1. **Problem:** Solve $\frac{4}{3} + \frac{2}{5}$. 2. **Formula:** To add fractions with unlike denominators, find the least common denominator (LCD), convert each fraction, then add numerators. 3. **Step 1:** Find LCD of 3 and 5, which is 15. 4. **Step 2:** Convert fractions: $$\frac{4}{3} = \frac{4 \times 5}{3 \times 5} = \frac{20}{15}$$ $$\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}$$ 5. **Step 3:** Add numerators: $$\frac{20}{15} + \frac{6}{15} = \frac{20 + 6}{15} = \frac{26}{15}$$ 6. **Step 4:** Simplify if possible. $26$ and $15$ have no common factors other than 1, so answer is $\frac{26}{15}$ or $1 \frac{11}{15}$. **Final answer:** $\frac{26}{15}$ or $1 \frac{11}{15}$.