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МатематикаНайдите 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) \((\frac{2}{5}-\frac{2}{3})-(\frac{3}{7}-\frac{3}{5})\).
Ответ:
Ответ: a) \(-\frac{13}{12}\); б) \(\frac{1}{5}\); в) \(\frac{49}{30}\); г) \(-\frac{23}{70}\); д) \(-\frac{5}{18}\); е) \(\frac{16}{105}\)
a) \((\frac{1}{2}-\frac{2}{3})-(\frac{1}{3}+\frac{1}{4}) = (\frac{3}{6}-\frac{4}{6})-(\frac{4}{12}+\frac{3}{12}) = (\frac{-1}{6})-(\frac{7}{12}) = \frac{-2}{12}-\frac{7}{12} = \frac{-2-7}{12} = \frac{-9}{12} = -\frac{3}{4}\)
б) \((\frac{2}{3}-\frac{1}{5})+(\frac{1}{3}-\frac{2}{5}) = (\frac{10}{15}-\frac{3}{15})+(\frac{5}{15}-\frac{6}{15}) = \frac{7}{15}+(\frac{-1}{15}) = \frac{7}{15}-\frac{1}{15} = \frac{7-1}{15} = \frac{6}{15} = \frac{2}{5}\)
в) \((\frac{1}{2}-\frac{1}{5})-(\frac{1}{3}-\frac{3}{4}) = (\frac{5}{10}-\frac{2}{10})-(\frac{4}{12}-\frac{9}{12}) = \frac{3}{10}-(\frac{-5}{12}) = \frac{3}{10}+\frac{5}{12} = \frac{18}{60}+\frac{25}{60} = \frac{18+25}{60} = \frac{43}{60}\)
г) \((\frac{2}{5}-\frac{6}{7})-(\frac{3}{7}-\frac{9}{10}) = (\frac{14}{35}-\frac{30}{35})-(\frac{30}{70}-\frac{63}{70}) = \frac{-16}{35}-(\frac{-33}{70}) = \frac{-32}{70}+\frac{33}{70} = \frac{-32+33}{70} = \frac{1}{70}\)
д) \((\frac{5}{9}-\frac{1}{2})+(\frac{1}{6}-\frac{1}{3}) = (\frac{10}{18}-\frac{9}{18})+(\frac{1}{6}-\frac{2}{6}) = \frac{1}{18}+(\frac{-1}{6}) = \frac{1}{18}-\frac{3}{18} = \frac{1-3}{18} = \frac{-2}{18} = -\frac{1}{9}\)
е) \((\frac{2}{5}-\frac{2}{3})-(\frac{3}{7}-\frac{3}{5}) = (\frac{6}{15}-\frac{10}{15})-(\frac{15}{35}-\frac{21}{35}) = \frac{-4}{15}-(\frac{-6}{35}) = \frac{-28}{105}+\frac{18}{105} = \frac{-28+18}{105} = \frac{-10}{105} = -\frac{2}{21}\)
Ответ: a) \(-\frac{13}{12}\); б) \(\frac{1}{5}\); в) \(\frac{49}{30}\); г) \(-\frac{23}{70}\); д) \(-\frac{5}{18}\); е) \(\frac{16}{105}\)
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) \(-\frac{1}{3}+\frac{1}{4}-\frac{5}{12}\).
- Вычислите (№ 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) \((\frac{2}{7}-\frac{1}{14})-\frac{5}{21}\).
- 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).
- 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) \(3\frac{2}{5}-5\frac{1}{2}\); \(2\frac{1}{9}-9\frac{1}{4}\); \(3\frac{1}{7}-(-\frac{12}{5})\).
