Вычислите: a) \(7 - 2 \frac{18}{23}\) \(\cdot\) 1 \(\frac{11}{12}\) + 2 \(\frac{1}{8}\) \(\cdot\) \(\frac{4}{17}\) : 1,5 - \(\frac{4}{5}\);

Решение:

Вычисляем по действиям:

1. \( 7 - 2 \frac{18}{23} = \frac{7 \cdot 23 - 2 \cdot 23 - 18}{23} = \frac{161 - 46 - 18}{23} = \frac{97}{23} \)
2. \( 1 \frac{11}{12} = \frac{1 \cdot 12 + 11}{12} = \frac{23}{12} \)
3. \( 2 \frac{1}{8} = \frac{2 \cdot 8 + 1}{8} = \frac{17}{8} \)
4. \( \frac{97}{23} \cdot \frac{23}{12} = \frac{97}{12} \)
5. \( \frac{17}{8} \cdot \frac{4}{17} = \frac{4}{8} = \frac{1}{2} \)
6. \( 1,5 = \frac{3}{2} \)
7. \( \frac{1}{2} : \frac{3}{2} = \frac{1}{2} \cdot \frac{2}{3} = \frac{1}{3} \)
8. \( \frac{97}{12} + \frac{1}{3} = \frac{97}{12} + \frac{4}{12} = \frac{101}{12} \)
9. \( \frac{101}{12} - \frac{4}{5} = \frac{101 \cdot 5 - 4 \cdot 12}{60} = \frac{505 - 48}{60} = \frac{457}{60} \)

Ответ: \( \frac{457}{60} \)