Let's solve the expression $\frac{2}{2} \div \frac{3}{2} \div \frac{2}{3}$.

We can break this down step by step:

1. Simplify the first fraction: $\frac{2}{2} = 1$

2. Simplify the expression: $1 \div \frac{3}{2} \div \frac{2}{3}$

3. Dividing by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal. So, we rewrite the division: $1 \times \frac{2}{3} \times \frac{3}{2}$

4. Multiply the fractions: $\frac{2}{3} \times \frac{3}{2} = \frac{2 \times 3}{3 \times 2} = \frac{6}{6} = 1$

So, the value of the expression $\frac{2}{2} \div \frac{3}{2} \div \frac{2}{3}$ is 1.

Would you like further details or have any questions?

Here are five related questions:

1. What is the result of $\frac{3}{4} \div \frac{4}{3}$?
2. How do you multiply two fractions together?
3. What happens when you divide a fraction by itself?
4. Can you simplify $\frac{5}{10}$ before performing operations?
5. How does the order of operations affect fraction division?

Tip: When dividing by a fraction, always remember to multiply by its reciprocal for easier calculation.