Решение:
\( \frac{[(40\frac{7}{30} - 38\frac{5}{12}) : 10,9 + (\frac{7}{8} - \frac{7}{30}) \cdot 1\frac{9}{11}] \cdot 4,2}{0,008} = 700\)

\(
1) 40\frac{7}{30} - 38\frac{5}{12} = 40\frac{14}{60} - 38\frac{25}{60} = 39 + 1 + \frac{14}{60} - 38\frac{25}{60} = 39 + \frac{60}{60} + \frac{14}{60} - 38\frac{25}{60} = 39 -
\)

\(
- 38 + (\frac{60}{60} + \frac{14}{60} - \frac{25}{60}) = 1 + \frac{60 + 14 - 25}{60} = 1\frac{49}{60};
\)

\(
2) \frac{7}{8} - \frac{7}{30} = \frac{105}{120} - \frac{28}{120} = \frac{77}{120};
\)

\(
3) 1\frac{49}{60} : 10,9 = \frac{109}{60} : 10\frac{9}{10} = \frac{109}{60} : \frac{109}{10} = \frac{109}{60} \cdot \frac{10}{109} = \frac{109 \cdot 10}{60 \cdot 109} = \frac{1 \cdot 1}{6 \cdot 1} = \frac{1}{6};
\)

\(
4) \frac{77}{120} \cdot 1\frac{9}{11} = \frac{77}{120} \cdot \frac{20}{11} = \frac{77 \cdot 20}{120 \cdot 11} = \frac{7 \cdot 1}{6 \cdot 1} = \frac{7}{6} = 1\frac{1}{6};
\)

\(
5) \frac{1}{6} + 1\frac{1}{6} = 1\frac{2}{6} = 1\frac{1}{3};
\)

\(
6) 1\frac{1}{3} \cdot 4,2 = \frac{4}{3} \cdot 4,2 = \frac{4}{1} \cdot 1,4 = 5,6;
\)

\(
7) 5,6 : 0,008 = 700.
\)
Ответ: 700.

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