Решение:
\( [\frac{(2,4 + 1\frac{5}{7}) \cdot 4,375}{\frac{2}{3} - \frac{1}{6}} - \frac{(2,75 _ 1\frac{5}{6}) \cdot 21}{8\frac{3}{20} - 0,45}] : \frac{67}{200} = 100.\)

\(
1) 2,4 + 1\frac{5}{7} = 2\frac{4}{10} + 1\frac{5}{7} = 2\frac{2}{5} + 1\frac{5}{7} = 2\frac{14}{35} + 1\frac{25}{35} = 2 + 1 + \frac{14 + 25}{35} = 3 + \frac{39}{35} = 3 + 1 + \frac{4}{35} =
\)

\(
= 4\frac{4}{35};
\)

\(
2) 4\frac{4}{35} \cdot 4,375 = 4\frac{4}{35} \cdot 4\frac{375}{1000} = \frac{144}{35} \cdot 4\frac{3}{8} = \frac{144}{35} \cdot \frac{35}{8} = \frac{144 \cdot 35}{35 \cdot 8} = \frac{18 \cdot 1}{1 \cdot 1} = \frac{18}{1} = 18;
\)

\(
3) \frac{2}{3} - \frac{1}{6} = \frac{4}{6} - \frac{1}{6} = \frac{3}{6} = \frac{1}{2} = 0,5;
\)

\(
4) 18 : 0,5 = 36;
\)

\(
5) 2,75 - 1\frac{5}{6} = 2\frac{75}{100} - 1\frac{5}{6} = 2\frac{3}{4} - 1\frac{5}{6} = 2\frac{9}{12} - 1\frac{10}{12} = 1 + 1 + \frac{9}{12} - 1\frac{10}{12} = 1 + \frac{12}{12} + \frac{9}{12} -
\)

\(
- 1\frac{10}{12} = 1 - 1 + \frac{12 + 9 - 10}{12} = \frac{11}{12};
\)

\(
6) \frac{11}{12} \cdot 21 = \frac{11}{4} \cdot 7 = \frac{11 \cdot 7}{4} = \frac{77}{4} = 19\frac{1}{4};
\)

\(
7) 8\frac{3}{20} - 0,45 = 8\frac{3}{20} - \frac{45}{100} = 8\frac{3}{20} - \frac{9}{20} = 7 + 1 + \frac{3}{20} - \frac{9}{20} = 7 + \frac{20}{20} + \frac{3}{20} - \frac{9}{20} = 7 + \frac{20 + 3 - 9}{20} =
\)

\(
= 7\frac{14}{20} = 7\frac{7}{10}.
\)

\(
8) 19\frac{1}{4} : 7\frac{7}{10} = \frac{77}{4} : \frac{77}{10} = \frac{77}{4} \cdot \frac{10}{77} = \frac{77 \cdot 10}{4 \cdot 77} = \frac{1 \cdot 5}{2 \cdot 1} = \frac{5}{2} = 2\frac{1}{2} = 2,5;
\)

\(
9) 36 - 2,5 = 33,5;
\)

\(
10) 33\frac{1}{2} : \frac{67}{200} = \frac{67}{2} \cdot \frac{200}{67} = \frac{67 \cdot 200}{2 \cdot 67} = \frac{1 \cdot 100}{1 \cdot 1} = \frac{100}{1} = 100.
\)
Ответ: 100.

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