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PROCESS.

7)586

8317, Ans.

1829

Dividing 586 by 7, we have 83 as a quotient, and 53, or 17, remaining.

Dividing 17 by 7, we have 17. Hence the required result is 8317.

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53. If a year of 3651 days were divided into 12 months of

equal length, what would be the length of each month?

divided equally 1411

ounces of gold;

CASE II.

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

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2 divided by 1 is 2; hence 2 divided by is 7 times 2, and 2 divided by is of 7 times 2, which is 3 times 2, or 14, or 24.

We may obtain the same result by multiplying 2 by 3, which is the divisor inverted.

2. Divide by

PROCESS.

=

× = 1, Ans.

divided by 1 is ; hence divided by is 7 times, and divided by is of 7 times, or times, or 1.

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

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38. Divide of 2 of 7 by 17 of 2o1 of 13.

39. Divide of 7 of 15 by 1 of 2 of 8. 40. Divide of 25 of 54 by 7 of 42 of 81.

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54. What is the value of of 5 of 5 divided by 11 × 1 X 198?

130

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56. Divide 1 × 1 × 6 by 6.

57. If 371⁄2 ounces of silver cost $314, what will 1 ounce cost? What will 150 ounces cost?

58. A earns $3 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 85 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. Multiplying 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 of 24, and 8 is 8 times, or of 24. Therefore 8 is of 24. From this solution we derive the following

RULE.

Divide the second number by the first.

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