# How do you divide (2 3/5) / (6 1/3)?

Jun 19, 2015

When dividing by a fraction, invert the fraction, then multiply.

#### Explanation:

When dividing by by a fraction, invert the fraction and multiply.

$a \div \frac{b}{c} = a \times \frac{c}{b}$ or $\frac{a}{\frac{b}{c}} = a \times \frac{c}{b}$

$\frac{\frac{23}{5}}{\frac{61}{3}}$=

$\frac{23}{5} \times \frac{3}{61} = \frac{69}{305}$

Jun 19, 2015

Formatting here is tricky. If you wanted $\frac{2 \frac{3}{5}}{6 \frac{1}{3}}$ (color(white)(1/1)Rather than $\frac{23}{5}$/61/3), then the answer is $\frac{39}{95}$

#### Explanation:

To divide mixed numbers (or to multiply them) first change form to an improper fraction:

$2 \frac{3}{5} = \frac{\left(2 \times 5\right) + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}$

$6 \frac{1}{3} = \frac{\left(6 \times 3\right) + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}$

Now, we can write:

$\frac{2 \frac{3}{5}}{6 \frac{1}{3}} = \frac{\frac{13}{5}}{\frac{19}{3}}$

Now invert the denominator (the bottom) and multiply:

$\frac{2 \frac{3}{5}}{6 \frac{1}{3}} = \frac{\frac{13}{5}}{\frac{19}{3}} = \frac{13}{5} \times \frac{3}{19}$

Multiplying fractions is the easiest thing to do with them. It's just top times top over bottom times bottom. (Easier still if we can reduce first, but we can't in this problem.) So we get:

$\frac{2 \frac{3}{5}}{6 \frac{1}{3}} = \frac{\frac{13}{5}}{\frac{19}{3}} = \frac{13}{5} \times \frac{3}{19} = \frac{13 \times 3}{5 \times 19}$

$= \frac{39}{95}$

the fraction cannot be reduced, so that's it, we are finished.