Simplify each of the following expressions.

1. $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 1 } { 6 }$

   Hint (a):

   Refer to the Math Note box below for help adding and subtracting fractions.

   

   Step 1(a):

   Change each fraction so that the denominator is $6$.

   $\left(\frac{1}{2}\right)\left(\frac{3}{3}\right)+\left(\frac{2}{3}\right)\left(\frac{2}{2}\right)+\frac{1}{6}=\frac{3}{6}+\frac{4}{6}+\frac{1}{6}$

   Step 2(a):

   Add the fractions together.

   $\frac{3}{6}+\frac{4}{6}+\frac{1}{6}=\frac{8}{6}=\frac{4}{3}$

   Answer (a):

   $\frac{4}{3}=1\frac{1}{3}$

2. $1 \frac { 2 } { 3 } - \frac { 5 } { 12 }$

   Hint (b):

   Try rewriting  $1\frac{2}{3}\text{ as }1\frac{8}{12}$. Does that help you to subtract? How?