1. Let's clarify the factoring process where $\frac{1}{3}$ was factored out. 2. Suppose you have an expression like $\frac{1}{3}x + \frac{2}{3}y$. 3. Factoring out $\frac{1}{3}$ means rewriting it as $\frac{1}{3}(x + 2y)$. 4. The $\frac{1}{3}$ is factored out and placed in front of the parentheses. 5. Inside the parentheses, the terms are simplified by dividing each original term by $\frac{1}{3}$. 6. This is why the $\frac{1}{3}$ disappears from inside the parentheses but remains multiplied outside. 7. So, the $\frac{1}{3}$ didn't vanish; it was just moved outside the parentheses as a common factor. 8. This is a standard factoring technique to simplify expressions and make them easier to work with.