$$1 \frac{2}{7} \cdot 1 \frac{1}{4} = \frac{1 \cdot 7 + 2}{7} \cdot \frac{1 \cdot 4 + 1}{4} = \frac{9}{7} \cdot \frac{5}{4} = \frac{45}{28} = 1 \frac{17}{28}$$
Ответ: $$1 \frac{17}{28}$$