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

Multiply the numerators to find the numerator of the result. Multiply the denominators to find the denominators of the result. Then [[../Reducing fractions|reduce]] the result. For example,

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

We can then reduce

$\frac{70}{462}=\frac{70÷2}{462÷2}=\frac{35}{231}=\frac{35÷7}{231÷7}=\frac{5}{33}$.

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

$\frac{2}{21}\times \frac{35}{22}=\frac{2}{3\cdot 7}\times \frac{5\cdot 7}{2\cdot 11}=\frac{2}{3\cdot 7}\times \frac{5\cdot 7}{2\cdot 11}=\frac{5}{33}$.