1. **State the problem:** Simplify the expression $\frac{1}{4} - \frac{1}{2}$.\n\n2. **Recall the rule for subtracting fractions:** To subtract fractions, they must have the same denominator. If they don't, find the least common denominator (LCD).\n\n3. **Find the LCD:** The denominators are 4 and 2. The LCD of 4 and 2 is 4.\n\n4. **Rewrite the fractions with the LCD:**\n$$\frac{1}{4} - \frac{1}{2} = \frac{1}{4} - \frac{2}{4}$$\n\n5. **Subtract the numerators:**\n$$\frac{1 - 2}{4} = \frac{-1}{4}$$\n\n6. **Final answer:** The simplified result is $\boxed{-\frac{1}{4}}$.