a) \( 4 \frac{1}{2}: 4= \) b) \( 8 \frac{1}{4}: 2= \)

To solve \( 4 \frac{1}{2} : 4 \), first convert \( 4 \frac{1}{2} \) to an improper fraction, which is \( \frac{9}{2} \). Now, divide \( \frac{9}{2} \) by \( 4 \), or multiply by its reciprocal \( \frac{1}{4} \): \[ \frac{9}{2} \times \frac{1}{4} = \frac{9}{8} = 1 \frac{1}{8}. \] Now for \( 8 \frac{1}{4} : 2 \), turn \( 8 \frac{1}{4} \) into an improper fraction, yielding \( \frac{33}{4} \). Next, divide by \( 2 \) or multiply by \( \frac{1}{2} \): \[ \frac{33}{4} \times \frac{1}{2} = \frac{33}{8} = 4 \frac{1}{8}. \] So the answers are: a) \( 1 \frac{1}{8} \) b) \( 4 \frac{1}{8} \)