To add the fractions $\frac{3}{7}$ and $\frac{1}{3}$, we first need to find a common denominator.

Step 1: Find the least common denominator (LCD)

The denominators are 7 and 3. The least common denominator is 21 because it is the smallest number that both 7 and 3 divide into evenly.

Step 2: Convert both fractions

Now, we convert each fraction to have a denominator of 21:

$\frac{3}{7} = \frac{3 \times 3}{7 \times 3} = \frac{9}{21}$

$\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}$

Step 3: Add the fractions

Now that both fractions have the same denominator, we can add them:

$\frac{9}{21} + \frac{7}{21} = \frac{9 + 7}{21} = \frac{16}{21}$

So, $\frac{3}{7} + \frac{1}{3} = \frac{16}{21}$.

Would you like any more details or have any questions about this process?

Here are some related questions:

1. How do you subtract fractions with different denominators?
2. What is the process for finding the least common denominator (LCD)?
3. Can you simplify a fraction if both the numerator and denominator have a common factor?
4. How do you multiply fractions?
5. What are some applications of adding fractions in real life?

Tip: Always simplify fractions to their lowest terms after performing arithmetic on them!