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 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.

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