\[3\frac{8}{9}\ :2\frac{13}{18} = \frac{35}{9}\ :\frac{49}{18} = \frac{35}{9} \cdot \frac{18}{45} =\]
\[= \frac{7 \cdot 2}{9} = \frac{14}{9} = 1\frac{5}{9}.\]