To multiply the mixed numbers \(2 \frac{1}{2}\) and \(3 \frac{1}{4}\), we first convert them to improper fractions.
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Convert \(2 \frac{1}{2}\) to an improper fraction: \[ 2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2} \]
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Convert \(3 \frac{1}{4}\) to an improper fraction: \[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \]
Now, multiply the two improper fractions: \[ \frac{5}{2} \times \frac{13}{4} = \frac{5 \times 13}{2 \times 4} = \frac{65}{8} \]
Next, we can convert \(\frac{65}{8}\) back to a mixed number:
- Divide \(65\) by \(8\): \(65 \div 8 = 8\) remainder \(1\)
- So, \(\frac{65}{8} = 8 \frac{1}{8}\)
The final answer is: \[ 2 \frac{1}{2} \times 3 \frac{1}{4} = 8 \frac{1}{8} \]