Решение.
\( \frac{(68\frac{7}{30} - 66\frac{5}{18}) : 6\frac{1}{9} + (\frac{7}{40} + \frac{3}{32}) \cdot 4,5}{0,04} = 38\frac{15}{64}.\)

\(
1) 68\frac{7}{30} - 66\frac{5}{18} = 68\frac{21}{90} - 66\frac{25}{90} = 67 + 1 + \frac{21}{90} - 66\frac{25}{90} = 67 + \frac{90}{90} + \frac{21}{90} - 66\frac{25}{90} = 67 -
\)

\(
- 66 + (\frac{90}{90} + \frac{21}{90} - \frac{25}{90}) = 1 + \frac{90 + 21 - 25}{90} = 1 + \frac{86}{90} = 1\frac{43}{45};
\)

\(
2) \frac{7}{40} + \frac{3}{32} = \frac{28}{160} + \frac{15}{160} = \frac{43}{160};
\)

\(
3) 1\frac{43}{45} : 6\frac{1}{9} = \frac{88}{45} : \frac{55}{9} = \frac{88}{45} \cdot \frac{9}{55} = \frac{88 \cdot 9}{45 \cdot 55} = \frac{8 \cdot 1}{5 \cdot 5} = \frac{8}{25};
\)

\(
4) \frac{43}{160} \cdot 4,5 = \frac{43}{160} \cdot 4\frac{5}{10} = \frac{43}{160} \cdot 4\frac{1}{2} = \frac{43}{160} \cdot \frac{9}{2} = \frac{43 \cdot 9}{160 \cdot 2} = \frac{387}{320} = 1\frac{67}{320};
\)

\(
5) \frac{8}{25} + 1\frac{67}{320} = \frac{512}{1600} + 1\frac{335}{1600} = 1\frac{847}{1600};
\)

\(
6) 1\frac{847}{1600} : 0,04 = \frac{2447}{1600} : \frac{4}{100} = \frac{2447}{1600} \cdot \frac{100}{4} = \frac{2447 \cdot 100}{1600 \cdot 4} = \frac{2447 \cdot 1}{16 \cdot 4} = \frac{2447}{64} = 38\frac{15}{64}.
\)
Ответ: \(38\frac{15}{64}\)

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