14. The circumference' of the earth is about 25,000 miles; what

is of that distance?

A. 12,500 miles.

A. 8,333 miles. A. 6,250 bushels A. 5,000 dollars A. 4,166 ounces. A. 3,571 pounds. A. 3,125 hours. A. 2,777 days. A. 2,500 drams.

A. 2,272 inches

A. 71.

4. 52.

A. 907.

A. 4,063 3.

12.

A. 3,545.

28. What is the value of 39052 29. The salary of the President of the United States is 25,000 dollars a year; what is that a month, allowing 12 months to the year? A. 2,083 dollars. 30. The President's salary then is about 2,083 dollars a month; what is it a week, allowing 4 weeks to a month? A. 5203 dollars. 31. Allow the President's salary to be just 520 dollars a week, what is it a day, there being 7 days in a week? A. 742 dollars. 32. Division has hitherto been performed partly in the mind, and partly on the slate, and is called Short Division, to distinguish it from Long Division, in which the divisor is so large that we are obliged to write down the whole operation.

XXIII. LONG DIVISION is when the divisor exceeds 12.

1. Recollect you are to proceed as in Short Division, excepting the entire work is to be written out.

2. Divide 15 dollars equally among 13 poor persons.

Div.

Divisor, 1 3) 1 5 (1 Quo. 1 3

Remainder, 2

PROOF. 13 times 1 are 13,

and 2 are 15, the dividend.

Proceeding as before, say 13 in 15, 1 time and 2 over, write the quotient figure 1, on the right of 15 to make room for 13 under the 15; then 13 from 15 leaves 2, as at first. A. 1 dollars.

3. Perform and prove the following examples in like manner.

(5.)

(6.)

(7.)

(8.)

(4.) 13) 16(14) 19 ( 15 ) 2 2 ( 16 ) 2 5 ( 17 ) 3 3 (

XXIII. Q. What is Long Division? How does it differ from Short Division? XII. 32. What is the first direction? 1. Where is the quotient written? 3. What is the proof that 13 is contained in 15, 1 time and 2 over?

1 CIRCUMFERENCE, [L. circumferentia.] The line that bounds a circle; distanco found; orbit; circle; any thing circular or orbicular.

9. Recollect to place the divisor on the left; the quotient on the right; and having multiplied the divisor and quotient together, to place their product under the dividend, then subtract one from the other.

10. How many times 27 in 40?

11. How many times 56 in 81? 12. How many times 75 in 96?

A. 11

A. 13

A. 1.

13. At 39 dollars a month, how many months' labor can be pro cured for 75 dollars? A. 13 months

14. What is the quotient of 39 divided by 18?

18) 39 (2

3 6
3

Here 18 is contained in 39; 2 times, for 3 times 18 are more than 39, and only 1 time 18 would leave a remainder larger than the divisor. See v. 14. A. 2 acres.

18. At 13 dollars a barrel, how many barrels of flour can be bought for 99 dollars?

A. 7 barrels. 19. At 25 dollars an acre, how much land would 103 dollars buy! 25) 103 (4 Here 25 is in 103, 4 times, for 5 times 25 are more than 103; and only 3 times 25 would leave a remainder larger than the divisor. A. 4 acres.

100
3

20. Hence if the divisor and the figure you put in the quotient make a product greater than the dividend; rub out the work and place a smaller figure in the quotient.

21. But if the remainder is as large, or larger than the divisor; rub out the work and place a larger figure in the quotient.

22. Divide 108 by 25.

23. Divide 125 by 30.

24. Divide 165 by 45.

25. Divide 250 by 67.

26. Divide 510 by 95.

27. Divide 908 by 99.

25. 5

45.

Remainder & Remainder 30 Remainder 30 Remainder 49 Remainder 35 Remainder.

67

28. Suppose 1,036 pounds of beef are to be shared equally among

125 soldiers, what is each man's portion?

1 2 5) 10 3 6 (8

Q. How can you find what figure to place in the quotient? 20, 21.

33. Divide 6,901 by 941.

Remainder 314. 34. How many building lots, at 950 dollars apiece, may be bought for 2,895 dollars?

A. 345 lots. 35. Suppose a regiment contains 1624 men, how many companies of 203 men each would be required to make such a regiment?

A. 8 companies.

36. Divide 10,835 by 37. Divide 26,008 by 38. Divide 59,246 by

2,083.
5,041

7,085.

39. Divide 56,738 by 20,301. 40. Divide 98,304 by 10,605. 41. Divide 90,090 by 20,303.

Remainder 8,878.

42. A father divided an estate of 813,824 dollars equally among his sons, giving to each 203,456 dollars. How many sons had he? A. 4 sons. 43. When flour is 13 dollars a barrel, how many barrels will 329 dollars purchase?

13) 3 2 9 (25 26

69
65

4

Say 2 times 13 are 26, writing the 26 under the 32. The 6 over is by Short Division to be prefixed to 9; or which is the same thing, bring down the 9, and annex1 it to the 6; then 13 in 69; 5 times, for 5 times 13 are 65, and 4 remainder. A. 25 barrels.

