Multiply. \[ 4 \frac{1}{2} \times \frac{1}{4} \] Write your answer as a mixed number in simplest form.

To multiply \(4 \frac{1}{2} \times \frac{1}{4}\), first convert the mixed number into an improper fraction. The mixed number \(4 \frac{1}{2}\) can be expressed as: \[ 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \] Now, we multiply \( \frac{9}{2} \) by \( \frac{1}{4} \): \[ \frac{9}{2} \times \frac{1}{4} = \frac{9 \times 1}{2 \times 4} = \frac{9}{8} \] Next, convert \( \frac{9}{8} \) into a mixed number. Since \(9\) divided by \(8\) is \(1\) with a remainder of \(1\): \[ \frac{9}{8} = 1 \frac{1}{8} \] Thus, the answer is: \[ \boxed{1 \frac{1}{8}} \]