What is the sum of 3 5/8 + 4 1/4 + 6 1/2 + 7 1/8?

To find the sum of the mixed numbers 3 5/8, 4 1/4, 6 1/2, and 7 1/8, it's helpful to first convert each mixed number to an improper fraction. This method simplifies the addition process.

1. For 3 5/8, converting to an improper fraction gives us:

( 3 \times 8 + 5 = 24 + 5 = 29/8 )

2. For 4 1/4:

( 4 \times 4 + 1 = 16 + 1 = 17/4 )

3. For 6 1/2:

( 6 \times 2 + 1 = 12 + 1 = 13/2 )

4. For 7 1/8:

( 7 \times 8 + 1 = 56 + 1 = 57/8 )

Now, we need a common denominator to add these fractions. The least common multiple of the denominators (8, 4, 2) is 8.

Next, we convert each fraction to have a denominator of 8: