$$4\frac{1}{2} : 6\frac{3}{4} = \frac{4 \cdot 2 + 1}{2} : \frac{6 \cdot 4 + 3}{4} = \frac{9}{2} : \frac{27}{4} = \frac{9}{2} \cdot \frac{4}{27} = \frac{9 \cdot 4}{2 \cdot 27} = \frac{9 \cdot 2 \cdot 2}{2 \cdot 9 \cdot 3} = \frac{2}{3}$$
Ответ: 2/3