B-2, 2. Вычислить: 2 : 2\frac{2}{3} + 1\frac{4}{5} \cdot 3\frac{1}{3} - 2\frac{5}{6}

Решение: 1. \(2\frac{2}{3} = \frac{2 \cdot 3 + 2}{3} = \frac{8}{3}\) 2. \(1\frac{4}{5} = \frac{1 \cdot 5 + 4}{5} = \frac{9}{5}\) 3. \(3\frac{1}{3} = \frac{3 \cdot 3 + 1}{3} = \frac{10}{3}\) 4. \(2 : \frac{8}{3} = 2 \cdot \frac{3}{8} = \frac{6}{8} = \frac{3}{4}\) 5. \(\frac{9}{5} \cdot \frac{10}{3} = \frac{9 \cdot 10}{5 \cdot 3} = \frac{90}{15} = 6\) 6. \(2\frac{5}{6} = \frac{2 \cdot 6 + 5}{6} = \frac{17}{6}\) 7. \(\frac{3}{4} + 6 - \frac{17}{6} = \frac{3}{4} + \frac{24}{4} - \frac{17}{6} = \frac{27}{4} - \frac{17}{6} = \frac{27 \cdot 3 - 17 \cdot 2}{12} = \frac{81 - 34}{12} = \frac{47}{12} = 3\frac{11}{12}\) Ответ: \(3\frac{11}{12}\)