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The product is 22.
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To find the product of \( 4 \times 5 \frac{1}{2} \), we first convert the mixed number \( 5 \frac{1}{2} \) into an improper fraction. This gives us \( 5 \frac{1}{2} = \frac{11}{2} \). Now, we can multiply: \( 4 \times \frac{11}{2} = \frac{4 \times 11}{2} = \frac{44}{2} = 22 \). The product is \( 22 \).