To simplify the mixed fraction \(41 \frac{2}{2}\), we first need to combine the whole number and the fraction.
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Convert \(41\) to a fraction: \[ 41 = \frac{41 \times 2}{2} = \frac{82}{2} \]
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Add the fraction \(\frac{2}{2}\) to \(\frac{82}{2}\): \[ \frac{82}{2} + \frac{2}{2} = \frac{84}{2} \]
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Now, simplify \(\frac{84}{2}\): \[ \frac{84}{2} = 42 \]
Thus, the mixed fraction \(41 \frac{2}{2}\) simplifies to \(42\).