Use adaptive quiz-based learning to study this topic faster and more effectively.

# Multiplication and division of fractions

To multiply fractions, the numerators are multiplied to give the new numerator, and the denominators are multiplied to give the new denominator. The fraction can then be simplified.

For instance: $\frac{\Tred{4}}{\Tblue{5}} \times \frac{\Tred{7}}{\Tblue{6}} = \frac{\Tred{4}\times \Tred{7}}{\Tblue{5}\times \Tblue{6}} = \frac{\Tred{28}}{\Tblue{30}} = \frac{14}{15}$

To divide fractions, we take the reciprocal of the fraction we are dividing by and multiply it by the other fraction.

For instance, $\displaystyle\frac{4}{5} \div \frac{\Tred{2}}{\Tblue{3}} = \frac{4}{5} \times \frac{\Tblue{3}}{\Tred{2}} = \frac{4\times \Tblue{3}}{5\times \Tred{2}} = \frac{12}{10} = \frac{6}{5}$

$1/3 \times 1/2$ is the same as finding half of a third, or a third of one half.