1. **State the problem:** Add the fractions $\frac{3}{9}$ and $\frac{5}{9}$. 2. **Formula used:** When adding fractions with the same denominator, add the numerators and keep the denominator the same: $$\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$$ 3. **Apply the formula:** Here, both fractions have denominator 9, so add numerators 3 and 5: $$\frac{3}{9} + \frac{5}{9} = \frac{3+5}{9} = \frac{8}{9}$$ 4. **Simplify if possible:** $\frac{8}{9}$ is already in simplest form because 8 and 9 have no common factors other than 1. 5. **Final answer:** $$\frac{3}{9} + \frac{5}{9} = \frac{8}{9}$$