7. Вычислите: а) 6+\frac{5}{9}: (3-\frac{17}{21}) - \frac{11}{30}.Запишите полностью решение и ответ. б) \frac{9}{10}+\frac{4}{9}: (2-1\frac{11}{21}) -1\frac{2}{3}.Запишите полностью решение и ответ.

a) Вычислим:

$$6+\frac{5}{9}: (3-\frac{17}{21}) - \frac{11}{30} = 6 + \frac{5}{9} : (\frac{3 \cdot 21}{21} - \frac{17}{21}) - \frac{11}{30} = 6 + \frac{5}{9} : \frac{63 - 17}{21} - \frac{11}{30} = 6 + \frac{5}{9} : \frac{46}{21} - \frac{11}{30} = 6 + \frac{5}{9} \cdot \frac{21}{46} - \frac{11}{30} = 6 + \frac{5 \cdot 21}{9 \cdot 46} - \frac{11}{30} = 6 + \frac{5 \cdot 7}{3 \cdot 46} - \frac{11}{30} = 6 + \frac{35}{138} - \frac{11}{30} = 6 + \frac{35 \cdot 5}{138 \cdot 5} - \frac{11 \cdot 23}{30 \cdot 23} = 6 + \frac{175}{690} - \frac{253}{690} = 6 + \frac{175-253}{690} = 6 + \frac{-78}{690} = 6 - \frac{13}{115} = \frac{6 \cdot 115}{115} - \frac{13}{115} = \frac{690}{115} - \frac{13}{115} = \frac{690-13}{115} = \frac{677}{115} = 5 \frac{102}{115}$$.

б) Вычислим:

$$\frac{9}{10}+\frac{4}{9}: (2-1\frac{11}{21}) -1\frac{2}{3} = \frac{9}{10} + \frac{4}{9} : (2 - \frac{1 \cdot 21 + 11}{21}) - \frac{1 \cdot 3 + 2}{3} = \frac{9}{10} + \frac{4}{9} : (2 - \frac{21+11}{21}) - \frac{3+2}{3} = \frac{9}{10} + \frac{4}{9} : (2 - \frac{32}{21}) - \frac{5}{3} = \frac{9}{10} + \frac{4}{9} : (\frac{2 \cdot 21}{21} - \frac{32}{21}) - \frac{5}{3} = \frac{9}{10} + \frac{4}{9} : \frac{42-32}{21} - \frac{5}{3} = \frac{9}{10} + \frac{4}{9} : \frac{10}{21} - \frac{5}{3} = \frac{9}{10} + \frac{4}{9} \cdot \frac{21}{10} - \frac{5}{3} = \frac{9}{10} + \frac{4 \cdot 21}{9 \cdot 10} - \frac{5}{3} = \frac{9}{10} + \frac{4 \cdot 7}{3 \cdot 10} - \frac{5}{3} = \frac{9}{10} + \frac{28}{30} - \frac{5}{3} = \frac{9 \cdot 3}{10 \cdot 3} + \frac{28}{30} - \frac{5 \cdot 10}{3 \cdot 10} = \frac{27}{30} + \frac{28}{30} - \frac{50}{30} = \frac{27+28-50}{30} = \frac{55-50}{30} = \frac{5}{30} = \frac{1}{6}$$.

Ответ: a) $$5 \frac{102}{115}$$; б) $$\frac{1}{6}$$