2. Вычислите: a) \(2\frac{1}{3}\cdot 3\frac{1}{5}-8\frac{4}{9}:2;\) б) \(5\frac{2}{7}\cdot 1\frac{1}{4}+5\frac{2}{7}\cdot 1\frac{3}{4}.\) Вариант 1

Решение:

1. a) \(2\frac{1}{3}\cdot 3\frac{1}{5}-8\frac{4}{9}:2 = \frac{7}{3}\cdot \frac{16}{5} - \frac{76}{9}:2 = \frac{7\cdot 16}{3\cdot 5} - \frac{76}{9}\cdot \frac{1}{2} = \frac{112}{15} - \frac{76\cdot 1}{9\cdot 2} = \frac{112}{15} - \frac{38}{9} = \frac{112\cdot 3}{15\cdot 3} - \frac{38\cdot 5}{9\cdot 5} = \frac{336}{45} - \frac{190}{45} = \frac{336-190}{45} = \frac{146}{45} = 3\frac{11}{45}\)
2. б) \(5\frac{2}{7}\cdot 1\frac{1}{4}+5\frac{2}{7}\cdot 1\frac{3}{4} = 5\frac{2}{7}\cdot (1\frac{1}{4} + 1\frac{3}{4}) = 5\frac{2}{7}\cdot (\frac{5}{4} + \frac{7}{4}) = 5\frac{2}{7}\cdot \frac{5+7}{4} = 5\frac{2}{7}\cdot \frac{12}{4} = \frac{37}{7}\cdot 3 = \frac{37\cdot 3}{7} = \frac{111}{7} = 15\frac{6}{7}\)

Ответ: a) \(3\frac{11}{45}\); б) \(15\frac{6}{7}\)