О $$2\frac{3}{4}-1\frac{1}{9}:\frac{5}{27}+\frac{5}{6}$$

Выполним действия с дробями.

1. $$1\frac{1}{9}:\frac{5}{27}=\frac{10}{9}:\frac{5}{27}=\frac{10}{9} \cdot \frac{27}{5}=\frac{10 \cdot 27}{9 \cdot 5}=\frac{270}{45}=6$$
2. $$2\frac{3}{4}=\frac{11}{4}$$
3. $$\frac{11}{4}-6=\frac{11}{4}-\frac{6 \cdot 4}{4}=\frac{11}{4}-\frac{24}{4}=-\frac{13}{4}=-3\frac{1}{4}$$
4. $$-3\frac{1}{4}+\frac{5}{6}=-\frac{13}{4}+\frac{5}{6}=-\frac{13 \cdot 3}{4 \cdot 3}+\frac{5 \cdot 2}{6 \cdot 2}=-\frac{39}{12}+\frac{10}{12}=-\frac{29}{12}=-2\frac{5}{12}$$

Ответ: $$-2\frac{5}{12}$$