Thực hiện phép tính một cách hợp lí (nếu có thể):
a) $\dfrac{5}{4}-{{\Big(\dfrac{1}{2} \Big)}^{2}}$
b) $\dfrac{2}{3}\cdot \dfrac{-3}{2}+\dfrac{-7}{2}\cdot \dfrac{2}{3}$
c) $\Big(\dfrac{1}{5}+\dfrac{4}{13} \Big)+\Big(\dfrac{-2}{5}+\dfrac{7}{13} \Big)-\Big(\dfrac{4}{5}-\dfrac{2}{13} \Big)$
\(a,\dfrac{5}{4}- \left(\dfrac{1}{2}\right)^2\)
\(=\dfrac{5}{4}-\dfrac{1}{4}\)
\(=1\)
\(b,\dfrac{2}{3}\cdot\dfrac{-3}{2}+\dfrac{-7}{2}\cdot\dfrac{2}{3}\)
\(=\dfrac{2}{3}\cdot\left(\dfrac{-3}{2}+\dfrac{-7}{2}\right)\)
\(=\dfrac{2}{3}\cdot-5\)
\(=-\dfrac{10}{3}\)
\(c,\left(\dfrac{1}{5}+\dfrac{4}{13}\right)+\left(\dfrac{-2}{5}+\dfrac{7}{13}\right)-\left(\dfrac{4}{5}-\dfrac{2}{13}\right)\)
\(=\dfrac{1}{5}+\dfrac{4}{13}-\dfrac{2}{5}+\dfrac{7}{13}-\dfrac{4}{5}+\dfrac{2}{13}\)
\(=\left(\dfrac{1}{5}-\dfrac{2}{5}-\dfrac{4}{5}\right)+\left(\dfrac{4}{13}+\dfrac{7}{13}+\dfrac{2}{13}\right)\)
\(=-1+1\)
`=0`