Question

[Cô Thu Hà]

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) $\Big(\dfrac{1}{5}+\dfrac{4}{13} \Big)+\Big(\dfrac{-2}{5}+\dfrac{7}{13} \Big)-\Big(\dfrac{4}{5}-\dfrac{2}{13} \Big)$

Answer 1

[456]

\(a,\dfrac{5}{4}- \left(\dfrac{1}{2}\right)^2\)

\(=\dfrac{5}{4}-\dfrac{1}{4}\)

\(=1\)

\(b,\dfrac{2}{3}\cdot\dfrac{-3}{2}+\dfrac{-7}{2}\cdot\dfrac{2}{3}\)

\(=\dfrac{2}{3}\cdot\left(\dfrac{-3}{2}+\dfrac{-7}{2}\right)\)

\(=\dfrac{2}{3}\cdot-5\)

\(=-\dfrac{10}{3}\)

\(c,\left(\dfrac{1}{5}+\dfrac{4}{13}\right)+\left(\dfrac{-2}{5}+\dfrac{7}{13}\right)-\left(\dfrac{4}{5}-\dfrac{2}{13}\right)\)

\(=\dfrac{1}{5}+\dfrac{4}{13}-\dfrac{2}{5}+\dfrac{7}{13}-\dfrac{4}{5}+\dfrac{2}{13}\)

\(=\left(\dfrac{1}{5}-\dfrac{2}{5}-\dfrac{4}{5}\right)+\left(\dfrac{4}{13}+\dfrac{7}{13}+\dfrac{2}{13}\right)\)

\(=-1+1\)

`=0`