1. **State the problem:** Add the mixed numbers $3 \frac{3}{10}$ and $2 \frac{1}{5}$. 2. **Convert mixed numbers to improper fractions:** $3 \frac{3}{10} = \frac{3 \times 10 + 3}{10} = \frac{33}{10}$ $2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$ 3. **Find a common denominator:** The denominators are 10 and 5. The least common denominator (LCD) is 10. 4. **Convert fractions to have the LCD:** $\frac{33}{10}$ stays the same. $\frac{11}{5} = \frac{11 \times 2}{5 \times 2} = \frac{22}{10}$ 5. **Add the fractions:** $$\frac{33}{10} + \frac{22}{10} = \frac{33 + 22}{10} = \frac{55}{10}$$ 6. **Simplify the fraction:** $$\frac{55}{10} = \frac{\cancel{55}}{\cancel{10}} = \frac{11}{2}$$ (Here, 55 and 10 are both divisible by 5.) 7. **Convert back to a mixed number:** $$\frac{11}{2} = 5 \frac{1}{2}$$ **Final answer:** $5 \frac{1}{2}$