6. Вычислите: \frac{4}{3}+\left(-5\frac{1}{2}+\frac{5}{4} \cdot \frac{1}{5}\right):\frac{9}{10}

\[\frac{4}{3} + \left(-5\frac{1}{2} + \frac{5}{4} \cdot \frac{1}{5}\right) : \frac{9}{10}\]

1. \(\frac{5}{4} \cdot \frac{1}{5} = \frac{1}{4}\)
2. \(-5\frac{1}{2} + \frac{1}{4} = -\frac{11}{2} + \frac{1}{4} = -\frac{22}{4} + \frac{1}{4} = -\frac{21}{4}\)
3. \(-\frac{21}{4} : \frac{9}{10} = -\frac{21}{4} \cdot \frac{10}{9} = -\frac{210}{36} = -\frac{35}{6}\)
4. \(\frac{4}{3} - \frac{35}{6} = \frac{8}{6} - \frac{35}{6} = -\frac{27}{6} = -\frac{9}{2} = -4\frac{1}{2}\)

Ответ: -4.5