44. Therefore, take at first only figures enough to contain the divisor, and having divided them, annex to the remainder the next figure of the dividend; after which divide as before, and so on till the figures of the dividend are all brought down.

45. Divide 278 by 13.

A. Quotient 21.

Remainder 5.

46. Divide 985 by 25.

A. Quotient 39.

Remainder 10.

47. Divide 988 by 46.

A. Quotient 21.

48. What is the quotient of 3,369 divided by 25? 25) 3 3 6 9 (1 34

25

86
75

1 19

100

19

Remainder 22.

52. When hay is 25 dollars a load, how much can be bought for 52,186 dollars?

Q. How many left-hand figures do you take first? 44. When there is a remainder in dividing, how do you proceed? 44.

1 ANNEX, [L. annecto.] To unite at the end; to subjoin; to affix, to connect with

25) 5 2 1 8 6 (2 0 8 7 5 0

218

200

186

175
1 1

Since 25 is not contained in 21, put a cipher in the quotient and bring down the 8, then divide as before. A. 2,087 loads. 53. When then the remainder with one figure annexed is too small; mark its place in the quotient by a cipher and bring down an-other figure, then divide as before Quotient 2,053102. Quotient 2,504 Quotient 3,208123.

35

12.

54. Divide 209,491 by 102. 55. Divide 280,483 by 112. 56. Divide 401,123 by 125. 57. If the remainder, with two figures annexed, is still too small, annex another figure of the dividend as before, and thus continue annexing till you obtain a number large enough to contain the divisor.

(58.)

(59.)

165) 49 58 25 (3005 A. 209) 6 270 8 3 6 (30004 A 627

495

825
825

60. Divide 115,611,740 by 2,312. 61. Divide 345,235,530 by 4,315.

836

836

2312

A. 5,0005, 180
A. 8,00081315.

62. A gentleman expended 1,253,763 dollars for land, paying for each acre 125 dollars; how many acres did he buy?

Dividend.

13

Divisor, 125) 1 2 5 3 7 6 3 ( 1 0 0 3 0,12 acres; Quotient.

245

63. What is the quotient of 95,658 divided by 245? A. 390108. 64. When the divisor is 103 and the dividend 42,024, what is the quotient? A. 408. 65. When the quotient is 408 and the dividend 42,024, what is the divisor? A. 103. 66. When the divisor is 103 and the quotient 408, what is the dividend? (103 times 408). A. 42,024. 67. When the quotient is 408, the divisor 103, and the remainder 98, what is the dividend? A. 42,122. 68. When the dividend is 42,122, and the divisor 103, what is the uotient and remainder? A. 408103 69. The salary of the President of the United States is 25,000 dollars per annum; what is that a day, allowing 365 days to the year? A. 6818 dollars.

GENERAL RULE.

365

98

70. Begin on the left-hand of the dividend, and take the fewest figures that will contain the divisor, and write the number of times it is contained in them on the right of the dividend, for the first quotient figure.

71. Multiply the divisor by this quotient figure, and place their pro

duct under the figures of the dividend used, subtract it therefrom and annex to the remainder the next figure of the dividend, which divide as before, and so on.

72. But if the remainder thus increased is still too small, write a cipher in the quotient and annex another figure, and so on till it does become large enough.

73. When the product of the divisor and quotient figure is too large, the latter must be diminished; but when the remainder is as large or larger than the divisor, the quotient figure must be increased. FIND HOW MANY TIMES; MULTIPLY; SUBTRACT; AND

74. ORDER.

BRING DOWN.

75. PROOF. The same as in Short Division.

76. Divide 14,150 by 115.

77. Divide 28,682 by 121.

78. Divide 2,360,557 by 1,021.

Quotient 123.15.
Remainder

5 121

Remainder 5

79. Divide 17,286 by 1,234.

80. Divide 14,797,541 by 12,321.

1021

Remainder 12321

81. A man bought a farm for 14,400 dollars, paying 75 dollars an How many acres did it contain?

acre.

5

A. 192 acres. 82. Suppose a farm of 192 acres cost 14,400 dollars, how much was it an acre? A. 75 dollars. 83. In 1 pound are 16 ounces; how many pounds in 223,365 ounces? A. 13,960 pounds. 84. London contained in 1831 a population of 1,471,405. Now allowing that 13 persons on an average occupy a single house, how many houses then would be required to accommodate all the inhabitants. A. 113,185 houses. A. 148,61811.

85. How much is 86. How much is

13

of 1,932,045?

93. According to the census of 1830, the entire population of the U. S,' was about 12,840,534, and the number of children who never attend school is about of the entire population; what was their number? A. 611,454.

XXIV. When the divisor is a composite number.

RULE.

1. Divide first by one factor and the quotient by the other.

What is the General Rule? 70, 71. In what cases are two or more figures to be annexed to the remainder? 72. When must the figure you place in the quotient be made larger or smaller? 73. What is the order of proceeding? 74. Proof? 75.

1 U. S., for the United States of America.