Выполним вычитание:
$$11 - 1\frac{11}{38} = 11 - \frac{1 \cdot 38 + 11}{38} = 11 - \frac{38 + 11}{38} = 11 - \frac{49}{38} = \frac{11 \cdot 38}{38} - \frac{49}{38} = \frac{418}{38} - \frac{49}{38} = \frac{418 - 49}{38} = \frac{369}{38} = 9 \frac{27}{38}$$
Ответ: $$9 \frac{27}{38}$$