1.006. (13,75+9\frac{1}{6})\cdot 1,2\frac{(6,8-3\frac{2}{3})\cdot 5\frac{5}{6}}{(10,3-8\frac{5}{9}):\frac{5}{9}}32\frac{2}{3}-27\frac{1}{6}

1.006.

Решение:

$$\begin{aligned} &(13,75+9\frac{1}{6})\cdot 1,2 = (13,75 + \frac{55}{6}) \cdot \frac{12}{10} = (\frac{1375}{100} + \frac{55}{6}) \cdot \frac{6}{5} = (\frac{55}{4} + \frac{55}{6}) \cdot \frac{6}{5} = 55(\frac{1}{4} + \frac{1}{6}) \cdot \frac{6}{5} = 55(\frac{3+2}{12}) \cdot \frac{6}{5} = 55 \cdot \frac{5}{12} \cdot \frac{6}{5} = 55 \cdot \frac{1}{2} = 27,5 \end{aligned}$$ $$\begin{aligned} &\frac{(6,8-3\frac{2}{3})\cdot 5\frac{5}{6}}{(10,3-8\frac{5}{9}):\frac{5}{9}} = \frac{(6,8 - \frac{11}{3}) \cdot \frac{35}{6}}{(10,3-\frac{77}{9}):\frac{5}{9}} = \frac{(\frac{68}{10} - \frac{11}{3}) \cdot \frac{35}{6}}{(\frac{103}{10}-\frac{77}{9}):\frac{5}{9}} = \frac{(\frac{204-110}{30}) \cdot \frac{35}{6}}{(\frac{927-770}{90}):\frac{5}{9}} = \frac{\frac{94}{30} \cdot \frac{35}{6}}{\frac{157}{90}:\frac{5}{9}} = \frac{\frac{47}{15} \cdot \frac{35}{6}}{\frac{157}{90} \cdot \frac{9}{5}} = \frac{\frac{47 \cdot 7}{3 \cdot 6}}{\frac{157}{10 \cdot 5}} = \frac{\frac{329}{18}}{\frac{157}{50}} = \frac{329}{18} \cdot \frac{50}{157} = \frac{329 \cdot 25}{9 \cdot 157} = \frac{8225}{1413} \approx 5,82 \end{aligned}$$ $$\begin{aligned} &32\frac{2}{3}-27\frac{1}{6} = \frac{98}{3} - \frac{163}{6} = \frac{196-163}{6} = \frac{33}{6} = \frac{11}{2} = 5,5 \end{aligned}$$

Ответ: \((13,75+9\frac{1}{6})\cdot 1,2 = 27,5\), \(\frac{(6,8-3\frac{2}{3})\cdot 5\frac{5}{6}}{(10,3-8\frac{5}{9}):\frac{5}{9}} \approx 5,82\), \(32\frac{2}{3}-27\frac{1}{6}=5,5\)