5. Вычислите: 10 +9 : (2 - 1\frac{11}{21}) - 1\frac{2}{3}. Запишите полностью решение и ответ.

5. Вычислите: $$10 \frac{9}{10} + \frac{4}{9} : \left(2 - 1\frac{11}{21}\right) - 1\frac{2}{3}$$. Запишите полностью решение и ответ.

$$10 \frac{9}{10} + \frac{4}{9} : \left(2 - 1\frac{11}{21}\right) - 1\frac{2}{3} = \frac{10 \cdot 10+9}{10} + \frac{4}{9} : \left(\frac{2}{1} - \frac{21+11}{21}\right) - \frac{3+2}{3} = \frac{109}{10} + \frac{4}{9} : \left(\frac{2}{1} - \frac{32}{21}\right) - \frac{5}{3} = \frac{109}{10} + \frac{4}{9} : \left(\frac{2 \cdot 21}{1 \cdot 21} - \frac{32}{21}\right) - \frac{5}{3} = \frac{109}{10} + \frac{4}{9} : \left(\frac{42}{21} - \frac{32}{21}\right) - \frac{5}{3} = \frac{109}{10} + \frac{4}{9} : \frac{42-32}{21} - \frac{5}{3} = \frac{109}{10} + \frac{4}{9} : \frac{10}{21} - \frac{5}{3} = \frac{109}{10} + \frac{4}{9} \cdot \frac{21}{10} - \frac{5}{3} = \frac{109}{10} + \frac{4 \cdot 21}{9 \cdot 10} - \frac{5}{3} = \frac{109}{10} + \frac{2 \cdot 7}{3 \cdot 5} - \frac{5}{3} = \frac{109}{10} + \frac{14}{15} - \frac{5}{3} = \frac{109 \cdot 3}{10 \cdot 3} + \frac{14 \cdot 2}{15 \cdot 2} - \frac{5 \cdot 10}{3 \cdot 10} = \frac{327}{30} + \frac{28}{30} - \frac{50}{30} = \frac{327+28-50}{30} = \frac{305}{30} = \frac{61}{6} = 10\frac{1}{6}$$

Ответ: $$10\frac{1}{6}$$