To add the fractions \( \frac{1}{50} + \frac{3}{5} \), we first need a common denominator. The least common multiple of 50 and 5 is 50.
Next, we convert \( \frac{3}{5} \) to have a denominator of 50:
\[ \frac{3}{5} = \frac{3 \times 10}{5 \times 10} = \frac{30}{50} \]
Now that we have both fractions with the same denominator, we can add them:
\[ \frac{1}{50} + \frac{30}{50} = \frac{1 + 30}{50} = \frac{31}{50} \]
The resulting fraction \( \frac{31}{50} \) is already in simplified form, as 31 is a prime number and does not divide 50.
Thus, the final answer is:
\[ \boxed{\frac{31}{50}} \]