To find the sum of \(2 \frac{1}{5}\) and \(1 \frac{3}{5}\), we can first convert the mixed numbers into improper fractions:
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Convert \(2 \frac{1}{5}\): \[ 2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \]
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Convert \(1 \frac{3}{5}\): \[ 1 \frac{3}{5} = \frac{1 \times 5 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} \]
Now, we can add these two fractions:
\[ \frac{11}{5} + \frac{8}{5} = \frac{11 + 8}{5} = \frac{19}{5} \]
Next, we can convert \(\frac{19}{5}\) back to a mixed number:
\[ \frac{19}{5} = 3 \frac{4}{5} \]
Therefore, the sum of \(2 \frac{1}{5}\) and \(1 \frac{3}{5}\) is \(3 \frac{4}{5}\).