\[1\frac{4}{35} \cdot 1\frac{2}{13} = \frac{39}{35} \cdot \frac{15}{13} = \frac{3 \cdot 13 \cdot 5 \cdot 3}{7 \cdot 5 \cdot 13} =\]
\[= \frac{9}{7} = 1\frac{2}{7}\]