Numbers: Fractions
Multiplication of fractions
Multiplying fractions
When multiplying fractions, we multiply the numerators and we multiply the denominators:
\[ \dfrac{\orange{\text{numerator}}}{\blue{\text{denominator}}} \times \dfrac{\orange{\text{numerator}}}{\blue{\text{denominator}}} = \dfrac{\orange{\text{numerator}}\times \orange{\text{numerator}}}{\blue{\text{denominator}} \times \blue{\text{denominator}}} \]
Example
\[\begin{array}{rcl}
\dfrac{\orange{5}}{\blue{7}} \times \dfrac{\orange{2}}{\blue{9}} &=&
\dfrac{\orange{5}\times\orange{2}}{\blue{7}\times \blue{9}}\\
&=& \dfrac{10}{63}
\end{array} \]
#{{7}\over{10}} \times {{4}\over{7}}=# #{{2}\over{5}}#
#\begin{array}{rcl}\displaystyle {{7}\over{10}} \times {{4}\over{7}}&=&\dfrac{7 \times 4}{10 \times 7} \\ &&\phantom{xxx}\blue{ \text{multiplied fractions by calculating } \frac{ \text{numerator } \times \text{ numerator}}{\text{denominator } \times \text{ denominator} }}\\
&=& \dfrac{28}{70} \\ &&\phantom{xxx}\blue{\text{multiplied}}\\
&=& \displaystyle {{2}\over{5}} \\ &&\phantom{xxx}\blue{\text{simplified}}
\end{array}#
#\begin{array}{rcl}\displaystyle {{7}\over{10}} \times {{4}\over{7}}&=&\dfrac{7 \times 4}{10 \times 7} \\ &&\phantom{xxx}\blue{ \text{multiplied fractions by calculating } \frac{ \text{numerator } \times \text{ numerator}}{\text{denominator } \times \text{ denominator} }}\\
&=& \dfrac{28}{70} \\ &&\phantom{xxx}\blue{\text{multiplied}}\\
&=& \displaystyle {{2}\over{5}} \\ &&\phantom{xxx}\blue{\text{simplified}}
\end{array}#
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