# How do you simplify 7 1/2 - (1/9 + 2/3) div 3/2?

Mar 20, 2016

$\frac{15}{2} - \frac{1 + 6}{9} \cdot \frac{2}{3}$
$\frac{15}{2} - \frac{7}{9} \cdot \frac{2}{3}$
$\frac{15}{2} - \frac{14}{27}$
$\frac{405 - 28}{54}$
$\frac{377}{54}$
$6.981$

Mar 20, 2016

$6 \frac{53}{54}$

#### Explanation:

Converting mixed fraction to simple fraction and
Simplifying the fraction within the parenthesis to begin with, using PEMDAS or BODMAS

$\frac{15}{2} - \left(\frac{1 + 6}{9}\right) \div \frac{3}{2}$
$\frac{15}{2} - \frac{7}{9} \div \frac{3}{2}$
Next is solving of $\div$ by converting it to $\times$ and writing reciprocal of divisor
$\frac{15}{2} - \frac{7}{9} \times \frac{2}{3}$
$\frac{15}{2} - \frac{14}{27}$
We are left with $-$sign

$\frac{405 - 28}{54}$
$\frac{377}{54}$
Stating the result as a mixed fraction
$6 \frac{53}{54}$