Answer
$ \frac{16}{21}$.
Work Step by Step
We can perform vertical addition using the same techniques as horizontal addition. The LCM of the original denominators, $7$ and $3$, is $21$. Therefore, we can rewrite the original fractions with a denominator of 21.
$\frac{3}{7} + \frac{1}{3} = \frac{3 \cdot 3}{7 \cdot 3} + \frac{1 \cdot 7}{3 \cdot 7} = \frac{9}{21} + \frac{7}{21} = \frac{9 + 7}{21} = \frac{16}{21}$.
