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59. How many times is 8 contained in 9150; and how many are there over ?

59. Suppose 568 to be a dividend, and 7 the divisor; what is the quotient, and the remainder?

60. Suppose 1953 to be a dividend, and 7 the divi sor; what is the quotient, and the remainder?

61. Divide 564 by 7, and prove the work to be right.

The remainder, in division, is an undivided part of the dividend: therefore, the remainder must be added to the product of the divisor and quotient, to make the product equal to the dividend. 62. Divide 109 by 6, and prove the work to be right. 63. Divide 817 by 5, and prove the work to be right.

SECTION 3. The method of dividing taught in the two preceding sections, is called Short division: the method taught in this section; is called Long division. In long division, we place the quotient on the right hand of the dividend, and perform some operations under the dividend, heretofore performed in the mind. 1. How many times is 4 contained in 95307?

Perceiving that 4 is contained in 9, twice, we place 2 in the quotient, multiply the divisor by

2, and subtract the product (8) 4)95307 (23826 from 9. This is the same as 8

saying in short divisien, '4 in 9,

2 times, and 1 over.' Now. 15

since the 1 over must be joined 12

with the 5, we bring the 5 down 33

to the right of the 1: and then, 32

perceiving that 4 is contained in 10

15, 3 tiines, we place 3 in the 8

quotient, multiply the divisor

by 3, and subtract the product 27

as before. Thus we proceed to 24

bring down every figure of the Remainder 3

dividend, and unite it with the previous remainder.

Divisor

Dividend

Quotient

48

Perform the following examples by long division.
2. How many times 5 are there in 7163 ?
3. How many times 7 are there in 88 704 ?
4. How many times 6 are there in 97 547 ?
5. How many times 3 are there in 8 057 251 ?
6. How many times 4 are there in 8 708 983 ?
7. How many times 5 are there in 6 457 080 ?
8. How many times 8 are there in 25 648 ?

The divisor not being contain. 8)25648(3206

ed once in the left hand figure 24

of the dividend, we join this fig16 ure with the next.

After bring16

ing down the 4, we find the divi

sor is not contained in it; there48

fore, we place a 0 in the quotient,

and bring down the next figure. 9. How many times 5 are there in 43 906 ? 10. How many times 9 are there in 70 223 ? 11 How many times 6 are there in 901 500 : 12. How many times 7 are there in 161 635 ? 13. How many times 24 are there in 3762 ? 24)3762(156

This operation is performea

in the same manner that it would 24

have been, if the divisor had 136

consisted of only one figure. 120

The two following examples 162

will show the method of deter144

mining when a figure placed in

the quotient is too great, and 18

when it is too small. 4. How many times is 18 contained in 12 532 ?

In this example, we have 18)12532(697 chosen 7 for the last figure of the 108

quotient; but it appears, that 7 173

times 18 are more than 112, 102

therefore 18 is not contained 7

times in 112. Then and the 112

product arising from it must be 126 rubbed out, and a smaller figure

must be placed in the quotient.

K*

15. How many times is 35 contained in 45 817?

Here we have chosen 8 for 35)45817(1308

the last figure of the quotient; 35

but, after subtracting 3 times 108

35 from 317, there remains, 37. 105

This remainder will contain 317

35, once more; therefore, we 280

must rub out the 8 and the 37

work resulting from it, and

must put 9 in the place of 8. 16. How many times is 47 contained in 804? 17. How many times is 53 contained in 1625 ? 18 How many times is 68 contained in 94 605 ? 19. How many times is 71 contained in 661 419 ? 20. How many times is 108 contains d in 216 ? 21. How many times is 325 contai _d in 7134 ? 22. How many times is 476 conta jed in 92 107 ? 23. How many times is 504 conned in 1008 ? 24. How many times is 651 cor ined in 43 126 ?

