Вопрос:

2 7 + ( 5 7 − 3 8 ); к) 4 2 5 + ( − 2 5 − 3 7 ); (8 3 4 − 7 2 9 )+ ( 2,25 + 2 9 ); м) 3,15 + ( 2 3 − 2,15); 5 12 − ( 1 12 − 2 3 ); о) 4 5 8 − (2 3 8 + 1 4 ); −8 14 15 − ( 1 3 − 4 15 ); p) (7 11 18 − 3,2) − (2 5 18 + 1,8).

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Ответ:

Краткое пояснение: Решаем примеры, выполняя действия с дробями и десятичными числами.
а) \[\frac{2}{7} + \left(\frac{5}{7} - \frac{3}{8}\right) = \frac{2}{7} + \left(\frac{40}{56} - \frac{21}{56}\right) = \frac{2}{7} + \frac{19}{56} = \frac{16}{56} + \frac{19}{56} = \frac{35}{56} = \frac{5}{8}\]
к) \[4\frac{2}{5} + \left(-\frac{2}{5} - \frac{3}{7}\right) = \frac{22}{5} + \left(-\frac{14}{35} - \frac{15}{35}\right) = \frac{22}{5} - \frac{29}{35} = \frac{154}{35} - \frac{29}{35} = \frac{125}{35} = \frac{25}{7} = 3\frac{4}{7}\]
л) \[\left(8\frac{3}{4} - 7\frac{2}{9}\right) + \left(2.25 + 2\frac{7}{9}\right) = \left(\frac{35}{4} - \frac{65}{9}\right) + \left(\frac{225}{100} + \frac{25}{9}\right) = \left(\frac{315}{36} - \frac{260}{36}\right) + \left(\frac{9}{4} + \frac{25}{9}\right) = \frac{55}{36} + \left(\frac{81}{36} + \frac{100}{36}\right) = \frac{55}{36} + \frac{181}{36} = \frac{236}{36} = \frac{59}{9} = 6\frac{5}{9}\]
м) \[3.15 + \left(\frac{2}{3} - 2.15\right) = 3.15 + \left(\frac{2}{3} - \frac{215}{100}\right) = 3.15 + \left(\frac{2}{3} - \frac{43}{20}\right) = 3.15 + \left(\frac{40}{60} - \frac{129}{60}\right) = 3.15 - \frac{89}{60} = 3.15 - 1.4833 = 1.6667 \approx 1.67\]
н) \[\frac{5}{12} - \left(\frac{1}{12} - \frac{2}{3}\right) = \frac{5}{12} - \left(\frac{1}{12} - \frac{8}{12}\right) = \frac{5}{12} + \frac{7}{12} = \frac{12}{12} = 1\]
о) \[4\frac{5}{8} - \left(2\frac{3}{8} + 1\frac{1}{4}\right) = \frac{37}{8} - \left(\frac{19}{8} + \frac{5}{4}\right) = \frac{37}{8} - \left(\frac{19}{8} + \frac{10}{8}\right) = \frac{37}{8} - \frac{29}{8} = \frac{8}{8} = 1\]
п) \[-8\frac{14}{15} - \left(\frac{1}{3} - \frac{4}{15}\right) = -\frac{134}{15} - \left(\frac{5}{15} - \frac{4}{15}\right) = -\frac{134}{15} - \frac{1}{15} = -\frac{135}{15} = -9\]
р) \[\left(7\frac{11}{18} - 3.2\right) - \left(2\frac{5}{18} + 1.8\right) = \left(\frac{137}{18} - \frac{32}{10}\right) - \left(\frac{41}{18} + \frac{18}{10}\right) = \left(\frac{137}{18} - \frac{16}{5}\right) - \left(\frac{41}{18} + \frac{9}{5}\right) = \left(\frac{685}{90} - \frac{288}{90}\right) - \left(\frac{205}{90} + \frac{162}{90}\right) = \frac{397}{90} - \frac{367}{90} = \frac{30}{90} = \frac{1}{3}\]

Ответ: a) 5/8; к) 3 4/7; л) 6 5/9; м) ≈ 1.67; н) 1; о) 1; п) -9; р) 1/3

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