1. The problem asks whether $\frac{2}{3}$ is the reciprocal of $-\frac{2}{3}$. 2. Recall that the reciprocal of a number $x$ is defined as $\frac{1}{x}$. 3. Let's find the reciprocal of $-\frac{2}{3}$. 4. The reciprocal is: $$\frac{1}{-\frac{2}{3}} = -\frac{3}{2}$$ 5. Compare this to $\frac{2}{3}$: $\frac{2}{3} \neq -\frac{3}{2}$ 6. Therefore, $\frac{2}{3}$ is not the reciprocal of $-\frac{2}{3}$. Final answer: No, $\frac{2}{3}$ is not the reciprocal of $-\frac{2}{3}$. The reciprocal of $-\frac{2}{3}$ is $-\frac{3}{2}$.