We are asked to evaluate the expression $-\frac{1}{5} + 2\frac{4}{5}$.

1. Problem Description

We are asked to evaluate the expression $-\frac{1}{5} + 2\frac{4}{5}$.

2. Solution Steps

First, convert the mixed number $2\frac{4}{5}$ to an improper fraction.

$2\frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10+4}{5} = \frac{14}{5}$

Now we have

$-\frac{1}{5} + \frac{14}{5}$

Since the denominators are the same, we can combine the numerators:

$-\frac{1}{5} + \frac{14}{5} = \frac{-1+14}{5} = \frac{13}{5}$

Now, convert the improper fraction $\frac{13}{5}$ back to a mixed number.

$\frac{13}{5} = \frac{10+3}{5} = \frac{10}{5} + \frac{3}{5} = 2 + \frac{3}{5} = 2\frac{3}{5}$

3. Final Answer

$2\frac{3}{5}$