Вопрос:

4.373 Вычислите значение выражения наиболее удобным способом: a) 2-(-50) 8-11; 6) 15-4-(-2)-(-25); в) 0,4(-0,08) (-1,5) 12,5; e) -0,220 (-0,5) (-2)

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Ответ:

Краткое пояснение: Для упрощения вычислений используем переместительное и сочетательное свойства умножения.
a) 2 ⋅ (−50) ⋅ 8 ⋅ 11 = 2 ⋅ 8 ⋅ (−50) ⋅ 11 = 16 ⋅ (−50) ⋅ 11 = −800 ⋅ 11 = −8800
б) 15 ⋅ 4 ⋅ (−2) ⋅ (−25) = 15 ⋅ (−2) ⋅ 4 ⋅ (−25) = −30 ⋅ (−100) = 3000
в) 0,4 ⋅ (−0,08) ⋅ (−1,5) ⋅ 12,5 = 0,4 ⋅ 12,5 ⋅ (−0,08) ⋅ (−1,5) = 5 ⋅ 0,12 = 0,6
г) \(-\frac{2}{7}\) ⋅ \(\frac{11}{18}\) ⋅ \(-\frac{7}{8}\) ⋅ \(\frac{9}{11}\) = \(-\frac{2}{7}\) ⋅ \(-\frac{7}{8}\) ⋅ \(\frac{11}{18}\) ⋅ \(\frac{9}{11}\) = \(\frac{2}{8}\) ⋅ \(\frac{9}{18}\) = \(\frac{1}{4}\) ⋅ \(\frac{1}{2}\) = \(\frac{1}{8}\)
д) −2\(\frac{1}{4}\) ⋅ \((-1\frac{5}{9})\) ⋅ (−4) ⋅ (−9) = \(-\frac{9}{4}\) ⋅ \(-\frac{14}{9}\) ⋅ (−4) ⋅ (−9) = \(\frac{9}{4}\) ⋅ \(\frac{14}{9}\) ⋅ 4 ⋅ 9 = \(\frac{9}{9}\) ⋅ \(\frac{4}{4}\) ⋅ 14 ⋅ 9 = 14 ⋅ 9 = 126
e) −0,2 ⋅ 2\(\frac{5}{8}\) ⋅ (−0,5) ⋅ \(-\frac{8}{21}\) = −0,2 ⋅ (−0,5) ⋅ 2\(\frac{5}{8}\) ⋅ \(-\frac{8}{21}\) = 0,1 ⋅ \(\frac{21}{8}\) ⋅ \(-\frac{8}{21}\) = -0,1

Ответ: а) -8800; б) 3000; в) 0,6; г) \(\frac{1}{8}\); д) 126; е) -0,1

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