## Statement

When dividing by a fraction, you multiply by the reciprocal.

$$ a \div \frac{b}{c} = a * \frac{c}{b} $$

## Proof

Write the fraction using negative exponents.

$$ a \div \frac{b}{c} = a \div (b * c^{-1}) $$

Now write the division using negative exponents as well.

$$ a \div \frac{b}{c} = a * (b * c^{-1})^{-1} $$

Append the powers to the factors.

$$ a \div \frac{b}{c} = a * b^{-1} * (c^{-1})^{-1} $$

$$ a \div \frac{b}{c} = a * b^{-1} * c^1 $$

Finally, write $ b^{-1} * c $ as a fraction again.

$$ a \div \frac{b}{c} = a * \frac{c}{b} $$