1. **Problem:** Solve $\frac{1}{2} \div \frac{1}{4}$ using a model and calculation. 2. **Formula:** Dividing fractions means multiplying the first fraction by the reciprocal of the second: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 3. **Apply the formula:** $$\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1}$$ 4. **Multiply numerators and denominators:** $$\frac{1 \times 4}{2 \times 1} = \frac{4}{2}$$ 5. **Simplify the fraction:** $$\frac{\cancel{4}}{\cancel{2}} = 2$$ 6. **Explanation:** Dividing $\frac{1}{2}$ by $\frac{1}{4}$ asks how many $\frac{1}{4}$ parts fit into $\frac{1}{2}$. Since $\frac{1}{2}$ is twice as big as $\frac{1}{4}$, the answer is 2. **Final answer:** $$\boxed{2}$$