1. The problem is to add the mixed numbers $2 \frac{3}{5}$ and $1 \frac{2}{5}$. 2. First, convert the mixed numbers to improper fractions. For $2 \frac{3}{5}$: $$2 \times 5 + 3 = 10 + 3 = 13$$ so it becomes $\frac{13}{5}$. For $1 \frac{2}{5}$: $$1 \times 5 + 2 = 5 + 2 = 7$$ so it becomes $\frac{7}{5}$. 3. Now add the improper fractions: $$\frac{13}{5} + \frac{7}{5} = \frac{13 + 7}{5} = \frac{20}{5}$$. 4. Simplify the fraction by dividing numerator and denominator by 5: $$\frac{\cancel{20}^4}{\cancel{5}^1} = 4$$. 5. The final answer is $4$.