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

Решение:

1. \( 1 \frac{3}{4} = \frac{7}{4} \)
2. \( 2 \frac{1}{3} = \frac{7}{3} \)
3. \( \frac{7}{4} + \frac{7}{3} = \frac{21}{12} + \frac{28}{12} = \frac{49}{12} \)
4. \( 7 \frac{1}{2} = \frac{15}{2} \)
5. \( 1 \frac{2}{3} = \frac{5}{3} \)
6. \( \frac{15}{2} - \frac{5}{3} = \frac{45}{6} - \frac{10}{6} = \frac{35}{6} \)
7. \( \frac{49}{12} : \frac{35}{6} = \frac{49}{12} \cdot \frac{6}{35} = \frac{49}{2 \cdot 35} = \frac{7 \cdot 7}{2 \cdot 5 \cdot 7} = \frac{7}{10} \)

Ответ: \( \frac{7}{10} \)