$${\frac{3}{7}} : {\frac{9}{14}} = {\frac{3}{7}} \cdot {\frac{14}{9}} = {\frac{3 \cdot 14}{7 \cdot 9}} = {\frac{3 \cdot 2 \cdot 7}{7 \cdot 3 \cdot 3}} = {\frac{2}{3}}$$
Ответ: $$\frac{2}{3}$$