To add the fractions \( \frac{1}{6} \) and \( \frac{3}{5} \), we need to find a common denominator. The least common multiple (LCM) of 6 and 5 is 30.
Now, we can convert each fraction:
\[ \frac{1}{6} = \frac{1 \times 5}{6 \times 5} = \frac{5}{30} \] \[ \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \]
Now we can add the two fractions:
\[ \frac{5}{30} + \frac{18}{30} = \frac{5 + 18}{30} = \frac{23}{30} \]
Therefore, \( \frac{1}{6} + \frac{3}{5} = \frac{23}{30} \).