ычислите: 6:\frac{18}{23}+2\frac{2}{3}\cdot(\frac{3}{14}-4\frac{13}{28}) . Запишите

Ответ: -9\frac{1}{3}

Решаем по действиям:

1) \(\frac{3}{14} - 4\frac{13}{28} = \frac{3}{14} - \frac{4 \cdot 28 + 13}{28} = \frac{3}{14} - \frac{112 + 13}{28} = \frac{3}{14} - \frac{125}{28} = \frac{3 \cdot 2}{14 \cdot 2} - \frac{125}{28} = \frac{6}{28} - \frac{125}{28} = \frac{6 - 125}{28} = \frac{-119}{28} = -4\frac{7}{28} = -4\frac{1}{4}\)

2) \(2\frac{2}{3} \cdot (-4\frac{1}{4}) = \frac{2 \cdot 3 + 2}{3} \cdot \frac{-4 \cdot 4 - 1}{4} = \frac{8}{3} \cdot \frac{-17}{4} = \frac{8 \cdot (-17)}{3 \cdot 4} = \frac{2 \cdot (-17)}{3 \cdot 1} = \frac{-34}{3} = -11\frac{1}{3}\)

3) \(6 : \frac{18}{23} = 6 \cdot \frac{23}{18} = \frac{6 \cdot 23}{18} = \frac{1 \cdot 23}{3} = \frac{23}{3} = 7\frac{2}{3}\)

4) \(7\frac{2}{3} + (-11\frac{1}{3}) = 7\frac{2}{3} - 11\frac{1}{3} = \frac{7 \cdot 3 + 2}{3} - \frac{11 \cdot 3 + 1}{3} = \frac{23}{3} - \frac{34}{3} = \frac{23 - 34}{3} = \frac{-11}{3} = -3\frac{2}{3}\)

Ответ: -3\frac{2}{3}

Ответ: -3\frac{2}{3}