1. **State the problem:** Multiply the fraction $\frac{3}{4}$ by 300. 2. **Formula used:** To multiply a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same: $$\frac{a}{b} \times c = \frac{a \times c}{b}$$ 3. **Apply the formula:** $$\frac{3}{4} \times 300 = \frac{3 \times 300}{4}$$ 4. **Calculate the numerator:** $$3 \times 300 = 900$$ 5. **Substitute back:** $$\frac{900}{4}$$ 6. **Simplify the fraction by dividing numerator and denominator by 2:** $$\frac{\cancel{900}^{\div 2}}{\cancel{4}^{\div 2}} = \frac{450}{2}$$ 7. **Simplify again by dividing numerator and denominator by 2:** $$\frac{\cancel{450}^{\div 2}}{\cancel{2}^{\div 2}} = \frac{225}{1} = 225$$ 8. **Final answer:** $$225$$