# How do you divide rational mixed numbers?

Apr 3, 2015

First, transform mixed rational numbers into improper fractions (the ones with numerator greater than denominator).
Then perform a division according to general rules of operation on fractions.

For instance, you have to divide $30 \frac{3}{5}$ by $6 \frac{3}{8}$.

The first number produces $30 \frac{3}{5} = \frac{153}{5}$ and
the second number produces $6 \frac{3}{8} = \frac{51}{8}$.

Now we can divide:
$\frac{\frac{153}{5}}{\frac{51}{8}} = \frac{153 \cdot 8}{5 \cdot 51}$

The resulting fraction can be reduced and, if it is improper, transformed mixed rational number.

$\frac{153 \cdot 8}{5 \cdot 51} = \frac{3 \cdot 8}{5} = \frac{24}{5} = 4 \frac{4}{5}$