To find the sum of \( 6 \frac{3}{5} \) and \( 2 \frac{4}{5} \), we can first convert the mixed numbers into improper fractions.
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Convert \( 6 \frac{3}{5} \): \[ 6 \frac{3}{5} = 6 \times 5 + 3 = 30 + 3 = 33 \] So, \( 6 \frac{3}{5} = \frac{33}{5} \).
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Convert \( 2 \frac{4}{5} \): \[ 2 \frac{4}{5} = 2 \times 5 + 4 = 10 + 4 = 14 \] So, \( 2 \frac{4}{5} = \frac{14}{5} \).
Now, we can add the two improper fractions: \[ \frac{33}{5} + \frac{14}{5} = \frac{33 + 14}{5} = \frac{47}{5} \]
Next, we can convert \( \frac{47}{5} \) back into a mixed number. Divide 47 by 5: \[ 47 \div 5 = 9 \quad \text{(whole number)} \quad \text{with a remainder of } 2. \] Thus, \( \frac{47}{5} = 9 \frac{2}{5} \).
So, the sum of \( 6 \frac{3}{5} \) and \( 2 \frac{4}{5} \) is: \[ \boxed{9 \frac{2}{5}}. \]