56. Тип 13 № 11394: Вычислите \(1\frac{1}{4} + \frac{5}{17} - 2\frac{4}{15} - 2\frac{1}{8} + \frac{51}{56}\)

Решение:

1. \(1\frac{1}{4} = \frac{1 \cdot 4 + 1}{4} = \frac{5}{4}\)
2. \(2\frac{4}{15} = \frac{2 \cdot 15 + 4}{15} = \frac{34}{15}\)
3. \(2\frac{1}{8} = \frac{2 \cdot 8 + 1}{8} = \frac{17}{8}\)
4. \(\frac{5}{4} + \frac{5}{17} = \frac{5 \cdot 17 + 5 \cdot 4}{4 \cdot 17} = \frac{85 + 20}{68} = \frac{105}{68}\)
5. \(\frac{105}{68} - \frac{34}{15} = \frac{105 \cdot 15 - 34 \cdot 68}{68 \cdot 15} = \frac{1575 - 2312}{1020} = \frac{-737}{1020}\)
6. \(\frac{-737}{1020} - \frac{17}{8} = \frac{-737 \cdot 2 - 17 \cdot 255}{1020 \cdot 2} = \frac{-1474 - 4335}{2040} = \frac{-5809}{2040}\)
7. \(\frac{-5809}{2040} + \frac{51}{56} = \frac{-5809 \cdot 7 + 51 \cdot 255}{2040 \cdot 7} = \frac{-40663 + 13005}{14280} = \frac{-27658}{14280} = \frac{-13829}{7140}\)

Ответ: \(\frac{-13829}{7140}\)