\(\left\(4\frac{2}{3}-2\frac{5}{9}\cdot2\frac{4}{7}\right\)+\(\left\)\(2\frac{1}{7}+1\frac{2}{3}\right\)

Решение:

1. \( 4\frac{2}{3} = \frac{14}{3} \)
2. \( 2\frac{5}{9} = \frac{23}{9} \)
3. \( 2\frac{4}{7} = \frac{18}{7} \)
4. \( \frac{23}{9} \cdot \frac{18}{7} = \frac{23 \cdot 2}{7} = \frac{46}{7} \)
5. \( \frac{14}{3} - \frac{46}{7} = \frac{98 - 138}{21} = \frac{-40}{21} \)
6. \( 2\frac{1}{7} = \frac{15}{7} \)
7. \( 1\frac{2}{3} = \frac{5}{3} \)
8. \( \frac{15}{7} + \frac{5}{3} = \frac{45 + 35}{21} = \frac{80}{21} \)
9. \( \frac{-40}{21} + \frac{80}{21} = \frac{40}{21} \)

Ответ: \(\frac{40}{21}\)