Question
Multiply. \[ 4 \frac{1}{2} \times \frac{1}{4} \] Write your answer as a mixed number in simplest form.
Ask by Lowe Pierce. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \( 1 \frac{1}{8} \).
Solution
To multiply the mixed number \( 4 \frac{1}{2} \) by \( \frac{1}{4} \), follow these steps:
1. **Convert the Mixed Number to an Improper Fraction:**
\( 4 \frac{1}{2} = \frac{(4 \times 2) + 1}{2} = \frac{9}{2} \)
2. **Multiply the Fractions:**
\[
\frac{9}{2} \times \frac{1}{4} = \frac{9 \times 1}{2 \times 4} = \frac{9}{8}
\]
3. **Convert the Improper Fraction to a Mixed Number:**
\[
\frac{9}{8} = 1 \frac{1}{8}
\]
**Final Answer:**
\[
1 \frac{1}{8}
\]
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Simplify this solution The Deep Dive
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: \[ \boxed{1 \frac{1}{8}} \]
