Вопрос:

2. Выполните действия (Вариант 1): 1) 1/19 + 15/19 - 13/19; 2) 6 5/27 - 4 12/27 + 6 16/27; 3) 1 - 9/17; 4) 9 3/12 - 5 9/12. Выполните действия (Вариант 2): 1) 7/27 + 12/27 - 13/27; 2) 4 16/32 - 1 4/32 + 3 5/32; 3) 1 - 24/36; 4) 7 12/26 - 2 21/26.

Ответ:

Вариант 1: 1) \(\frac{1}{19} + \frac{15}{19} - \frac{13}{19} = \frac{1+15-13}{19} = \frac{3}{19}\) 2) \(6 \frac{5}{27} - 4 \frac{12}{27} + 6 \frac{16}{27} = (6-4+6) + (\frac{5}{27} - \frac{12}{27} + \frac{16}{27}) = 8 + \frac{5-12+16}{27} = 8 + \frac{9}{27} = 8 + \frac{1}{3} = 8 \frac{1}{3}\) 3) \(1 - \frac{9}{17} = \frac{17}{17} - \frac{9}{17} = \frac{17-9}{17} = \frac{8}{17}\) 4) \(9 \frac{3}{12} - 5 \frac{9}{12} = (9-5) + (\frac{3}{12} - \frac{9}{12}) = 4 - \frac{6}{12} = 4 - \frac{1}{2} = 3 \frac{1}{2}\) Вариант 2: 1) \(\frac{7}{27} + \frac{12}{27} - \frac{13}{27} = \frac{7+12-13}{27} = \frac{6}{27} = \frac{2}{9}\) 2) \(4 \frac{16}{32} - 1 \frac{4}{32} + 3 \frac{5}{32} = (4-1+3) + (\frac{16}{32} - \frac{4}{32} + \frac{5}{32}) = 6 + \frac{16-4+5}{32} = 6 + \frac{17}{32} = 6 \frac{17}{32}\) 3) \(1 - \frac{24}{36} = \frac{36}{36} - \frac{24}{36} = \frac{36-24}{36} = \frac{12}{36} = \frac{1}{3}\) 4) \(7 \frac{12}{26} - 2 \frac{21}{26} = (7-2) + (\frac{12}{26} - \frac{21}{26}) = 5 - \frac{9}{26} = 4 + \frac{26}{26} - \frac{9}{26} = 4 + \frac{17}{26} = 4 \frac{17}{26}\)
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