№3 (3 балла) Выполните действия: a) \frac{17}{23} - \frac{9}{23} + \frac{7}{23}; б) 14\frac{2}{13} - (8\frac{7}{13} + \frac{9}{13}); в) 11\frac{5}{27} - 5\frac{8}{27} + 4\frac{3}{27}.

Решим данные примеры:

1. а) $$\frac{17}{23} - \frac{9}{23} + \frac{7}{23} = \frac{17 - 9 + 7}{23} = \frac{15}{23}.$$
2. б) $$14\frac{2}{13} - (8\frac{7}{13} + \frac{9}{13}) = 14\frac{2}{13} - 8\frac{7+9}{13} = 14\frac{2}{13} - 8\frac{16}{13} = 14\frac{2}{13} - 8 - \frac{16}{13} = 14\frac{2}{13} - 8 - 1\frac{3}{13} = 14\frac{2}{13} - 9\frac{3}{13} = 13\frac{15}{13} - 9\frac{3}{13} = (13-9) + (\frac{15}{13} - \frac{3}{13}) = 4 + \frac{15-3}{13} = 4 + \frac{12}{13} = 4\frac{12}{13}.$$
3. в) $$11\frac{5}{27} - 5\frac{8}{27} + 4\frac{3}{27} = 11\frac{5}{27} - 5\frac{8}{27} + 4\frac{3}{27} = 10\frac{32}{27} - 5\frac{8}{27} + 4\frac{3}{27} = (10-5+4) + (\frac{32}{27} - \frac{8}{27} + \frac{3}{27}) = 9 + \frac{32-8+3}{27} = 9 + \frac{27}{27} = 9 + 1 = 10.$$

Ответ: а) $$\frac{15}{23}$$, б) $$4\frac{12}{13}$$, в) $$10$$