1. The problem is to add the fractions $\frac{1}{5}$ and $\frac{2}{5}$.\n\n2. When adding fractions with the same denominator, you add the numerators and keep the denominator the same. The formula is: $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$$ where $a$ and $b$ are numerators and $c$ is the common denominator.\n\n3. Applying the formula: $$\frac{1}{5} + \frac{2}{5} = \frac{1+2}{5}$$\n\n4. Simplify the numerator: $$\frac{3}{5}$$\n\n5. The final answer is $\frac{3}{5}$. This fraction cannot be simplified further because 3 and 5 have no common factors other than 1.