To multiply the mixed number \(2 \frac{1}{4}\) by \(5\), we first convert the mixed number into an improper fraction.
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Convert \(2 \frac{1}{4}\) to an improper fraction: \[ 2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4} \]
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Now, multiply \(\frac{9}{4}\) by \(5\): \[ \frac{9}{4} \times 5 = \frac{9 \times 5}{4} = \frac{45}{4} \]
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Convert \(\frac{45}{4}\) back to a mixed number:
- Divide \(45\) by \(4\): \[ 45 \div 4 = 11 \quad \text{(with a remainder of } 1\text{)} \]
- So, \(45 = 4 \times 11 + 1\), which gives us the mixed number \(11 \frac{1}{4}\).
Thus, the answer in simplest form is: \[ \boxed{11 \frac{1}{4}} \]
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