Bài 1: - \(\dfrac{5}{7}\) x \(\dfrac{31}{33}\) + \(\dfrac{-5}{7}\) x \(\dfrac{2}{33}\) + 2\(\dfrac{5}{7}\)
= - \(\dfrac{5}{7}\) \(\times\) ( \(\dfrac{31}{33}\) + \(\dfrac{2}{33}\)) + 2 + \(\dfrac{5}{7}\)
= - \(\dfrac{5}{7}\) + 2 + \(\dfrac{5}{7}\)
= 2
2, \(\dfrac{3}{14}\): \(\dfrac{1}{28}\) - \(\dfrac{13}{21}\): \(\dfrac{1}{28}\) + \(\dfrac{29}{42}\): \(\dfrac{1}{28}\) - 8
= (\(\dfrac{3}{14}\) - \(\dfrac{13}{21}\) + \(\dfrac{29}{42}\)) : \(\dfrac{1}{28}\) - 8
= \(\dfrac{2}{7}\) x 28 - 8
= 8 - 8
= 0
3, \(\dfrac{37}{43}\) . \(\dfrac{17}{29}\) - \(\dfrac{21}{41}\).\(\dfrac{1}{2}\) + \(\dfrac{9}{58}\): 1\(\dfrac{6}{37}\) - \(\dfrac{6}{29}\): 1\(\dfrac{20}{21}\)
= \(\dfrac{37}{43}\). \(\dfrac{17}{29}\) - \(\dfrac{21}{41}\) . \(\dfrac{1}{2}\) + \(\dfrac{9}{58}\).\(\dfrac{37}{43}\) - \(\dfrac{6}{29}\).\(\dfrac{21}{41}\)
= (\(\dfrac{37}{43}\).\(\dfrac{17}{29}\) + \(\dfrac{9}{58}\).\(\dfrac{37}{43}\)) - (\(\dfrac{21}{41}\).\(\dfrac{1}{2}\) + \(\dfrac{6}{29}\).\(\dfrac{21}{41}\))
= \(\dfrac{37}{43}\).( \(\dfrac{17}{29}\) + \(\dfrac{9}{58}\)) - \(\dfrac{21}{41}\).( \(\dfrac{1}{2}\) + \(\dfrac{6}{29}\))
= \(\dfrac{37}{43}\).\(\dfrac{43}{58}\) - \(\dfrac{21}{41}\).\(\dfrac{41}{58}\)
= \(\dfrac{37}{58}\) - \(\dfrac{21}{58}\)
= \(\dfrac{16}{58}\)
= \(\dfrac{8}{29}\)
(- \(\dfrac{3}{5}\) + \(\dfrac{4}{9}\)): \(\dfrac{2}{7}\) - (-\(\dfrac{14}{9}\) + \(\dfrac{2}{5}\)): \(\dfrac{2}{7}\)
= [ - \(\dfrac{3}{5}\) + \(\dfrac{4}{9}\) + \(\dfrac{14}{9}\) - \(\dfrac{2}{5}\)]: \(\dfrac{2}{7}\)
= [ -( \(\dfrac{3}{5}\) + \(\dfrac{2}{5}\)) + (\(\dfrac{4}{9}\) + \(\dfrac{14}{9}\))]: \(\dfrac{2}{7}\)
= [ - 1 + 2] x \(\dfrac{7}{2}\)
= \(\dfrac{7}{2}\)
4) \(\left(\dfrac{-3}{5}+\dfrac{4}{9}\right):\dfrac{2}{7}-\left(\dfrac{-14}{9}+\dfrac{2}{5}\right):\dfrac{2}{7}\)
\(=\left(\dfrac{-3}{5}+\dfrac{4}{9}+\dfrac{14}{9}-\dfrac{2}{5}\right):\dfrac{2}{7}\)
\(=\left[\left(\dfrac{-3}{5}-\dfrac{2}{5}\right)+\left(\dfrac{4}{9}+\dfrac{14}{9}\right)\right].\dfrac{2}{7}\)
\(=\left(-1+2\right).\dfrac{2}{7}\)
\(=1.\dfrac{2}{7}\)
\(=\dfrac{2}{7}\)
5, \(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}-\dfrac{2}{7}-\dfrac{2}{13}}\) : \(\dfrac{\dfrac{3}{4}-\dfrac{3}{16}-\dfrac{3}{64}}{1-\dfrac{1}{4}-\dfrac{1}{16}}\) + \(\dfrac{5}{8}\)
= \(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{2.\left(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}\right)}\): \(\dfrac{\dfrac{3}{4}.\left(1-\dfrac{1}{4}-\dfrac{1}{16}\right)}{1-\dfrac{1}{4}-\dfrac{1}{16}}\) + \(\dfrac{5}{8}\)
= \(\dfrac{1}{2}\) : \(\dfrac{3}{4}\) + \(\dfrac{5}{8}\)
= \(\dfrac{2}{3}\) + \(\dfrac{5}{8}\)
= \(\dfrac{31}{24}\)
6, \(\dfrac{0,4-\dfrac{2}{9}+\dfrac{2}{11}}{1,4-\dfrac{7}{9}+\dfrac{7}{11}}\) - \(\dfrac{\dfrac{1}{3}-0,25+\dfrac{1}{5}}{1\dfrac{1}{6}-0,875+0,7}\)
= \(\dfrac{2\times\left(0,2-\dfrac{1}{9}+\dfrac{1}{11}\right)}{7\times\left(0,2-\dfrac{1}{9}+\dfrac{1}{11}\right)}\) - \(\dfrac{2\times\left(\dfrac{1}{6}-0,125+0,1\right)}{7\times\left(\dfrac{1}{6}-0,125+0,1\right)}\)
= \(\dfrac{2}{7}\) - \(\dfrac{2}{7}\)
= 0
7, \(\dfrac{4}{9}\) : (\(\dfrac{1}{15}\) - \(\dfrac{2}{3}\)) + \(\dfrac{4}{9}\) .( \(\dfrac{1}{11}\) - \(\dfrac{5}{22}\))
= \(\dfrac{4}{9}\): (- \(\dfrac{3}{5}\)) + \(\dfrac{4}{9}\). (- \(\dfrac{3}{22}\))
= - \(\dfrac{20}{27}\) - \(\dfrac{2}{33}\)
= - \(\dfrac{238}{297}\)