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24. Divide 5863 by 7. PROCESS. Dividing 5863 by 7, we have 83 as a quotient, and 7)5863 53, or 17, remaining. 8317, Ans.

Dividing 17 by 7, we have 11. Hence the required result is 8311

RULE.

Divide the numerator or multiply the denominator. Divide

25. 2 by 8. 34. 531 by 17. 43. 184 by 207. 26. by 5. 35. 37. by 15. 44. 27: by 341. 27. 13} by 11. 36. 62 by 25. 45. 8623 by 5. 28. 18 h by 14. 37. is by 12. 46. 9363 by 7. 29. 450 by 27. 38. 321 by 21. 47. 1001 by 11. 30. if by 11. 39. i7 by 23. 48. 38543 by 12. 31. 25} by 6. 40. 343 by 35. 49. 21684 by 30. 32. 871 by 12. 41. 19: by 128. 50. 4285 by 45. 33. 425 by 18. 42. 325 by 300. 51. 204511 by 15.

52. Seven miners divided equally 1412: ounces of gold; what was each man's share ?

53. If a year of 3651 days were divided into 12 months of equal length, what would be the length of each month?

CASE II.

82. To divide an integer or a fraction by a fraction.

WRITTEN EXERCISES.

1. Divide 2 by

PROCESS.—2 = 5 2 x } 4, or 24, Ans. 2 divided by 1 is 2; hence 2 divided by 4 is 7 times 2, and 2 divided by is } of 7 times 2, which is } times 2, or 14, or 24.

We may obtain the same result by multiplying 2 by }, which is the divisor inverted.

2. Divide by 4. PROCESS.— =

{ *} = 1%, Ans. divided by 1 is ; hence s divided by 4 is 7 times s, and divided by is } of 7 times ļ, or } times ], or 14.

We may obtain the same result by multiplying s by }, which is the divisor inverted; hence the

RULE.

Invert the divisor and proceed as in multiplication. 3. Divide il by 14.

19 3 361 19

24 57 PROCESS.

Ans. 512 24 512 19 64

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84

Divide

14. ^ by ã. 22. 141 by 115. 30. 19% by 1. 15. j by 15.

23. 154 by 13. 31. 328 by 183. 16. ii by zi

24. 102 by 214. 32. 125. by 623. 17. 4* by 19

25. 301 by us. 33. 35by 122'-. 18. 8 by . 26. 1234 by 10 34. 1084 by 1411 19. iäz by

27. 205 by 183. 35. 2, by 8. 20. 1901 by 31. 28. 314 by 238. 36. 213 by 5%. 21. 851 by 17.

29. 99 by 36 37. 172 by 83. 38. Divide şof of z by 12 of 1 of f} 39. Divide i of į of jy by of 25 of 78. 40. Divide { of 35 of $1 by of 43 of 81:

41. Divide of 34 of 106 by 1 of 495 of 10 Required the price per lb., yd., etc.

42. If 22 lb. of sugar cost $1.405.
43. If 75; yd. of cloth cost $454.
44. If 102 sheep cost $1183}.
45. If 218 tons of coal cost $14711.
46. If 473 lb. of flour cost $1.52.
47. If 16 barrels of flour cost $70.
48. If 198 tons of hay cost $13613.
49. If 25bu. of apples cost $41}.
50. If 1134 yd. of calico cost $5.44.
51. If 754 lb. of beef cost $3.315
52. If 316 cords of wood cost $191.
53. If 60 oranges cost $11.

54. What is the value of g of of 54 divided by 11 x 4 X 188?

55. Divide ji X A X 11: by $ x 53. 56. Divide 14 x 14 x 6 by 6.

57. If 371 ounces of silver cost $314, what will 1 ounce cost? What will 150 ounces cost ?

58. A earns $3.1 a day, and his expenses are $11 a week; how

many weeks must he labor to pay for 10 acres of land at $30 an acre ?

59. B sowed 63{ bushels of oats on a field, averaging 31 bushels to the acre; what was the field worth, at $80% an acre ? 60. How many times will a vessel whose capacity is 793 gallons hold the contents of each of two cans whose capacities are 53 and 8á gallons, respectively? and how many times will it hold the sum of their contents ?

COMPLEX FRACTIONS.

83. A Complex Fraction is one whose numerator or denominator, or both, are fractional.

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A complex fraction may be regarded as a problem in division of fractions, and solved by Art. 82.

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Another method of reducing a complex fraction to a simple one is to multiply both numerator and denominator by the L. C. M. of the denominators.

Thus, in the problem above, the L. C. M. of 8 and 12 is 24. Multiply, ing both terms of the fraction by 24, we have

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84. To find what fractional part one number is of another.

1. What part of 24 is 8?

1 is 4 of 24, and 8 is 8 times 24, or ļof 24. Therefore 8 is į of 24. From this solution we derive the following

RULE.

Divide the second number by the first.

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