To find the sum of the fractions \( \frac{9}{20} + 1 \frac{7}{20} \), we first need to convert the mixed number \( 1 \frac{7}{20} \) into an improper fraction.
-
Convert \( 1 \frac{7}{20} \): \[ 1 \frac{7}{20} = \frac{20 \cdot 1 + 7}{20} = \frac{20 + 7}{20} = \frac{27}{20} \]
-
Now we can add the two fractions: \[ \frac{9}{20} + \frac{27}{20} \]
Since both fractions have the same denominator, we can directly add the numerators: \[ \frac{9 + 27}{20} = \frac{36}{20} \]
- To simplify \( \frac{36}{20} \), we can divide both the numerator and the denominator by their greatest common divisor (gcd), which is 4: \[ \frac{36 \div 4}{20 \div 4} = \frac{9}{5} \]
Therefore, the sum of the fractions \( \frac{9}{20} + 1 \frac{7}{20} \) is: \[ \frac{9}{5} \]