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МатематикаВычислите (№ 588-589): a) \(\frac{3}{7}-(\frac{1}{2}+\frac{1}{4})\); в) \(-\frac{2}{5}+(\frac{1}{10}-\frac{7}{15})\); б) \(-\frac{3}{7}+(\frac{1}{14}-\frac{2}{21})\); г) \(\frac{2}{5}-(\frac{9}{10}-\frac{1}{3})\); д) \(\frac{3}{14}-\frac{11}{28}-\frac{1}{2}\); e) \((\frac{2}{7}-\frac{1}{14})-\frac{5}{21}\).
Ответ:
Ответ: а) \(-\frac{1}{28}\); б) \(-\frac{23}{42}\); в) \(-\frac{17}{30}\); г) \(\frac{1}{6}\); д) \(-\frac{11}{28}\); е) \(-\frac{1}{6}\)
а) \(\frac{3}{7}-(\frac{1}{2}+\frac{1}{4}) = \frac{3}{7}-(\frac{2}{4}+\frac{1}{4}) = \frac{3}{7}-\frac{3}{4} = \frac{12}{28}-\frac{21}{28} = \frac{12-21}{28} = \frac{-9}{28} = -\frac{9}{28}\)
б) \(-\frac{3}{7}+(\frac{1}{14}-\frac{2}{21}) = -\frac{3}{7}+(\frac{3}{42}-\frac{4}{42}) = -\frac{3}{7}+(-\frac{1}{42}) = -\frac{18}{42}-\frac{1}{42} = \frac{-18-1}{42} = -\frac{19}{42}\)
в) \(-\frac{2}{5}+(\frac{1}{10}-\frac{7}{15}) = -\frac{2}{5}+(\frac{3}{30}-\frac{14}{30}) = -\frac{2}{5}+(-\frac{11}{30}) = -\frac{12}{30}-\frac{11}{30} = \frac{-12-11}{30} = -\frac{23}{30}\)
г) \(\frac{2}{5}-(\frac{9}{10}-\frac{1}{3}) = \frac{2}{5}-(\frac{27}{30}-\frac{10}{30}) = \frac{2}{5}-\frac{17}{30} = \frac{12}{30}-\frac{17}{30} = \frac{12-17}{30} = \frac{-5}{30} = -\frac{1}{6}\)
д) \(\frac{3}{14}-\frac{11}{28}-\frac{1}{2} = \frac{6}{28}-\frac{11}{28}-\frac{14}{28} = \frac{6-11-14}{28} = \frac{-19}{28} = -\frac{19}{28}\)
е) \((\frac{2}{7}-\frac{1}{14})-\frac{5}{21} = (\frac{4}{14}-\frac{1}{14})-\frac{5}{21} = \frac{3}{14}-\frac{5}{21} = \frac{9}{42}-\frac{10}{42} = \frac{9-10}{42} = \frac{-1}{42} = -\frac{1}{42}\)
Ответ: а) \(-\frac{1}{28}\); б) \(-\frac{23}{42}\); в) \(-\frac{17}{30}\); г) \(\frac{1}{6}\); д) \(-\frac{11}{28}\); е) \(-\frac{1}{6}\)
Похожие
- Выполните действия: a) \(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\); в) \(\frac{3}{7}-\frac{11}{14}+\frac{1}{28}\); д) \(\frac{2}{3}-\frac{1}{5}+\frac{4}{15}\); б) \(\frac{1}{9}-\frac{1}{3}+\frac{11}{18}\); г) \(\frac{1}{8}-\frac{1}{2}+\frac{1}{4}\); e) \(-\frac{1}{3}+\frac{1}{4}-\frac{5}{12}\).
- a) -3,5+(4,1 – 7,1); б) (-2,3-7,1) -4,2; в) -0,15-(-2,7-0,15); г) (-4,1-0,42) + 7; д) -2,9-(3,11-0,49); e) 7,4-(8,1 – 9,17).
- Найдите значение выражения (№ 590-591): a) \((\frac{1}{2}-\frac{2}{3})-(\frac{1}{3}+\frac{1}{4})\); б) \((\frac{2}{3}-\frac{1}{5})+(\frac{1}{3}-\frac{2}{5})\); в) \((\frac{1}{2}-\frac{1}{5})-(\frac{1}{3}-\frac{3}{4})\); г) \((\frac{2}{5}-\frac{6}{7})-(\frac{3}{7}-\frac{9}{10})\); д) \((\frac{5}{9}-\frac{1}{2})+(\frac{1}{6}-\frac{1}{3})\); e) \((\frac{2}{5}-\frac{2}{3})-(\frac{3}{7}-\frac{3}{5})\).
- 591 a) (3,5 - 2,9) - (3,7-9,1); б) (1,4-3,1)+(5,6-8,7); в) (7,2-9,13)-(4-8,23); г) (0,48 - 1,2) - (0,92 – 1,4); д) (1,5-6,1) + (1,9 – 9,1); e) (3,9-10)-(8 -9,29).
- 592 Вычислите: a) \(3\frac{1}{2}-5\frac{1}{3}\); \(-\frac{1}{3}+2\frac{1}{5}\); \(-1\frac{1}{2}-3\frac{1}{9}\); б) \(-7\frac{1}{3}-1\frac{1}{2}\); \(-3\frac{1}{2}+\frac{1}{9}\); \(-4\frac{1}{5}-(-\frac{1}{2})\); в) \(3\frac{2}{5}-5\frac{1}{2}\); \(2\frac{1}{9}-9\frac{1}{4}\); \(3\frac{1}{7}-(-\frac{12}{5})\).
