Question

3 5/8 x 4 1/2 as a mixed fraction

Answer 1

To multiply the mixed numbers \(3 \frac{5}{8}\) and \(4 \frac{1}{2}\), we first convert each mixed number into an improper fraction.

1. **Convert \(3 \frac{5}{8}\) to an improper fraction:**
\[
3 \frac{5}{8} = \frac{3 \times 8 + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8}
\]

2. **Convert \(4 \frac{1}{2}\) to an improper fraction:**
\[
4 \frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}
\]

3. **Multiply the two improper fractions:**
\[
\frac{29}{8} \times \frac{9}{2} = \frac{29 \times 9}{8 \times 2} = \frac{261}{16}
\]

4. **Convert \(\frac{261}{16}\) back to a mixed number:**
Divide 261 by 16:
- \(261 \div 16 = 16\) (whole number part)
- Remainder: \(261 - (16 \times 16) = 261 - 256 = 5\)

So,
\[
\frac{261}{16} = 16 \frac{5}{16}
\]

Thus, the product of \(3 \frac{5}{8}\) and \(4 \frac{1}{2}\) as a mixed fraction is \(16 \frac{5}{16}\).