1. **State the problem:** Multiply $\frac{1}{2}$ by 58.5. 2. **Formula used:** Multiplication of a fraction by a number is given by: $$\text{Result} = \frac{a}{b} \times c = \frac{a \times c}{b}$$ 3. **Apply the formula:** Here, $a=1$, $b=2$, and $c=58.5$. $$\frac{1}{2} \times 58.5 = \frac{1 \times 58.5}{2}$$ 4. **Calculate the numerator:** $$1 \times 58.5 = 58.5$$ 5. **Divide by the denominator:** $$\frac{58.5}{2} = 29.25$$ 6. **Final answer:** $$\boxed{29.25}$$ This means half of 58.5 is 29.25.