5 4/32 + 9/16

To add \( 5 \frac{4}{32} \) and \( \frac{9}{16} \), we first convert the mixed number into an improper fraction.

1. Convert \( 5 \frac{4}{32} \) to an improper fraction: \[ 5 \frac{4}{32} = \frac{5 \times 32 + 4}{32} = \frac{160 + 4}{32} = \frac{164}{32} \]

2. Next, we need a common denominator to add \( \frac{164}{32} \) and \( \frac{9}{16} \). The least common multiple of 32 and 16 is 32.

3. Convert \( \frac{9}{16} \) to have a denominator of 32: \[ \frac{9}{16} = \frac{9 \times 2}{16 \times 2} = \frac{18}{32} \]

4. Now add the two fractions: \[ \frac{164}{32} + \frac{18}{32} = \frac{164 + 18}{32} = \frac{182}{32} \]

5. Simplify \( \frac{182}{32} \): \[ \frac{182 \div 2}{32 \div 2} = \frac{91}{16} \]

The final result is: \[ \frac{91}{16} \]

If you prefer it as a mixed number: \[ 91 \div 16 = 5 \quad \text{with a remainder of } 11, \quad \text{so} \quad \frac{91}{16} = 5 \frac{11}{16} \]

Therefore, \( 5 \frac{4}{32} + \frac{9}{16} = \frac{91}{16} \) or \( 5 \frac{11}{16} \).