To add the fractions \( \frac{2}{5} \) and \( \frac{1}{4} \), we need to find a common denominator.
The denominators are 5 and 4. The least common multiple of 5 and 4 is 20.
Next, we convert each fraction to have the common denominator of 20:
\[ \frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \]
\[ \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20} \]
Now we can add the two fractions:
\[ \frac{8}{20} + \frac{5}{20} = \frac{13}{20} \]
The fraction \( \frac{13}{20} \) is already in simplest form.
So, the answer is:
\[ \frac{13}{20} \]
You can fill in the boxes as follows:
Numerator: 13
Denominator: 20