To add the fractions \( \frac{1}{10} \) and \( \frac{9}{20} \), we first need to find a common denominator.
The least common multiple of 10 and 20 is 20.
Next, we can convert \( \frac{1}{10} \) to a fraction with a denominator of 20:
\[ \frac{1}{10} = \frac{1 \times 2}{10 \times 2} = \frac{2}{20} \]
Now we can add:
\[ \frac{2}{20} + \frac{9}{20} = \frac{2 + 9}{20} = \frac{11}{20} \]
Thus,
\[ \frac{1}{10} + \frac{9}{20} = \frac{11}{20} \]