Algebra: Adding and subtracting fractions
Multiplication of fractions
The product of two fractions
We can multiply two fractions by multiplying the numerator by the numerator and multiplying the denominator by the denominator. \[\frac{\orange{a}}{\blue{b}} \cdot \frac{\purple{c}}{\green{d}}=\frac{\orange{a} \cdot \purple{c}}{\blue{b} \cdot \green{d}}\] |
Example \[\begin{array}{rcl} \dfrac{\orange{x}}{\blue{y}} \cdot \dfrac{\purple{5}}{\green{y^2}}&=&\dfrac{\orange{x} \cdot\purple{ 5}}{\blue{y }\cdot\green{ y^2}} \\ &=& \dfrac{{5 \cdot x}}{{y^3}}\end{array}\] |
#1#
#\begin{array}{rcl}
\dfrac{x}{y\cdot z^2} \cdot \dfrac{y\cdot z^2}{x} &=& \dfrac{ {x} \cdot {y\cdot z^2}}{{y\cdot z^2} \cdot {x}}\\
&& \phantom{xxx}\blue{\text{fractions multiplied by }}\\
&& \phantom{xxx}\blue{\text{multiplying numerator by numerator and denominator by denominator}}\\
&=& \displaystyle 1
\\ && \phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
#\begin{array}{rcl}
\dfrac{x}{y\cdot z^2} \cdot \dfrac{y\cdot z^2}{x} &=& \dfrac{ {x} \cdot {y\cdot z^2}}{{y\cdot z^2} \cdot {x}}\\
&& \phantom{xxx}\blue{\text{fractions multiplied by }}\\
&& \phantom{xxx}\blue{\text{multiplying numerator by numerator and denominator by denominator}}\\
&=& \displaystyle 1
\\ && \phantom{xxx}\blue{\text{simplified}}\\
\end{array}#
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