1. **State the problem:** Add the mixed numbers $3\frac{3}{5}$ and $2\frac{2}{15}$. 2. **Convert mixed numbers to improper fractions:** $3\frac{3}{5} = \frac{3 \times 5 + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}$ $2\frac{2}{15} = \frac{2 \times 15 + 2}{15} = \frac{30 + 2}{15} = \frac{32}{15}$ 3. **Find a common denominator:** The denominators are 5 and 15. The least common denominator (LCD) is 15. 4. **Convert fractions to have the same denominator:** $\frac{18}{5} = \frac{18 \times 3}{5 \times 3} = \frac{54}{15}$ $\frac{32}{15}$ stays the same. 5. **Add the fractions:** $\frac{54}{15} + \frac{32}{15} = \frac{54 + 32}{15} = \frac{86}{15}$ 6. **Convert the improper fraction back to a mixed number:** Divide 86 by 15: $86 \div 15 = 5$ remainder $11$, so $\frac{86}{15} = 5\frac{11}{15}$ **Final answer:** $5\frac{11}{15}$