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

$$\frac{4}{3} + (-5\frac{1}{2} + \frac{5}{4} \cdot \frac{1}{5}) : \frac{9}{10} = \frac{4}{3} + (-\frac{11}{2} + \frac{1}{4}) : \frac{9}{10} = \frac{4}{3} + (\frac{-22 + 1}{4}) : \frac{9}{10} = $$
$$ = \frac{4}{3} + (\frac{-21}{4}) : \frac{9}{10} = \frac{4}{3} + \frac{-21}{4} \cdot \frac{10}{9} = \frac{4}{3} - \frac{7 \cdot 5}{2 \cdot 3} = \frac{4}{3} - \frac{35}{6} = \frac{8 - 35}{6} = \frac{-27}{6} = -\frac{9}{2} = -4.5$$

Ответ: -4.5