3. Вычисли наиболее удобным способом: a) \(\frac{12}{13} + \frac{4}{16} + \frac{1}{13} + \frac{3}{16} =\) б) \(\frac{8}{50} + \frac{6}{27} + \frac{27}{50} + \frac{37}{50} =\) в) \(\frac{28}{33} - \frac{2}{33} - \frac{28}{33} =\) г) \(\frac{6}{7} + \frac{18}{19} - \frac{18}{19} =\) д) \(\frac{25}{57} - (\frac{2}{57} + \frac{23}{57}) =\) е) \(2 - (1\frac{1}{3} + \frac{2}{3}) =\)

Решение:

1. а) \(\frac{12}{13} + \frac{4}{16} + \frac{1}{13} + \frac{3}{16} = (\frac{12}{13} + \frac{1}{13}) + (\frac{4}{16} + \frac{3}{16}) = \frac{13}{13} + \frac{7}{16} = 1 + \frac{7}{16} = 1\frac{7}{16}\)


2. б) \(\frac{8}{50} + \frac{6}{27} + \frac{27}{50} + \frac{37}{50} = (\frac{8}{50} + \frac{27}{50} + \frac{37}{50}) + \frac{6}{27} = \frac{72}{50} + \frac{6}{27} = \frac{36}{25} + \frac{2}{9} = \frac{36 \cdot 9 + 2 \cdot 25}{225} = \frac{324 + 50}{225} = \frac{374}{225} = 1\frac{149}{225}\)


3. в) \(\frac{28}{33} - \frac{2}{33} - \frac{28}{33} = \frac{28 - 2 - 28}{33} = \frac{-2}{33}\)


4. г) \(\frac{6}{7} + \frac{18}{19} - \frac{18}{19} = \frac{6}{7}\)


5. д) \(\frac{25}{57} - (\frac{2}{57} + \frac{23}{57}) = \frac{25}{57} - \frac{25}{57} = 0\)


6. е) \(2 - (1\frac{1}{3} + \frac{2}{3}) = 2 - (\frac{4}{3} + \frac{2}{3}) = 2 - \frac{6}{3} = 2 - 2 = 0\)

Ответ: а) 1⅗⁄₆; б) 1⅗⁄₂₅; в) -⅓⁄₃₃; г) ⅖⁄₇; д) 0; е) 0.