To add the fractions \( \frac{5}{1} \) and \( \frac{1}{2} \) with the same denominator \(2\), we first need to express \( \frac{5}{1} \) with a denominator of \(2\).
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Convert \( \frac{5}{1} \) to have a denominator of \(2\): \[ \frac{5}{1} = \frac{5 \times 2}{1 \times 2} = \frac{10}{2} \]
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Now, we can add the fractions with the same denominator: \[ \frac{10}{2} + \frac{1}{2} = \frac{10 + 1}{2} = \frac{11}{2} \]
So, the sum is \( \frac{11}{2} \).