Divide fractions

To divide fractions, the numerator is multiplied by the reciprocal of the denominator. This converts the division to an equivalent multiplication.

\frac{4 / 5}{3 / 7} = \frac{4}{5} \cdot \frac{7}{3}

This rule can be proven by expanding with the reciprocal of the denominator.

\frac{4 / 5}{3 / 7} = \frac{4 / 5}{3 / 7} \cdot \frac{7 / 3}{7 / 3}

This can now be simplified by performing the multiplications.

\frac{4 / 5}{3 / 7} \cdot \frac{7 / 3}{7 / 3}

Multiply fractions

\frac{4 / 5 \cdot 7 / 3}{3 / 7 \cdot 7 / 3}

Rewrite $a / b$ as $\frac{a}{b}$

\frac{\frac{4}{5} \cdot \frac{7}{3}}{\frac{3}{7} \cdot \frac{7}{3}}

$\frac{a}{b} \cdot \frac{b}{a} = 1$

\frac{\frac{4}{5} \cdot \frac{7}{3}}{1}

$\frac{a}{1} = a$

\frac{4}{5} \cdot \frac{7}{3}

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