1.006. \(\frac{\left(13,75+\frac{9}{4}\right)\cdot1,2}+\frac{\left(6,8-\frac{3}{5}\right)\cdot\frac{5}{6}}}{\left(10,3-8\frac{1}{2}\right)\cdot\frac{5}{9}}+\frac{\left(\frac{2}{3}-3\frac{1}{6}\right)\cdot56}-27\frac{1}{6}= ?\)

Решение:

1. Вычислим числитель первой дроби:

\(\left(13,75+\frac{9}{4}\right)\cdot1,2 = \left(\frac{1375}{100}+\frac{9}{4}\right)\cdot\frac{12}{10} = \left(\frac{55}{4}+\frac{9}{4}\right)\cdot\frac{6}{5} = \frac{64}{4}\cdot\frac{6}{5} = 16\cdot\frac{6}{5} = \frac{96}{5}\)

\(\frac{\left(6,8-\frac{3}{5}\right)\cdot\frac{5}{6}} = \left(\frac{68}{10}-\frac{3}{5}\right)\cdot\frac{5}{6} = \left(\frac{34}{5}-\frac{3}{5}\right)\cdot\frac{5}{6} = \frac{31}{5}\cdot\frac{5}{6} = \frac{31}{6}\)

\(\frac{96}{5}+\frac{31}{6} = \frac{576+155}{30} = \frac{731}{30}\)

2. Вычислим знаменатель первой дроби:

\(\left(10,3-8\frac{1}{2}\right)\cdot\frac{5}{9} = \left(\frac{103}{10}-\frac{17}{2}\right)\cdot\frac{5}{9} = \left(\frac{103-85}{10}\right)\cdot\frac{5}{9} = \frac{18}{10}\cdot\frac{5}{9} = \frac{9}{5}\cdot\frac{5}{9} = 1\)

3. Вычислим вторую часть дроби:

\(\left(\frac{2}{3}-3\frac{1}{6}\right)\cdot56 = \left(\frac{2}{3}-\frac{19}{6}\right)\cdot56 = \left(\frac{4-19}{6}\right)\cdot56 = -\frac{15}{6}\cdot56 = -\frac{5}{2}\cdot56 = -5\cdot28 = -140\)

4. Объединим все части:

\(\frac{\frac{731}{30}}{1} + (-140) - 27\frac{1}{6} = \frac{731}{30} - 140 - \frac{163}{6} = \frac{731 - 4200 - 815}{30} = \frac{731 - 5015}{30} = \frac{-4284}{30} = -142,8\)

Ответ: -142,8.