| 4 × 5 | or | 20 | |
| 11 × 7 | 77 |
The rule of the last article, therefore, admits of this modification: If the two numerators or the two denominators have a common measure, divide by that common measure, and use the quotients instead of the dividends.
123. In dividing a fraction by a whole number, for example, ⅔ by 15, consider 15 as the fraction ¹⁵/₁. The rule gives ²/⁴⁵ as the quotient. Therefore, to divide a fraction by a whole number, multiply the denominator by that whole number.
EXERCISES.
| Dividend. | Divisor. | Quotient. |
|---|---|---|
| 41 | 63 | 41 |
| 33 | 11 | 189 |
| 467 | 907 | 47167 |
| 151 | 101 | 136957 |
| 7813 | 601 | 13 |
| 5071 | 11 | 461 |
| What are | ¹/₅ × ¹/₅ × ¹/₅ - ²/₁₇× ²/₁₇ × ²/₁₇ | , |
| ¹/₅ - ²/₁₇ | ||
| and | ⁸/₁₁ × ⁸/₁₁ - ³/₁₁ × ³/₁₁ | ? |
| ⁸/₁₁ - ³/₁₁ | ||
| Answer, | 559 | and 1. |
| 7225 | ||
A can reap a field in 12 days, B in 6, and C in 4 days; in what time can they all do it together?[16]—Answer, 2 days.
In what time would a cistern be filled by cocks which would separately fill it in 12, 11, 10, and 9 hours?—Answer, (2⁴⁵⁴/₇₆₃) hours.
124. The principal results of this section may be exhibited algebraically as follows; let a, b, c, &c. stand for any whole numbers. Then
| (107) | a | = | 1 | × | a |
| b | a | ||||
| (108) | a | = | ma | ||
| b | ma | ||||