1. **State the problem:** Find half of one-fourth, i.e., calculate $\frac{1}{2}$ of $\frac{1}{4}$. 2. **Formula used:** To find a fraction of another fraction, multiply the two fractions: $$\text{Fraction of a fraction} = \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Apply the formula:** $$\frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8}$$ 4. **Explain simplification:** Here, the numerator is $1$ and the denominator is $8$. There are no common factors to cancel, so the fraction is already in simplest form. 5. **Final answer:** Half of one-fourth is $\frac{1}{8}$.