To solve \( 4\frac{1}{5} - 2\frac{2}{5} \), we can first convert the mixed numbers into improper fractions.
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Convert \( 4\frac{1}{5} \): \[ 4\frac{1}{5} = 4 \times 5 + 1 = 20 + 1 = 21 \] So, \( 4\frac{1}{5} = \frac{21}{5} \).
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Convert \( 2\frac{2}{5} \): \[ 2\frac{2}{5} = 2 \times 5 + 2 = 10 + 2 = 12 \] So, \( 2\frac{2}{5} = \frac{12}{5} \).
Now we can subtract the two improper fractions: \[ \frac{21}{5} - \frac{12}{5} = \frac{21 - 12}{5} = \frac{9}{5} \]
Next, we can convert \( \frac{9}{5} \) back to a mixed number: \[ \frac{9}{5} = 1\frac{4}{5} \]
Therefore, the solution to \( 4\frac{1}{5} - 2\frac{2}{5} \) is: \[ \boxed{1\frac{4}{5}} \]