5. Вычислите наиболее удобным способом: a) $$1\frac{1}{2}\cdot2\frac{2}{5}+8\frac{1}{2}\cdot2\frac{2}{5}$$; б) $$9\frac{17}{18}\cdot\frac{6}{11}+28\frac{6}{9}\cdot\frac{6}{11}$$.

a) $$1\frac{1}{2}\cdot2\frac{2}{5}+8\frac{1}{2}\cdot2\frac{2}{5} = 2\frac{2}{5}\cdot(1\frac{1}{2}+8\frac{1}{2}) = 2\frac{2}{5}\cdot(9+\frac{1}{2}+\frac{1}{2})=2\frac{2}{5}\cdot10 = \frac{12}{5}\cdot10 = \frac{12\cdot10}{5} = \frac{12\cdot2}{1} = 24$$

б) $$9\frac{17}{18}\cdot\frac{6}{11}+28\frac{8}{9}\cdot\frac{6}{11} = \frac{6}{11}\cdot(9\frac{17}{18}+28\frac{8}{9}) = \frac{6}{11}\cdot(9\frac{17}{18}+28\frac{16}{18}) = \frac{6}{11}\cdot(37\frac{33}{18}) = \frac{6}{11}\cdot(37+1\frac{15}{18}) = \frac{6}{11}\cdot(38\frac{5}{6}) = \frac{6}{11}\cdot\frac{233}{6} = \frac{233}{11} = 21\frac{2}{11}$$

Ответ: а) 24; б) $$21\frac{2}{11}$$