Question
Multiply. \[ \frac{3}{4} \times 4 \frac{1}{2} \] Write your answer as a mixed number in simplest form.
Ask by Pierce Malone. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The answer is \(3 \frac{3}{8}\).
Solution
To multiply \(\frac{3}{4}\) by \(4 \frac{1}{2}\), 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:**
\[
\frac{3}{4} \times \frac{9}{2} = \frac{3 \times 9}{4 \times 2} = \frac{27}{8}
\]
3. **Convert the improper fraction back to a mixed number:**
\[
\frac{27}{8} = 3 \frac{3}{8}
\]
**Final Answer:** \(3 \frac{3}{8}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To multiply \( \frac{3}{4} \) by \( 4 \frac{1}{2} \), we first need to convert \( 4 \frac{1}{2} \) into an improper fraction. The mixed number \( 4 \frac{1}{2} \) can be rewritten as: \[ 4 \times 2 + 1 = 8 + 1 = 9 \] So, \( 4 \frac{1}{2} = \frac{9}{2} \). Now, we multiply: \[ \frac{3}{4} \times \frac{9}{2} = \frac{3 \times 9}{4 \times 2} = \frac{27}{8} \] Next, we convert \( \frac{27}{8} \) back into a mixed number. We divide 27 by 8, which goes 3 times (since \( 3 \times 8 = 24 \)) with a remainder of: \[ 27 - 24 = 3 \] Thus, we can express \( \frac{27}{8} \) as: \[ 3 \frac{3}{8} \] The final answer in simplest form is: \[ \boxed{3 \frac{3}{8}} \]
