1.007. (\frac{1}{6}+0,1+\frac{1}{15}):(\frac{1}{6}+0,1-\frac{1}{15})\cdot 2,52\frac{(0,5-\frac{1}{3}+0,25-\frac{1}{5})}{(\frac{7}{7}-0,125)}(\frac{0,05}{7}+5,7)

1.007.

Решение:

$$\begin{aligned} &(\frac{1}{6}+0,1+\frac{1}{15}):(\frac{1}{6}+0,1-\frac{1}{15}) \cdot 2,52 = (\frac{1}{6}+\frac{1}{10}+\frac{1}{15}):(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}) \cdot \frac{252}{100} = (\frac{5+3+2}{30}):(\frac{5+3-2}{30}) \cdot \frac{63}{25} = (\frac{10}{30}):(\frac{6}{30}) \cdot \frac{63}{25} = \frac{1}{3} \cdot \frac{30}{6} \cdot \frac{63}{25} = \frac{10}{6} \cdot \frac{63}{25} = \frac{5}{3} \cdot \frac{63}{25} = \frac{1}{3} \cdot \frac{63}{5} = \frac{21}{5} = 4,2 \end{aligned}$$ $$\begin{aligned} &\frac{(0,5-\frac{1}{3}+0,25-\frac{1}{5})}{(\frac{7}{7}-0,125)} = \frac{(\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5})}{(1-\frac{125}{1000})} = \frac{\frac{30-20+15-12}{60}}{\frac{1000-125}{1000}} = \frac{\frac{13}{60}}{\frac{875}{1000}} = \frac{\frac{13}{60}}{\frac{7}{8}} = \frac{13}{60} \cdot \frac{8}{7} = \frac{13}{15} \cdot \frac{2}{7} = \frac{26}{105} \approx 0,25 \end{aligned}$$ $$\begin{aligned} &(\frac{0,05}{7}+5,7) = (\frac{5}{700}+\frac{57}{10}) = \frac{5}{700}+\frac{3990}{700} = \frac{3995}{700} = \frac{799}{140} \approx 5,71 \end{aligned}$$

Ответ: \((\frac{1}{6}+0,1+\frac{1}{15}):(\frac{1}{6}+0,1-\frac{1}{15}) \cdot 2,52 = 4,2\), \(\frac{(0,5-\frac{1}{3}+0,25-\frac{1}{5})}{(\frac{7}{7}-0,125)} \approx 0,25\), \((\frac{0,05}{7}+5,7) \approx 5,71\)