11. \(2 \frac{5}{6} - 3 \frac{4}{5} * 1 \frac{1}{9}\) : (-3,75) =

Преобразуем смешанные числа в неправильные дроби:
2 \(\frac{5}{6}\) = \(\frac{2*6 + 5}{6}\) = \(\frac{17}{6}\)
3 \(\frac{4}{5}\) = \(\frac{3*5 + 4}{5}\) = \(\frac{19}{5}\)
1 \(\frac{1}{9}\) = \(\frac{1*9 + 1}{9}\) = \(\frac{10}{9}\)
Подставим в выражение:
\(\frac{17}{6} - \frac{19}{5} * \frac{10}{9}\) : (-3,75) = \(\frac{17}{6} - \frac{19*10}{5*9}\) : (-3,75) = \(\frac{17}{6} - \frac{19*2}{1*9}\) : (-3,75) = \(\frac{17}{6} - \frac{38}{9}\) : (-3,75)
Приведем дроби к общему знаменателю (18):
\(\frac{17*3}{6*3} - \frac{38*2}{9*2}\) : (-3,75) = \(\frac{51}{18} - \frac{76}{18}\) : (-3,75) = -\(\frac{25}{18}\) : (-3,75) = -\(\frac{25}{18}\) : \(- \frac{375}{100}\) = -\(\frac{25}{18}\) * \(- \frac{100}{375}\) = \(\frac{25*100}{18*375}\) = \(\frac{25*4}{18*15}\) = \(\frac{100}{270}\) = \(\frac{10}{27}\)

Ответ: \(\frac{10}{27}\)