First, let's add the fractions \( \frac{9}{20} \) and \( \frac{7}{20} \):
\[ \frac{9}{20} + \frac{7}{20} = \frac{9 + 7}{20} = \frac{16}{20} \]
Next, we need to simplify \( \frac{16}{20} \):
- The greatest common divisor (GCD) of 16 and 20 is 4.
- Dividing both the numerator and the denominator by 4 gives us:
\[ \frac{16 \div 4}{20 \div 4} = \frac{4}{5} \]
Now, let's list the fractions you've provided to confirm the result:
- \( \frac{4}{10} \) simplifies to \( \frac{2}{5} \).
- \( \frac{4}{5} \) is already in simplest form.
- \( \frac{16}{20} \) simplifies to \( \frac{4}{5} \).
- \( \frac{16}{40} \) simplifies to \( \frac{2}{5} \).
The final answer to the sum \( \frac{9}{20} + \frac{7}{20} \) is:
\[ \frac{4}{5} \]