To add \( \frac{5}{8} \) plus \( 2 \) (whole) plus \( \frac{1}{5} \), we first convert all numbers to a common denominator.
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Convert \( 2 \) (whole) to a fraction: \[ 2 = \frac{2 \times 40}{40} = \frac{80}{40} \]
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Next, we need a common denominator for \( \frac{5}{8} \) and \( \frac{1}{5} \). The least common multiple of \( 8 \) and \( 5 \) is \( 40 \).
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Convert \( \frac{5}{8} \) to a fraction with a denominator of \( 40 \): \[ \frac{5}{8} = \frac{5 \times 5}{8 \times 5} = \frac{25}{40} \]
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Convert \( \frac{1}{5} \) to a fraction with a denominator of \( 40 \): \[ \frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40} \]
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Now we can add them together: \[ \frac{25}{40} + \frac{80}{40} + \frac{8}{40} = \frac{25 + 80 + 8}{40} = \frac{113}{40} \]
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Finally, we can convert \( \frac{113}{40} \) to a mixed number: \[ 113 \div 40 = 2 \quad \text{remainder } 33 \] So, \( \frac{113}{40} = 2 \frac{33}{40} \).
Thus, the final answer is: \[ 2 \frac{33}{40} \]