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

Решение:

Выполним действия по порядку:

1. 
   \[ \frac{5}{9} \cdot 2\frac{4}{7} = \frac{5}{9} \cdot \frac{18}{7} = \frac{5 ' 2}{7} = \frac{10}{7} \]
   
2. 
   \[ 4\frac{2}{3} - \frac{10}{7} = \frac{14}{3} - \frac{10}{7} = \frac{98}{21} - \frac{30}{21} = \frac{68}{21} \]
   
3. 
   \[ 2\frac{1}{7} + 1\frac{2}{3} = \frac{15}{7} + \frac{5}{3} = \frac{45}{21} + \frac{35}{21} = \frac{80}{21} \]
   
4. 
   \[ \frac{68}{21} + \frac{80}{21} = \frac{148}{21} \]
   

Ответ: \(\frac{148}{21}\)