The expression $\frac{1}{2} \div 2$ can be simplified as follows:

1. Division by a number is equivalent to multiplying by its reciprocal. So, $\frac{1}{2} \div 2$ is the same as $\frac{1}{2} \times \frac{1}{2}$.

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

So, $\frac{1}{2} \div 2 = \frac{1}{4}$.

Would you like further details or have any questions?

Here are five related questions:

1. What is $\frac{1}{4} \div 2$?
2. How do you divide fractions in general?
3. What is $2 \div \frac{1}{2}$?
4. How do you simplify $\frac{1}{2} \times \frac{1}{3}$?
5. What is $\frac{3}{4} \div \frac{1}{2}$?

Tip: Always remember that dividing by a number is the same as multiplying by its reciprocal!