1. **Stating the problem:** What fraction of a wall can be painted if you can paint $\frac{4}{9}$ of the wall in $\frac{3}{4}$ of an hour? 2. **Understanding the problem:** We want to find the fraction of the wall painted in 1 full hour. 3. **Formula used:** If $\text{fraction painted} = \frac{4}{9}$ in $\frac{3}{4}$ hour, then the rate of painting per hour is: $$\text{rate} = \frac{\frac{4}{9}}{\frac{3}{4}} = \frac{4}{9} \times \frac{4}{3}$$ 4. **Calculating the rate:** Multiply the fractions: $$\frac{4}{9} \times \frac{4}{3} = \frac{4 \times 4}{9 \times 3} = \frac{16}{27}$$ 5. **Interpretation:** This means you can paint $\frac{16}{27}$ of the wall in 1 hour. **Final answer:** $$\boxed{\frac{16}{27}}$$