Add the following fractions and simplify if possible

Explanation

To build \(\frac17\) and \(\frac23\) so that their denominators are 21, multiply each by a form of 1

$\frac17 + \frac23 = \frac17 \color{red}{\cdot \frac33} + \frac23 \color{blue}{\cdot \frac77}$

Multiply the numerators.  Multiply the denominators.  The denominators are now the same

$= \frac{3}{21} + \frac{14}{21}$

Add the numerators and write the sum over the common denominator 21

$= \frac{3 + 14}{21}$

Since 17 and 21 has no common factors other than 1, this fraction is in simplest form

$= \frac{17}{21}$