1. The problem is to simplify the fraction $\frac{4}{9}$ and check if it can be expressed as $\frac{2}{3}$.\n\n2. The formula for simplifying fractions is to divide the numerator and denominator by their greatest common divisor (GCD).\n\n3. Find the GCD of 4 and 9. Since 4 factors as $2^2$ and 9 factors as $3^2$, they have no common factors other than 1. So, $\text{GCD}(4,9) = 1$.\n\n4. Simplify the fraction by dividing numerator and denominator by 1:\n$$\frac{\cancel{4}}{\cancel{9}} = \frac{4}{9}$$\nNo change occurs, so $\frac{4}{9}$ is already in simplest form.\n\n5. Compare $\frac{4}{9}$ with $\frac{2}{3}$ by cross-multiplying:\n$$4 \times 3 = 12 \quad \text{and} \quad 2 \times 9 = 18$$\nSince 12 $\neq$ 18, $\frac{4}{9} \neq \frac{2}{3}$.\n\nFinal answer: $\frac{4}{9}$ cannot be simplified to $\frac{2}{3}$; they are different fractions.