1. **State the problem:** Simplify the expression $\frac{x}{2} \div \frac{1}{2}$. 2. **Recall the division rule for fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{x}{2} \div \frac{1}{2} = \frac{x}{2} \times \frac{2}{1}.$$ 3. **Multiply the fractions:** Multiply numerators and denominators: $$\frac{x}{2} \times \frac{2}{1} = \frac{x \times 2}{2 \times 1} = \frac{2x}{2}.$$ 4. **Simplify the fraction:** Cancel the common factor 2 in numerator and denominator: $$\frac{\cancel{2}x}{\cancel{2}} = x.$$ 5. **Final answer:** The simplified expression is $x$.