# How can you evaluate 7/2-1/6-5/9+7/3?

Jul 15, 2015

Choose a multiplier for each term to give them a common denominator, then add the numerators to get:

$\frac{7}{2} - \frac{1}{6} - \frac{5}{9} + \frac{7}{3} = \frac{63}{18} - \frac{3}{18} - \frac{10}{18} + \frac{42}{18} = \frac{92}{18} = \frac{46}{9}$

#### Explanation:

$\frac{7}{2} - \frac{1}{6} - \frac{5}{9} + \frac{7}{3}$

$= \left(\frac{9}{9} \cdot \frac{7}{2}\right) - \left(\frac{3}{3} \cdot \frac{1}{6}\right) - \left(\frac{2}{2} \cdot \frac{5}{9}\right) + \left(\frac{6}{6} \cdot \frac{7}{3}\right)$

$= \frac{63}{18} - \frac{3}{18} - \frac{10}{18} + \frac{42}{18}$

$= \frac{63 - 3 - 10 + 42}{18} = \frac{92}{18} = \frac{46}{9}$