Вычислите 35 36 (1 2 + 5 14 ) - 5 6 : 10 27

Решение:

1. \[ \frac{35}{36} \cdot \left( \frac{1}{2} + \frac{5}{14} \right) = \frac{35}{36} \cdot \left( \frac{7}{14} + \frac{5}{14} \right) = \frac{35}{36} \cdot \frac{12}{14} = \frac{35}{36} \cdot \frac{6}{7} = \frac{5 \cdot 7}{6 · 6} \cdot \frac{6}{7} = \frac{5}{6} \]
2. \[ \frac{5}{6} : \frac{10}{27} = \frac{5}{6} \cdot \frac{27}{10} = \frac{5 \cdot 27}{6 \cdot 10} = \frac{1 \u00B7 3 \u00B7 5 \u00B7 3}{2 \u00B7 3 \u00B7 2 \u00B7 5} = \frac{3}{4} \]

Ответ: 3/4