Rule.—Multiply all the numerators together for the numerator, and all the denominators for the denominator.
Example.—Reduce ⅜ of ⅙ of ½ of 9 to a simple fraction.
| Numerators | 3 × 1 | × | 1 × 9 | = | 27 | = | 9 | Answer. |
| Denominators | 8 × 6 | × | 2 × 1 | 96 | 32 |
To reduce fractions of different denominators to equivalent fractions, having a common denominator.
Rule.—Multiply each numerator by all the denominators except its own for the new numerators, and multiply all the denominators together for a common denominator.[42]
Example.—Reduce ⅜, ⅔, and ⅘ to fractions having a common denominator.
3 × 3 × 5 = 45
2 × 8 × 4 = 80
4 × 8 × 3 = 96
8 × 3 × 5 = 120 Answer, 45 120 , 80 120 , 96 120 .
ADDITION OF FRACTIONS.
Rule.—Bring compound fractions to simple fractions; reduce all the fractions to a common denominator, then add all the numerators together, and place their sum over the common denominator. When mixed numbers are given, find the sum of the fractions, to which add the whole numbers.