$${\frac{3}{14}} : 9 = {\frac{3}{14}} \cdot {\frac{1}{9}} = {\frac{3}{14 \cdot 9}} = {\frac{3}{14 \cdot 3 \cdot 3}} = {\frac{1}{14 \cdot 3}} = {\frac{1}{42}}$$
Ответ: $$\frac{1}{42}$$