# How do you multiply  5/8 div 2/5?

May 4, 2018

Actually you don't this is division problem treat it as a division problem

#### Explanation:

This problem can be set up as a fraction divided by a fraction.

$\frac{\frac{5}{8}}{\frac{2}{5}}$

To simply and solve multiply both the top and the bottom fraction by the inverse of the bottom fractions. This will cause the bottom fraction to become 1.

$\frac{2}{5} \times \frac{5}{2} = 1$

$\left(\frac{5}{8}\right) \times \frac{5}{2} / \left(\frac{2}{5}\right) \times \frac{5}{2}$

$\frac{\frac{5}{2}}{\frac{5}{2}} = 1$

so multiplying both the top and bottom by 5/2 is the same as multiplying by 1

# (5/8) xx 5/2 /(2/5) xx 5/2 = ( 5/8 ) xx ( 5/2)

$\frac{5}{8} \times \frac{5}{2} = \frac{25}{16}$

There are no common factors but the improper fraction can be changed into a mixed number

$\frac{25}{16} = 1 \frac{9}{16}$