# Question #abb94

Nov 13, 2017

See a solution process below:

#### Explanation:

First, convert each of the mixed numbers to an improper fraction:

$3 \frac{2}{3} = 3 + \frac{2}{3} = \left(\frac{3}{3} \times 3\right) + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{9 + 2}{3} = \frac{11}{3}$

$1 \frac{1}{2} = 1 + \frac{1}{2} = \left(\frac{2}{2} \times 1\right) + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{2 + 1}{2} = \frac{3}{2}$

To add or subtract fractions they must be over common denominators:

$\frac{11}{3} \times \frac{2}{2} = \frac{22}{6}$

$\frac{3}{2} \times \frac{3}{3} = \frac{9}{6}$

We can now write the problem as:

$\frac{22}{6} - \frac{9}{6} = \frac{22 - 9}{6} = \frac{13}{6}$

We can now convert this result back to a mixed number:

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