6. $$4\frac{1}{3} \cdot 5 + 2,4 : (-0,1) - \frac{14}{15} : 1\frac{2}{5}$$

INSIGHT

Решение:

1. \(4\frac{1}{3} = \frac{13}{3}\)
2. \(\frac{13}{3} \cdot 5 = \frac{65}{3}\)
3. \(2,4 = \frac{24}{10} = \frac{12}{5}\)
4. \(\frac{12}{5} : (-0,1) = \frac{12}{5} : \left(-\frac{1}{10}\right) = \frac{12}{5} \cdot (-10) = -24\)
5. \(1\frac{2}{5} = \frac{7}{5}\)
6. \(-\frac{14}{15} : \frac{7}{5} = -\frac{14}{15} \cdot \frac{5}{7} = -\frac{14 \cdot 5}{15 \cdot 7} = -\frac{2 \cdot 1}{3 \cdot 1} = -\frac{2}{3}\)
7. \(\frac{65}{3} + (-24) - \left(-\frac{2}{3}\right) = \frac{65}{3} - 24 + \frac{2}{3}\)
8. \(\frac{65}{3} + \frac{2}{3} - 24 = \frac{67}{3} - 24 = \frac{67 - 24 \cdot 3}{3} = \frac{67 - 72}{3} = -\frac{5}{3}\)

Ответ: -\(\frac{5}{3}\)