1. **Stating the problem:** We need to find half of a quilt that is itself half of 2. 2. **Understanding the problem:** The phrase "1/2 of a quilt 1/2 2" can be interpreted as finding $\frac{1}{2}$ of $\frac{1}{2}$ of 2. 3. **Formula used:** To find a fraction of a number, multiply the fraction by the number. 4. **Calculation:** $$\frac{1}{2} \times \frac{1}{2} \times 2$$ 5. **Simplify step-by-step:** $$= \frac{1}{2} \times \cancel{\frac{1}{2} \times 2}$$ $$= \frac{1}{2} \times 1$$ $$= \frac{1}{2}$$ 6. **Explanation:** Multiplying $\frac{1}{2}$ by 2 cancels out to 1, then multiplying by the remaining $\frac{1}{2}$ gives $\frac{1}{2}$. 7. **Final answer:** $$\boxed{\frac{1}{2}}$$