Bài 3
a) \(\dfrac{31}{23}-\left(\dfrac{7}{32}+\dfrac{8}{23}\right)\)
\(=\dfrac{31}{23}-\dfrac{7}{32}-\dfrac{8}{23}\)
\(=\left(\dfrac{31}{23}-\dfrac{8}{23}\right)-\dfrac{7}{32}\)
\(=1-\dfrac{7}{32}\)
\(=\dfrac{25}{32}\)
b) \(\left(\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}\right)-\left(\dfrac{79}{67}-\dfrac{28}{41}\right)\)
\(=\dfrac{1}{3}+\dfrac{12}{67}+\dfrac{13}{41}-\dfrac{79}{67}+\dfrac{28}{11}\)
\(=\left(\dfrac{12}{67}-\dfrac{79}{67}\right)+\left(\dfrac{13}{41}+\dfrac{28}{41}\right)+\dfrac{1}{3}\)
\(=-1+1+\dfrac{1}{3}\)
\(=0+\dfrac{1}{3}\)
\(=\dfrac{1}{3}\)
c) \(\left(-30,75\right)+\left(\dfrac{31}{10}-69,25\right)-\left(-6,9\right)\)
\(=\left(-30,75\right)+\dfrac{31}{10}-69,25+6,9\)
\(=\left[\left(-30,75\right)-69,25\right]+\left(3,1+6,9\right)\)
\(=\left(-100\right)+10\)
\(=-90\)
d) \(\left(-34,5\right).\dfrac{11}{25}-65,5\dfrac{11}{25}\)
\(=\dfrac{11}{25}.\left(-34,5-65,5\right)\)
\(=\dfrac{11}{25}.\left(-100\right)\)
\(=-44\)
e) \(\left(-\dfrac{1}{5}+\dfrac{3}{7}\right):\dfrac{5}{4}+\left(-\dfrac{4}{5}+\dfrac{4}{7}\right):\dfrac{5}{4}\)
\(=\left(-\dfrac{1}{5}+\dfrac{3}{7}-\dfrac{4}{5}+\dfrac{4}{7}\right):\dfrac{5}{4}\)
\(=\left[\left(-\dfrac{1}{5}-\dfrac{4}{5}\right)+\left(\dfrac{3}{7}+\dfrac{4}{7}\right)\right]:\dfrac{5}{4}\)
\(=\left(-1+1\right):\dfrac{5}{4}\)
\(=0:\dfrac{5}{4}\)
\(=0\)
f) \(\left(-\dfrac{2}{3}+\dfrac{3}{13}\right):\dfrac{7}{8}+\left(-\dfrac{1}{3}+\dfrac{10}{13}\right):\dfrac{7}{8}\)
\(=\left(-\dfrac{2}{3}+\dfrac{3}{13}-\dfrac{1}{3}+\dfrac{10}{13}\right):\dfrac{7}{8}\)
\(=\left[\left(-\dfrac{2}{3}-\dfrac{1}{3}\right)+\left(\dfrac{3}{13}+\dfrac{10}{13}\right)\right]:\dfrac{7}{8}\)
\(=\left(-1+1\right):\dfrac{7}{8}\)
\(=0:\dfrac{7}{8}\)
\(=0\)
