8. What fraction of \( 6 \frac{1}{2} \) is \( 8 \frac{1}{4} \) ?

To find what fraction of \( 6 \frac{1}{2} \) is \( 8 \frac{1}{4} \), we first convert the mixed numbers into improper fractions. For \( 6 \frac{1}{2} \): \[ 6 \frac{1}{2} = 6 \times 2 + 1 = 12 + 1 = 13 \quad \text{thus, } \quad 6 \frac{1}{2} = \frac{13}{2} \] For \( 8 \frac{1}{4} \): \[ 8 \frac{1}{4} = 8 \times 4 + 1 = 32 + 1 = 33 \quad \text{thus, } \quad 8 \frac{1}{4} = \frac{33}{4} \] Next, we determine what fraction \( \frac{33}{4} \) is of \( \frac{13}{2} \). This requires us to divide \( \frac{33}{4} \) by \( \frac{13}{2} \): \[ \text{Fraction} = \frac{\frac{33}{4}}{\frac{13}{2}} = \frac{33}{4} \times \frac{2}{13} = \frac{33 \times 2}{4 \times 13} = \frac{66}{52} \] Now we simplify \( \frac{66}{52} \). Both 66 and 52 can be divided by 2: \[ \frac{66 \div 2}{52 \div 2} = \frac{33}{26} \] Thus, \( 8 \frac{1}{4} \) is \( \frac{33}{26} \) of \( 6 \frac{1}{2} \).