17. Найдите значение выражения

Решение:

1. а) \( \left( \frac{17}{25} \cdot 2\frac{1}{7} - 2\frac{4}{7} \cdot 1\frac{2}{5} \right) \cdot 2\frac{7}{9} \)
2. \( = \left( \frac{17}{25} \cdot \frac{15}{7} - \frac{18}{7} \cdot \frac{7}{5} \right) \cdot \frac{25}{9} \)
3. \( = \left( \frac{17 \cdot 15}{25 \cdot 7} - \frac{18 \cdot 7}{7 \cdot 5} \right) \cdot \frac{25}{9} \)
4. \( = \left( \frac{17 \cdot 3}{5 \cdot 7} - \frac{18}{5} \right) \cdot \frac{25}{9} \)
5. \( = \left( \frac{51}{35} - \frac{18 \cdot 7}{5 \cdot 7} \right) \cdot \frac{25}{9} \)
6. \( = \left( \frac{51 - 126}{35} \right) \cdot \frac{25}{9} \)
7. \( = \frac{-75}{35} \cdot \frac{25}{9} = \frac{-15 \cdot 5}{7 \cdot 5} \cdot \frac{25}{9} = \frac{-15}{7} \cdot \frac{25}{9} \)
8. \( = \frac{(-5 \cdot 3) \cdot 25}{7 \cdot (3 \cdot 3)} = \frac{-5 \cdot 25}{7 \cdot 3} = \frac{-125}{21} \)
9. б) \( \frac{1}{2} + \left( 5\frac{1}{6} - 3\frac{3}{4} + \frac{1}{2} \right) \cdot \frac{10}{23} \)
10. \( = \frac{1}{2} + \left( \frac{31}{6} - \frac{15}{4} + \frac{1}{2} \right) \cdot \frac{10}{23} \)
11. \( = \frac{1}{2} + \left( \frac{31 \cdot 2 - 15 \cdot 3 + 1 \cdot 6}{12} \right) \cdot \frac{10}{23} \)
12. \( = \frac{1}{2} + \left( \frac{62 - 45 + 6}{12} \right) \cdot \frac{10}{23} \)
13. \( = \frac{1}{2} + \frac{23}{12} \cdot \frac{10}{23} = \frac{1}{2} + \frac{10}{12} = \frac{1}{2} + \frac{5}{6} \)
14. \( = \frac{3}{6} + \frac{5}{6} = \frac{8}{6} = \frac{4}{3} \)

Ответ: а) \( -\frac{125}{21} \), б) \( \frac{4}{3} \).