Question

Thực hiện phép tính.

a)\(\dfrac{2}{5}\)+\(\dfrac{3}{5}\):(−\(\dfrac{3}{2}\))+\(\dfrac{1}{2}\);

b)2\(\dfrac{1}{3}\)+(−\(\dfrac{1}{3}\))²−\(\dfrac{3}{2}\);

c)(\(\dfrac{7}{8}\)−0,25):(\(\dfrac{5}{6}\)−0,75)²;

d)(−0,75)−[(−2)+\(\dfrac{3}{2}\)]:1,5+(−\(\dfrac{5}{4}\))

 

Answer 1

a)

\(\dfrac{2}{5}+\dfrac{3}{5}:\left(-\dfrac{3}{2}\right)+\dfrac{1}{2}\)

\(=\dfrac{2}{5}+\dfrac{3}{5}.\dfrac{-2}{3}+\dfrac{1}{2}\)

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

\(=0+\dfrac{1}{2}\)

\(=\dfrac{1}{2}\)

b)

\(2\dfrac{1}{3}+\left(-\dfrac{1}{3}\right)^2-\dfrac{3}{2}\)

\(=\dfrac{7}{3}+\dfrac{1}{9}-\dfrac{3}{2}\)

\(=\dfrac{21}{9}+\dfrac{1}{9}-\dfrac{3}{2}\)

\(=\dfrac{22}{9}-\dfrac{3}{2}\)

\(=\dfrac{44}{18}-\dfrac{27}{18}\)

\(=\dfrac{17}{18}\)

c)

\(\left(\dfrac{7}{8}-0,25\right):\left(\dfrac{5}{6}-0,75\right)^2\)

\(=\left(\dfrac{7}{8}-\dfrac{1}{4}\right):\left(\dfrac{5}{6}-\dfrac{3}{4}\right)^2\)

\(=\left(\dfrac{7}{8}-\dfrac{2}{8}\right):\left(\dfrac{20}{24}-\dfrac{18}{24}\right)^2\)

\(=\dfrac{5}{8}:\left(\dfrac{1}{12}\right)^2\)

\(=\dfrac{5}{8}:\dfrac{1}{144}\)

\(=\dfrac{5}{8}.\dfrac{144}{1}\)

\(=90\)

d)

\(\left(-0,75\right)-\left[\left(-2\right)+\dfrac{3}{2}\right]:1,5+\left(-\dfrac{5}{4}\right)\)

\(=\dfrac{-3}{4}-\left[\left(-2\right)+\dfrac{3}{2}\right]:\dfrac{3}{2}+\dfrac{-5}{4}\)

\(=\dfrac{-3}{4}-\dfrac{-1}{2}:\dfrac{3}{2}+\dfrac{-5}{4}\)

\(=\dfrac{-3}{4}-\dfrac{-1}{2}.\dfrac{2}{3}+\dfrac{-5}{4}\)

\(=\dfrac{-3}{4}-\dfrac{-1}{3}+\dfrac{-5}{4}\)

\(=\dfrac{-9}{12}-\dfrac{-4}{12}+\dfrac{-5}{4}\)

\(=\dfrac{-5}{12}+\dfrac{-5}{4}\)

\(=\dfrac{-5}{12}+\dfrac{-15}{12}\)

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

Answer 2

a) \(\dfrac{2}{5}\)+\(\dfrac{3}{5}\):(-\(\dfrac{3}{2}\))+\(\dfrac{1}{2}\)

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

=0+\(\dfrac{1}{2}\)

=\(\dfrac{1}{2}\)