$$1\frac{1}{6}:2\frac{1}{4}=\frac{7}{6}:\frac{9}{4}=\frac{7}{6}\cdot \frac{4}{9}=\frac{7\cdot 4}{6 \cdot 9}=\frac{7\cdot 2}{3 \cdot 9}=\frac{14}{27}$$
Ответ: $$\frac{14}{27}$$