$$38\frac{6}{11} : 2 = (38:2) + (\frac{6}{11} : 2) = 19 + \frac{6}{11 \cdot 2} = 19 + \frac{6}{22} = 19 + \frac{3}{11} = 19\frac{3}{11}$$
Ответ: $$19\frac{3}{11}$$