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Решение:

1. \( 4 \frac{4}{5} : 1 \frac{5}{7} = \frac{24}{5} : \frac{12}{7} = \frac{24}{5} \cdot \frac{7}{12} = \frac{2 \cdot 7}{5} = \frac{14}{5} \)


2. \( \frac{1}{3} + \frac{14}{5} = \frac{5 + 42}{15} = \frac{47}{15} \)


3. \( \frac{47}{15} \cdot 2 \frac{1}{7} = \frac{47}{15} \cdot \frac{15}{7} = \frac{47}{7} \)


4. \( \frac{47}{7} - 7 \frac{1}{7} = \frac{47}{7} - \frac{50}{7} = -\frac{3}{7} \)


5. \( 1 - \frac{2}{3} = \frac{1}{3} \)


6. \( \frac{1}{3} : \frac{5}{22} = \frac{1}{3} \cdot \frac{22}{5} = \frac{22}{15} \)


7. \( \frac{22}{15} : 7 \frac{1}{3} = \frac{22}{15} : \frac{22}{3} = \frac{22}{15} \cdot \frac{3}{22} = \frac{3}{15} = \frac{1}{5} \)


8. \( -\frac{3}{7} \cdot \frac{1}{5} = -\frac{3}{35} \)

Ответ: \( -\frac{3}{35} \).