6). \( (2 \frac{3}{8} + 3 \frac{7}{24}) : (4 \frac{2}{3} - 1 \frac{1}{8}) \)

Решение:

1. \( 2 \frac{3}{8} = \frac{19}{8} \)
2. \( 3 \frac{7}{24} = \frac{76}{24} \)
3. \( \frac{19}{8} + \frac{76}{24} = \frac{19 \cdot 3}{8 \cdot 3} + \frac{76}{24} = \frac{57}{24} + \frac{76}{24} = \frac{133}{24} \)
4. \( 4 \frac{2}{3} = \frac{14}{3} \)
5. \( 1 \frac{1}{8} = \frac{9}{8} \)
6. \( \frac{14}{3} - \frac{9}{8} = \frac{14 \cdot 8}{3 \cdot 8} - \frac{9 \cdot 3}{8 \cdot 3} = \frac{112}{24} - \frac{27}{24} = \frac{85}{24} \)
7. \( \frac{133}{24} : \frac{85}{24} = \frac{133}{24} \cdot \frac{24}{85} = \frac{133}{85} = \frac{19}{5} \)
8. \( \frac{19}{5} = 3 \frac{4}{5} \)

Ответ: \( 3 \frac{4}{5} \)