1. **State the problem:** Simplify the expression $\frac{4}{11} - \frac{1}{2}$.\n\n2. **Find a common denominator:** The denominators are 11 and 2. The least common denominator (LCD) is $11 \times 2 = 22$.\n\n3. **Rewrite each fraction with the LCD:**\n$$\frac{4}{11} = \frac{4 \times 2}{11 \times 2} = \frac{8}{22}$$\n$$\frac{1}{2} = \frac{1 \times 11}{2 \times 11} = \frac{11}{22}$$\n\n4. **Subtract the fractions:**\n$$\frac{8}{22} - \frac{11}{22} = \frac{8 - 11}{22} = \frac{-3}{22}$$\n\n5. **Simplify the fraction if possible:** The fraction $\frac{-3}{22}$ is already in simplest form.\n\n**Final answer:** $\boxed{\frac{-3}{22}}$