5.88. Упростите выражение: a) $$\frac{1}{27}a - (\frac{4}{9}a - \frac{1}{3}a)$$; б) $$\frac{5}{7}(\frac{7}{5}a - 7) - 9(2\frac{1}{3}a + \frac{5}{9})$$; в) $$\frac{4}{5}(1,5c - 4,5) - \frac{3}{9}(2,7c - 6,3)$$; г) $$\frac{1}{9}(0,9b - 1,8) - \frac{1}{2}(0,2b - 0,4)$$.

Решение: a) $$\frac{1}{27}a - (\frac{4}{9}a - \frac{1}{3}a) = \frac{1}{27}a - \frac{4}{9}a + \frac{1}{3}a = \frac{1}{27}a - \frac{12}{27}a + \frac{9}{27}a = \frac{1 - 12 + 9}{27}a = \frac{-2}{27}a = -\frac{2}{27}a$$ б) $$\frac{5}{7}(\frac{7}{5}a - 7) - 9(2\frac{1}{3}a + \frac{5}{9}) = \frac{5}{7} \cdot \frac{7}{5}a - \frac{5}{7} \cdot 7 - 9(\frac{7}{3}a + \frac{5}{9}) = a - 5 - 9 \cdot \frac{7}{3}a - 9 \cdot \frac{5}{9} = a - 5 - 21a - 5 = -20a - 10$$ в) $$\frac{4}{5}(1,5c - 4,5) - \frac{3}{9}(2,7c - 6,3) = \frac{4}{5}(1,5c) - \frac{4}{5}(4,5) - \frac{1}{3}(2,7c) + \frac{1}{3}(6,3) = 1,2c - 3,6 - 0,9c + 2,1 = 0,3c - 1,5$$ г) $$\frac{1}{9}(0,9b - 1,8) - \frac{1}{2}(0,2b - 0,4) = \frac{1}{9}(0,9b) - \frac{1}{9}(1,8) - \frac{1}{2}(0,2b) + \frac{1}{2}(0,4) = 0,1b - 0,2 - 0,1b + 0,2 = 0$$ Ответ: a) $$-\frac{2}{27}a$$ б) $$-20a - 10$$ в) $$0,3c - 1,5$$ г) $$0$$