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Rule

# Cross Product Property

The cross product property, also known as cross-multiplication, is a faster method to simplify an equation which has fractions on both sides of the equal sign. An example is $\frac{x}{5}=\frac{2}{7}.$

The procedure is that both sides are multiplied by $5$ and $7,$ the denominators of both sides. The result is that the denominators and multiplier undo each other.
$\dfrac{x}{{\color{#0000FF}{5}}}=\dfrac{2}{{\color{#FF0000}{7}}}$
$\dfrac{x\cdot {\color{#FF0000}{7}}}{{\color{#0000FF}{5}}}=2$
$x\cdot {\color{#FF0000}{7}}= {\color{#0000FF}{5}} \cdot 2$
With cross multiplication, these steps are done at the same time.