To add the fractions \( \frac{3}{8} \) and \( \frac{3}{5} \), we first need to find a common denominator. The least common multiple (LCM) of the denominators 8 and 5 is 40.
Now, we can convert each fraction to have the common denominator of 40:
\[ \frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} \]
\[ \frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40} \]
Now we can add the two fractions:
\[ \frac{15}{40} + \frac{24}{40} = \frac{15 + 24}{40} = \frac{39}{40} \]
Therefore,
\[ \frac{3}{8} + \frac{3}{5} = \frac{39}{40} \]