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Multiplication of fractions

  • To multiply to fractions, multiply the numerators and the denominators.
  • Common factors can be cancelled either during the multiplication or at the end to give answer in simplest form.
  • To multiply mixed numbers, convert them to improper fractions first.

For example:

\begin{eqnarray*} \frac{7}{8} \times \frac{16}{21} &=& \frac{7 \times 16}{8\times 21} \\ 
&=& \frac{\cancelto{1}{7} \times \cancelto{2}{16}}{\cancelto{1}{8}\times \cancelto{3}{21}} \\ 
&=& \frac{1 \times 2}{1 \times 3} \\ 
&=& \frac{2}{3}

To do

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