1. The problem is to subtract the fractions $\frac{1}{2}$ and $\frac{1}{8}$. 2. To subtract fractions, they must have a common denominator. The denominators here are 2 and 8. 3. The least common denominator (LCD) of 2 and 8 is 8. 4. Convert $\frac{1}{2}$ to an equivalent fraction with denominator 8: $$\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}$$ 5. Now subtract the fractions: $$\frac{4}{8} - \frac{1}{8} = \frac{4 - 1}{8} = \frac{3}{8}$$ 6. The result is $\frac{3}{8}$, which is already in simplest form. Final answer: $\frac{3}{8}$