1 3/32 + 5/8

To add \( 1 \frac{3}{32} \) and \( \frac{5}{8} \), we can first convert \( 1 \frac{3}{32} \) into an improper fraction.

1. Convert \( 1 \frac{3}{32} \) to an improper fraction: \[ 1 \frac{3}{32} = \frac{32 \cdot 1 + 3}{32} = \frac{32 + 3}{32} = \frac{35}{32} \]

2. Now we add \( \frac{35}{32} \) and \( \frac{5}{8} \). We need a common denominator. The least common multiple of 32 and 8 is 32.

3. Convert \( \frac{5}{8} \) to have a denominator of 32: \[ \frac{5}{8} = \frac{5 \cdot 4}{8 \cdot 4} = \frac{20}{32} \]

4. Now we can add the two fractions: \[ \frac{35}{32} + \frac{20}{32} = \frac{35 + 20}{32} = \frac{55}{32} \]

5. Convert \( \frac{55}{32} \) back to a mixed number:

   • \( 55 \div 32 = 1 \) with a remainder of \( 23 \). Thus, \[ \frac{55}{32} = 1 \frac{23}{32} \]

So, the final answer is: \[ 1 \frac{23}{32} \]