# How do you multiply 6 1/2 div 1 1/8?

Jun 2, 2016

$\frac{52}{9} = 5 \frac{7}{9}$

#### Explanation:

The first step here is to change the $\textcolor{b l u e}{\text{mixed numbers into improper fractions}}$

$\Rightarrow 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2}$

and $1 \frac{1}{8} = 1 + \frac{1}{8} = \frac{8}{8} + \frac{1}{8} = \frac{9}{8}$

rArr6 1/2÷1 1/8=13/2÷9/8

To divide 2 fractions : change ÷ to × and invert (turn) the 2nd fraction.

rArr13/2÷9/8=13/2xx8/9

now that we have multiplication we can cancel out any common factors between the numerators and denominators.

$\Rightarrow \frac{13}{{\cancel{2}}^{1}} \times \frac{{\cancel{8}}^{4}}{9} = \frac{13 \times 4}{1 \times 9} = \frac{52}{9} = 5 \frac{7}{9}$