1. **State the problem:** Divide $\frac{1}{2}$ by $\frac{1}{4}$. Write the answer in simplest form. 2. **Recall the division rule for fractions:** To divide by a fraction, multiply by its reciprocal. 3. **Apply the rule:** $$\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1}$$ 4. **Multiply the numerators and denominators:** $$= \frac{1 \times 4}{2 \times 1} = \frac{4}{2}$$ 5. **Simplify the fraction:** $$= \frac{\cancel{4}^{2} \times 2}{\cancel{2}^{1} \times 2} = \frac{2}{1} = 2$$ 6. **Final answer:** $$\boxed{2}$$