1. The problem is to simplify the expression $\frac{-5}{2} \times \frac{1}{2}$.\n\n2. Multiply the numerators together: $-5 \times 1 = -5$.\n\n3. Multiply the denominators together: $2 \times 2 = 4$.\n\n4. The product is therefore $\frac{-5}{4}$.\n\n5. This fraction cannot be simplified further because 5 and 4 have no common factors other than 1.\n\nFinal answer: $\frac{-5}{4}$