Tính hợp lí :
\(\dfrac{51}{96}+\dfrac{3}{11}+\dfrac{17}{14}+\dfrac{-17}{22}-\dfrac{5}{7}\)
\(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
\(\dfrac{10}{19}\cdot\left(-\dfrac{4}{9}\right)-\dfrac{10}{19}\cdot\dfrac{11}{18}\)
a: \(\dfrac{51}{96}+\dfrac{3}{11}+\dfrac{17}{14}+\dfrac{-17}{22}-\dfrac{5}{7}\)
\(=\left(\dfrac{17}{14}-\dfrac{5}{7}\right)+\left(\dfrac{3}{11}-\dfrac{17}{22}\right)+\dfrac{17}{32}\)
\(=\dfrac{7}{14}+\dfrac{6-17}{22}+\dfrac{17}{32}=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{17}{32}=\dfrac{17}{32}\)
b: \(\left(-\dfrac{1}{2}\right)-\left(-\dfrac{3}{5}\right)+\left(-\dfrac{1}{9}\right)-\left(-\dfrac{2}{7}\right)+\dfrac{4}{35}-\dfrac{7}{18}\)
\(=\left(-\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{7}{18}\right)+\left(\dfrac{3}{5}+\dfrac{2}{7}+\dfrac{4}{35}\right)\)
\(=\dfrac{-9-2-7}{18}+\dfrac{21+10+4}{35}\)
\(=-\dfrac{18}{18}+\dfrac{35}{35}\)
=-1+1
=0
c: \(\dfrac{10}{19}\left(-\dfrac{4}{9}\right)-\dfrac{10}{19}\cdot\dfrac{11}{18}\)
\(=\dfrac{10}{19}\left(-\dfrac{4}{9}-\dfrac{11}{18}\right)\)
\(=\dfrac{10}{19}\cdot\dfrac{-8-11}{18}=\dfrac{-10}{18}=\dfrac{-5}{9}\)
