division, it is called the remainder.

14. Ex. 1. Divide 584 by 4.

Divisor, 4)584 Dividend.

We write down the dividend,

146 Quotient. 584, and draw a line beneath it. Write the divisor, 4, at the left of the dividend, and draw a curved line between them. We first find how many times 4 is contained in 5, the first figure of the dividend; it is contained 1 time and there is 1 remainder. We write the 1 under the 5, and suppose the remainder, 1, written at the left of the next figure, 4 is contained in 18, 4 8, making the number 18. times, with 2 remainder. The 4 we write below, and suppose the 2 written before the next figure, 4, making it 24. 4 is contained in 24, 6 times, without remainder. We write the 6 underneath, and the division is completed.

Division performed in this way is called short division.

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Divisor, 3)9 Dividend. 2)26 3)36 4)88 5)15 3)18

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6)72 2)444 4)256 3)963 7)847

9)279

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21.

22.

23.

24.

5)6825 6)4650 9)9972 4)4484

8)1312

16. When the divisor consists of two or more figures, it is more convenient to perform the operation in the following manner:

25. Divide 6432 by 12.

60

43

36

72

72

Divisor. Dividend. Quotient. Write the dividend, and draw 12) 6432 (53 6 a curved line on both sides. We first inquire how many times 12 is contained in 64, the first two figures of the dividend. We find that it is contained 5 times. We place the five at the right of the dividend, as the first figure of the quotient, and then, multiplying the divisor, 12, by 5, we obtain the number 60, which we write under the 64 of the dividend and subtract. To the remainder, 4, we annex 3, the next figure of the dividend, and find how many times the divisor, 12, is contained in 43. We place the result, 3, at the right of the 5 in the quotient, and, multiplying the divisor by 3, we obtain 36, which we write under the 43 and subtract.

To the remainder, 7, we annex the 2 of the dividend, and find how many times the divisor is contained in 72, which is 6 times. We write 6 in the quotient, and, as there is no remainder, the division is complete. Division performed in this way is called long division.

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44. How much sugar at 9 cents a pound can be bought for 81 cents?

45. If an acre of land cost 13 dollars, how many acres can you buy for 351 dollars?

46. If a man can walk 21 miles in a day, how long will it take him to walk 273 miles?

47. A man divided 23,796 dollars among his 6 children. How much did each receive?

48. A railroad company employed 25 workmen, and at the end of 2 months it took 1825 dollars to pay them. How much did each man receive?

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