Prealgebra for Two-Year Colleges/Appendix (procedures)/Multiplying fractions

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Multiply the numerators to find the numerator of the result. Multiply the denominators to find the denominators of the result. Then reduce the result. For example,

\frac{2}{21} \times \frac{35}{22} = \frac{70}{462}.

We can then reduce

\frac{70}{462} = \frac{70 {\color{Red}\div 2}}{462 {\color{Red}\div 2}} = \frac{35}{231} = \frac{35 {\color{Red}\div 7}}{231 {\color{Red}\div 7}} = \frac{5}{33}.

An easier way to multiply the same fractions is first find the prime factors of the numerators and denominators, then reduce, then multiply.

\frac{2}{21} \times \frac{35}{22} = \frac{2}{3 \cdot 7} \times \frac{5 \cdot 7}{2 \cdot 11} = \frac{\color{Red}\not{2}}{3 \cdot {\color{Blue}\not{7}}} \times \frac{5 \cdot {\color{Blue}\not{7}}}{{\color{Red}\not{2}} \cdot 11} = \frac{5}{33}.