1.009. \frac{0,4+8}{8}:5(\frac{5}{8}-0,8)\cdot 5:2\frac{(\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}}-5\cdot 2}{90}.

1.009.

Решение:

$$\begin{aligned} &\frac{0,4+8}{8} = \frac{8,4}{8} = \frac{84}{80} = \frac{21}{20} = 1,05 \end{aligned}$$ $$\begin{aligned} &5(\frac{5}{8}-0,8) = 5(\frac{5}{8}-\frac{8}{10}) = 5(\frac{25-32}{40}) = 5(-\frac{7}{40}) = -\frac{7}{8} = -0,875 \end{aligned}$$ $$\begin{aligned} &5:2 = \frac{5}{2} = 2,5 \end{aligned}$$ $$\begin{aligned} &2\frac{2}{5} = \frac{12}{5} \end{aligned}$$ $$\begin{aligned} &(8,9-2,6\frac{2}{3}) = \frac{89}{10} - \frac{8}{3} = \frac{267-80}{30} = \frac{187}{30} \end{aligned}$$ $$\begin{aligned} &\frac{7}{8}:(8,9-2,6\frac{2}{3}) = \frac{7}{8}:\frac{187}{30} = \frac{7}{8} \cdot \frac{30}{187} = \frac{7}{4} \cdot \frac{15}{187} = \frac{105}{748} \end{aligned}$$ $$\begin{aligned} &\frac{34}{2\frac{2}{5}} = \frac{34}{\frac{12}{5}} = \frac{34 \cdot 5}{12} = \frac{17 \cdot 5}{6} = \frac{85}{6} \end{aligned}$$ $$\begin{aligned} &(\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}} = \frac{105}{748} \cdot \frac{85}{6} = \frac{105 \cdot 85}{748 \cdot 6} = \frac{8925}{4488} \approx 1,99 \end{aligned}$$ $$\begin{aligned} &5 \cdot 2 = 10 \end{aligned}$$ $$\begin{aligned} &(\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}}-5\cdot 2 = \frac{8925}{4488} - 10 = \frac{8925 - 44880}{4488} = \frac{-35955}{4488} \approx -8,01 \end{aligned}$$ $$\begin{aligned} &\frac{(\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}}-5\cdot 2}{90} = \frac{\frac{-35955}{4488}}{90} = \frac{-35955}{4488 \cdot 90} = \frac{-35955}{403920} \approx -0,09 \end{aligned}$$

Ответ: \(\frac{0,4+8}{8} = 1,05\), \(5(\frac{5}{8}-0,8) = -0,875\), \(5:2 = 2,5\), \(2\frac{2}{5} = \frac{12}{5}\), \((8,9-2,6\frac{2}{3}) = \frac{187}{30}\), \(\frac{7}{8}:(8,9-2,6\frac{2}{3}) = \frac{105}{748}\), \(\frac{34}{2\frac{2}{5}} = \frac{85}{6}\), \((\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}} \approx 1,99\), \(5 \cdot 2 = 10\), \((\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}}-5\cdot 2 \approx -8,01\), \(\frac{(\frac{7}{8}:(8,9-2,6\frac{2}{3}))\cdot \frac{34}{2\frac{2}{5}}-5\cdot 2}{90} \approx -0,09\)