60. Тип 13 № 14112: Вычислите \(2\frac{1}{3} + \frac{4}{9} \cdot 3\frac{3}{8} - 1\frac{6}{7} : \frac{26}{63}\)

Решение:

1. \(2\frac{1}{3} = \frac{2 \cdot 3 + 1}{3} = \frac{7}{3}\)
2. \(3\frac{3}{8} = \frac{3 \cdot 8 + 3}{8} = \frac{27}{8}\)
3. \(1\frac{6}{7} = \frac{1 \cdot 7 + 6}{7} = \frac{13}{7}\)
4. \(\frac{4}{9} \cdot \frac{27}{8} = \frac{4 \cdot 27}{9 \cdot 8} = \frac{108}{72} = \frac{3}{2}\)
5. \(\frac{13}{7} : \frac{26}{63} = \frac{13 \cdot 63}{7 \cdot 26} = \frac{819}{182} = \frac{9}{2}\)
6. \(\frac{7}{3} + \frac{3}{2} = \frac{7 \cdot 2 + 3 \cdot 3}{3 \cdot 2} = \frac{14 + 9}{6} = \frac{23}{6}\)
7. \(\frac{23}{6} - \frac{9}{2} = \frac{23 - 9 \cdot 3}{6} = \frac{23 - 27}{6} = \frac{-4}{6} = \frac{-2}{3}\)

Ответ: \(\frac{-2}{3}\)