But 3⁄5 = 33⁄55 = 3⁄55 × 11, so that, the eleventh part of 3⁄5 is 3⁄55; and, if we take 4 of these parts, we get 3⁄55 × 4 or 12⁄55.
Thus, 35 × 411 = 1255. Now 12 = 3 × 4, and 55 = 5 × 11.
Hence we have the following rule: To multiply two fractions together, multiply the numerators for a new numerator and the denominators for a new denominator.
As in Example 2 the work is shortened if we cancel common factors from the numerators and denominators.
Example: Multiply 22⁄91 by 13⁄77.
The product = 2 22 × 13 91 7 × 77 7 = 249 Ans.
Here, the 22 of the numerator and the 77 of the denominator contain a common factor, 11. Therefore, we cross out the 22 and write 2 above it, and cross out the 77 and write 7 under it. Similarly, we cancel the factor 13 from 13 and 91. There is now 2 left for numerator and 7 × 7 for denominator.
To multiply more than two fractions together, we proceed in the same way.
In multiplication of fractions, mixed numbers must first be expressed as improper fractions.
Example: Simplify 51⁄7 × 11⁄27 × 111⁄24.