15) \((\frac{2}{6} - 1\frac{5}{6}) : \frac{3}{15} + 4 \frac{1}{2} \cdot (1\frac{1}{5} - 1\frac{1}{12})\)

Решение:

Задание 15:

1. \( \frac{2}{6} - 1\frac{5}{6} = \frac{2}{6} - \frac{11}{6} = \frac{2 - 11}{6} = -\frac{9}{6} = -\frac{3}{2} \)
2. \( -\frac{3}{2} : \frac{3}{15} = -\frac{3}{2} \cdot \frac{15}{3} = -\frac{3 \cdot 15}{2 \cdot 3} = -\frac{15}{2} \)
3. \( 1\frac{1}{5} - 1\frac{1}{12} = \frac{6}{5} - \frac{13}{12} = \frac{6 \cdot 12}{60} - \frac{13 \cdot 5}{60} = \frac{72 - 65}{60} = \frac{7}{60} \)
4. \( 4 \frac{1}{2} \cdot \frac{7}{60} = \frac{9}{2} \cdot \frac{7}{60} = \frac{9 \cdot 7}{2 \cdot 60} = \frac{63}{120} = \frac{21}{40} \)
5. \( -\frac{15}{2} + \frac{21}{40} = -\frac{15 \cdot 20}{40} + \frac{21}{40} = \frac{-300 + 21}{40} = -\frac{279}{40} \)

Ответ: -\(\frac{279}{40}\).