To solve $1 \frac{4}{5} + 2 \frac{1}{5}$:

1. Convert the mixed numbers to improper fractions:

   $1 \frac{4}{5} = \frac{9}{5}$

   $2 \frac{1}{5} = \frac{11}{5}$

2. Add the fractions:

   $\frac{9}{5} + \frac{11}{5} = \frac{20}{5}$

3. Simplify:

   $\frac{20}{5} = 4$

So, $1 \frac{4}{5} + 2 \frac{1}{5} = 4$.