RULE FOR DIVISION. When ine divisor does not exceed 9, draw a line under the dividend, find how many times the divisor is contained in the left hand figure, or two left hand figures of the dividend, and write the figure expressing the number of times underneath: if there be a remainder over, conceive it to be prefixed to the next figure of the dividend, and divide the next figure as before. Thus proceed through the dividend. When the divisor is more than 9,

find how

many

times it is contained in the fewest figures that will contain it, on the left of the dividend, write the figure expressing the number of times to the right of the dividend, for the first quotient figure; multiply the divisor by this figure, and subtract the product from the figures of the dividend considered. Place the next figure of the dividend on the right of the remainder, and divide this number as before. Thus proceed through the dividend.

PROOF. Multiply the divisor and quotient together and to the product add the remainder: the sum will be equal to the dividend, if the work be right.

25. Divide 46242 by 252, and prove the operation. 252)46242(183

252 252

183 2104

756 2016

2016 882

252

126
7 56
1 26

46242 26 Divide 74 201 by 625, and prove the operation 27. Divide 408 732 by 9, and prove the operation. 28. Divide 15 362 by 88, and prove the operation. 29. Divide 57 026 by 492, and prove the operation. 30. Divide 982 700 by 53, and prove the operation. 31. Divide 162 941 by 256, and prove the operation. 32. Divide 648 035 by 14, and prove the operation. 33. Divide 106 401 by 333, and prove the operation. 34. Divide 62 509 by 4423, and prove the operation. 35. Divide 1 071 400 by 29, and prove the operation.

36. How many acres of land, at 22 dollars an acre, can be bought for 8514 dollars ?

37. Suppose a man to earn 35 dollars a month; how many months will it take him to earn 490 dollars ?

38. If a man travel 48 miles a day, in how many days will he perform a journey of 3264 miles ? 39. If 774 dollars be divided equally among 18 sail

many dollars will each sailor receive ? 40. If a man's income be 2555 dollars a year, how much is it a day, there being 365 days in a year?

41. The income of the Chancellor of England, is 99 280 dollars a year.

How much is it per day? 42. 63 gallons of water will fill a hogshead. How many hogsheads will 5166 gallons fill?

43. How many hogsheads can be filled from 19721 gallons ? --- and how many gallons will there be left ?

44. Suppose a regiment of 512 men have 8192 pounds of beef; how many pounds are there for each man?

45. Il a dividend be 46 319, and the divisor 807, what is the quotient? -- and what the remainder?

ors, how

SECTION 4.

ABBREVIATIONS, When there are ciphers on the right hand of a divisor, cut them off, and omit them in the operation; also cut off and omit the same number of figures from the right hand of the dividend. Finally, place the figures cut off from the dividend, on the right of the remainder.

1. How many times 900 are there in 741 725 ? 9|00)7417125

We divide 7417 by 9; there

remains 1, to which we annex the
824 125

25, making the true rem. 125.
2. How many times 70 are there in 8 563 512 ?
3. How many times 300 are there in 6374 ?
4. How many times 5000 are there in 46 578 ?
5. How many times 40 are there in 80 603 ?
6. How many vimes 600 are there 675 700 ?
7. How many times 8000 are there in 16 000 ?
8. Divide 65 237 by 59, and prove the operation.
9. Divide 567 289 by 100, and prove the operation.
10. How many times 570 are there in 35 871 ?
11. How many times 280 are there in 6423 ?
12. How many times 4200 are there in 91 621?
13. How

many

times 9060 are there in 287 000 ? When the divisor. is 10, 100, 1000, fc., cut off as many figures from the right hand of the dividend, as there are ciphers in the divisor; the other figures of the dividend will be the quotient, and the figures cut off will : be the remainder,

14. How many times 10 are there in 240 ?
15. How many times 10 in 435; and how many over ?
16. How many times 100 are there in 4000 ?
17. How many times 100 in 748; and how many over?

18. 100 cents are equal to 1 dollar. How many dollars are there in 5400 cents ?

19. In 642 cents, how many dollars are there; and how many cents over ?

20. In 1937 cents, how many dollars are there; and how many cents over ?

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