Thực hiện phép tính a) 2/5 + 3/5 : (-3/2) + 1/2; b) 2 1/2 + (-1/3)^2 - 3/2

Câu hỏi:

Trả lời:

a) $\frac{2}{5}+\frac{3}{5}:\left(-\frac{3}{2}\right)+\frac{1}{2}$

$=\frac{2}{5}+\frac{3}{5}.\frac{-2}{3}+\frac{1}{2}$

$=\frac{2}{5}+\frac{-2}{5}+\frac{1}{2}$

$=0+\frac{1}{2}=\frac{1}{2}$

b) $2\frac{1}{2}+{\left(-\frac{1}{3}\right)}^2-\frac{3}{2}$

$=\frac{5}{2}+\frac{1}{9}-\frac{3}{2}$

$$\begin{gathered} =\frac{42}{18}+\frac{2}{18}-\frac{27}{18} \\ =\frac{17}{18}. \end{gathered}$$

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

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

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

$=\left(\frac{7}{8}-\frac{2}{8}\right):{\left(\frac{10}{12}-\frac{9}{12}\right)}^2$

$=\frac{5}{8}:{\left(\frac{1}{12}\right)}^2$$$\begin{gathered} =\frac{5}{8}:\frac{1^2}{{12}^2} \\ =\frac{5}{8}{.12}^2=\frac{5.144}{8}=90. \end{gathered}$$

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

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

$=\frac{-3}{4}-\frac{-1}{2}:\frac{3}{2}+\left(\frac{-5}{4}\right)$

$=\frac{-3}{4}-\frac{-1}{2}:\frac{3}{2}+\left(\frac{-5}{4}\right)$

$=\frac{-3}{4}+\frac{1}{3}+\left(\frac{-5}{4}\right)$

$=\left(\frac{-3}{4}+\frac{-5}{4}\right)+\frac{1}{3}$

$=\frac{-8}{4}+\frac{1}{3}$

$=\frac{-24}{12}+\frac{4}{12}$

$=\frac{-20}{12}=\frac{-5}{3}$