1. The problem is to add the two fractions $\frac{4}{9}$ and $\frac{7}{9}$. 2. Since the denominators are the same (9), we can add the numerators directly. 3. Add the numerators: $4 + 7 = 11$. 4. Place the sum over the common denominator: $\frac{11}{9}$. 5. The resulting fraction is an improper fraction, which can also be written as a mixed number. 6. Divide 11 by 9: $11 \div 9 = 1$ remainder $2$. 7. Write as a mixed number: $1 \frac{2}{9}$. Final answer: $\frac{11}{9}$ or $1 \frac{2}{9}$.