# How do you evaluate 5\frac { 2} { 5} \div 4\frac { 1} { 2} =?

Feb 7, 2017

$1 \frac{1}{5}$

#### Explanation:

You have to make mixed numbers into improper factions when multiplying and dividing fractions.

$5 \frac{2}{5} = \frac{27}{5}$ and $4 \frac{1}{2} = \frac{9}{2}$.

When dividing fractions you have to change the divide to multiply and flip over the second fraction, in this case $\frac{9}{2}$. So the calculation is

$\frac{27}{5} \div \frac{9}{2} = \frac{27}{5} \times \frac{2}{9}$

There is a trick in doing this.

$27 \mathmr{and} 9$ have a common factor which is $9$.

So we divide the numerator and denominator by $9$

${\cancel{27}}^{3} / 5 \times \frac{2}{\cancel{9}}$

To get: $\frac{3}{5} \times \frac{2}{1} = \frac{6}{5} = \frac{5 + 1}{5} = \frac{5}{5} + \frac{1}{5} = 1 + \frac{1}{5} = 1 \frac{1}{5}$.

So the answer is $1 \frac{1}{5}$.