1. **State the problem:** We have a flour to sugar ratio of 4 cups flour to 1 cup sugar. We want to find how much sugar is needed if we use 2 cups of flour. 2. **Formula and explanation:** The ratio means for every 4 cups of flour, there is 1 cup of sugar. We can write this as a fraction: $$\frac{\text{sugar}}{\text{flour}} = \frac{1}{4}$$ 3. **Set up the proportion:** Let $x$ be the amount of sugar needed for 2 cups of flour. $$\frac{x}{2} = \frac{1}{4}$$ 4. **Solve for $x$:** Multiply both sides by 2: $$x = 2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$ 5. **Interpretation:** You need $\frac{1}{2}$ cup of sugar when using 2 cups of flour. **Final answer:** $\boxed{\frac{1}{2}}$ cup of sugar.