\(b,\dfrac{15}{37}.\left(\dfrac{38}{41}-\dfrac{74}{45}\right)+\dfrac{38}{41}.\left(\dfrac{82}{76}-\dfrac{15}{37}\right)\)
\(=\dfrac{15}{37}.\dfrac{38}{41}-\dfrac{15}{37}.\dfrac{74}{45}+\dfrac{38}{41}.\dfrac{82}{76}-\dfrac{38}{41}.\dfrac{15}{37}\)
\(=\left(\dfrac{15}{37}.\dfrac{38}{41}-\dfrac{38}{41}.\dfrac{15}{37}\right)-\dfrac{15}{37}.\dfrac{74}{45}+\left(\dfrac{-38}{41}.\dfrac{41}{38}\right)\)
\(=\left[\dfrac{38}{41}.\left(\dfrac{15}{37}-\dfrac{15}{37}\right)\right]-\dfrac{1.2}{3}-1\)
\(=0-\dfrac{2}{3}-1\)
\(=\dfrac{-2}{3}-\dfrac{3}{3}\)
\(=\dfrac{-5}{3}\)
\(c,\dfrac{2020}{2021}.\left(\dfrac{7}{6}-\dfrac{3}{4}\right)+\dfrac{2020}{2021}.\left(\dfrac{5}{6}-\dfrac{1}{4}\right)\)
\(=\dfrac{2020}{2021}.\left(\dfrac{14}{12}-\dfrac{9}{12}\right)+\dfrac{2020}{2021}.\left(\dfrac{10}{12}-\dfrac{3}{12}\right)\)
\(=\dfrac{2020}{2021}.\dfrac{5}{12}+\dfrac{2020}{2021}.\dfrac{7}{12}\)
\(=\dfrac{2020}{2021}.\left(\dfrac{5}{12}+\dfrac{7}{12}\right)\)
\(=\dfrac{2020}{2021}.1\)
\(=\dfrac{2020}{2021}\)
\(e,\dfrac{\dfrac{2}{7}+\dfrac{2}{5}+\dfrac{2}{17}-\dfrac{2}{25}}{\dfrac{3}{14}+\dfrac{3}{10}+\dfrac{3}{34}-\dfrac{3}{50}}\)
\(\dfrac{\dfrac{4}{14}+\dfrac{4}{10}+\dfrac{4}{34}-\dfrac{4}{50}}{\dfrac{3}{14}+\dfrac{3}{10}+\dfrac{3}{34}-\dfrac{3}{50}}\)
\(\dfrac{4.\left(\dfrac{1}{14}+\dfrac{1}{10}+\dfrac{1}{34}-\dfrac{1}{50}\right)}{3.\left(\dfrac{1}{14}+\dfrac{1}{10}+\dfrac{1}{34}-\dfrac{1}{50}\right)}\)
\(=\dfrac{4}{3}\)
\(f,\dfrac{0,375-0,3+\dfrac{3}{11}+\dfrac{3}{12}}{-0,625+0,5-\dfrac{5}{11}-\dfrac{5}{12}}\)
\(=\dfrac{\dfrac{3}{8}-\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}}{\dfrac{-5}{8}+\dfrac{5}{10}-\dfrac{5}{11}-\dfrac{5}{12}}\)
\(=\dfrac{\dfrac{3}{8}-\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}}{\dfrac{-5}{8}-\dfrac{-5}{10}+\dfrac{-5}{11}+\dfrac{-5}{12}}\)
\(=\dfrac{3.\left(\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}\right)}{-5.\left(\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}\right)}\)
\(=\dfrac{3}{-5}\)
\(=\dfrac{-3}{5}\)
\(b,\dfrac{15}{37}\cdot\left(\dfrac{38}{41}-\dfrac{74}{45}\right)+\dfrac{38}{41}\cdot\left(\dfrac{82}{76}-\dfrac{15}{37}\right)\)
\(=\dfrac{15}{37}\cdot-\dfrac{1324}{1845}+\dfrac{38}{41}\cdot\dfrac{947}{1406}\)
\(=\dfrac{1}{37}\cdot-\dfrac{1324}{123}+\dfrac{1}{41}\cdot\dfrac{947}{37}\)
\(=\dfrac{1}{37}\cdot-\dfrac{1324}{123}+\dfrac{1}{37}\cdot\dfrac{947}{41}\)
\(=\dfrac{1}{37}\cdot\left(-\dfrac{1324}{123}+\dfrac{947}{41}\right)\)
\(=\dfrac{1}{37}\cdot\dfrac{37}{3}\)
\(=\dfrac{1}{3}\)
\(c,\dfrac{2020}{2021}\cdot\left(\dfrac{7}{6}-\dfrac{3}{4}\right)+\dfrac{2020}{2021}\cdot\left(\dfrac{5}{6}-\dfrac{1}{4}\right)\)
\(=\dfrac{2020}{2021}\cdot\left(\dfrac{7}{6}-\dfrac{3}{4}+\dfrac{5}{6}-\dfrac{1}{4}\right)\)
\(=\dfrac{2020}{2021}\cdot\left[\left(\dfrac{7}{6}+\dfrac{5}{6}\right)-\left(\dfrac{3}{4}+\dfrac{1}{4}\right)\right]\)
\(=\dfrac{2020}{2021}\cdot\left[2-1\right]\)
\(=\dfrac{2020}{2021}\cdot1\)
\(=\dfrac{2020}{2021}\)
\(d,\left(1-\dfrac{2}{5}\right)\left(1-\dfrac{2}{7}\right)\left(1-\dfrac{2}{9}\right)...\left(1-\dfrac{2}{99}\right)\)
\(=\dfrac{3}{5}\cdot\dfrac{5}{7}\cdot\dfrac{7}{9}\cdot\cdot\cdot\dfrac{97}{99}\)
\(=\dfrac{3\cdot5\cdot7\cdot\cdot\cdot97}{5\cdot7\cdot9\cdot\cdot\cdot99}\)
\(=\dfrac{1}{33}\)
\(e,\dfrac{\dfrac{2}{7}+\dfrac{2}{5}+\dfrac{2}{17}-\dfrac{2}{25}}{\dfrac{3}{14}+\dfrac{3}{10}+\dfrac{3}{34}-\dfrac{3}{50}}\)
\(=\dfrac{2\cdot\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{25}\right)}{3\cdot\left(\dfrac{1}{14}+\dfrac{1}{10}+\dfrac{1}{34}-\dfrac{1}{50}\right)}\)
\(=2\cdot\dfrac{2}{3}\)
\(=\dfrac{4}{3}\)
\(f,\dfrac{0,375-0,3+\dfrac{3}{11}+\dfrac{3}{12}}{-0,625+0,5-\dfrac{5}{11}-\dfrac{5}{12}}\)
\(=\dfrac{\dfrac{3}{8}-\dfrac{3}{10}+\dfrac{3}{11}+\dfrac{3}{12}}{-\dfrac{5}{8}+\dfrac{5}{10}-\dfrac{5}{11}-\dfrac{5}{12}}\)
\(=\dfrac{3\cdot\left(\dfrac{1}{8}-\dfrac{1}{10}+\dfrac{1}{11}+\dfrac{1}{12}\right)}{5\cdot\left(-\dfrac{1}{8}+\dfrac{1}{10}-\dfrac{1}{11}-\dfrac{1}{12}\right)}\)
\(=\dfrac{3}{5}\cdot-1\)
\(=-\dfrac{3}{5}\)
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