a) \(\dfrac{-3}{4}\cdot\dfrac{7}{13}+\dfrac{3}{4}\cdot\dfrac{-6}{13}+\dfrac{5}{4}\)
\(=\dfrac{3}{4}\cdot\left(\dfrac{-7}{13}+\dfrac{-6}{13}\right)+\dfrac{5}{4}\)
\(=\dfrac{3}{4}\cdot-1+\dfrac{5}{4}\)
\(=\dfrac{-3+5}{4}\)
\(=\dfrac{1}{2}\)
b) \(6\cdot\dfrac{-7}{12}:\dfrac{-18}{49}\cdot81\)
\(=\dfrac{6\cdot-7}{12}:\dfrac{-18}{49}\cdot81\)
\(=\dfrac{-7}{2}:\dfrac{-18}{49}\cdot81\)
\(=\dfrac{-7}{2}\cdot\dfrac{49}{-18}\cdot81\)
\(=\dfrac{-343}{-36}\cdot81\)
\(=\dfrac{3087}{4}\)
c) \(\dfrac{-3}{5}+\dfrac{7}{12}-\dfrac{2}{5}-\dfrac{-5}{12}\)
\(=\dfrac{-3}{5}+\dfrac{7}{12}-\dfrac{2}{5}+\dfrac{5}{12}\)
\(=\left(\dfrac{-3}{5}-\dfrac{2}{5}\right)+\left(\dfrac{7}{12}+\dfrac{5}{12}\right)\)
\(=-1+1\)
\(=0\)
