1. Calculate $\frac{3}{10} + \frac{1}{5}$. Step 1: State the problem. We need to add two fractions: $\frac{3}{10}$ and $\frac{1}{5}$. Step 2: Find a common denominator. The denominators are 10 and 5. The least common denominator (LCD) is 10. Step 3: Convert $\frac{1}{5}$ to have denominator 10. $$\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}$$ Step 4: Add the fractions. $$\frac{3}{10} + \frac{2}{10} = \frac{3+2}{10} = \frac{5}{10}$$ Step 5: Simplify the fraction. $$\frac{5}{10} = \frac{1}{2}$$ Final answer: $\frac{1}{2}$. This problem involves adding fractions by finding a common denominator, converting fractions, adding numerators, and simplifying the result.