Cho biểu thức:

A = $\left(2+\frac{1}{3}-\frac{2}{5}\right)-\left(7-\frac{3}{5}-\frac{4}{3}\right)-\left(\frac{1}{5}+\frac{5}{3}-4\right)$

Hãy tính giá trị của A theo hai cách:

a) Tính giá trị của từng biểu thức trong dấu ngoặc trước.

b) Bỏ dấu ngoặc rồi nhóm các số hạng thích hợp.

a) $x+\frac{3}{5}=\frac{2}{3}$

$$\begin{gathered} x=\frac{2}{3}-\frac{3}{5} \\ x=\frac{10}{15}-\frac{9}{15} \\ x=\frac{1}{15} \end{gathered}$$

Vậy $x=\frac{1}{15}$

b) $\frac{3}{7}-x=\frac{2}{5}$

$$\begin{gathered} x=\frac{3}{7}-\frac{2}{5} \\ x=\frac{15}{35}-\frac{14}{35} \\ x=\frac{1}{35} \end{gathered}$$

Vậy $x=\frac{1}{35}$

c) $\frac{4}{9}-\frac{2}{3}x=\frac{1}{3}$

$$\begin{gathered} \frac{2}{3}x=\frac{4}{9}-\frac{1}{3} \\ \frac{2}{3}x=\frac{4}{9}-\frac{3}{9} \\ \frac{2}{3}x=\frac{1}{9} \\ x=\frac{1}{9}:\frac{2}{3} \\ x=\frac{1}{9}.\frac{3}{2} \\ x=\frac{1}{6} \end{gathered}$$

Vậy $x=\frac{1}{6}$

d) $\frac{3}{10}x-1\frac{1}{2}=\left(\frac{-2}{7}\right):\frac{5}{14}$

$$\begin{gathered} \frac{3}{10}x-\frac{3}{2}=\frac{-2}{7}.\frac{14}{5} \\ \frac{3}{10}x-\frac{3}{2}=\frac{-4}{5} \\ \frac{3}{10}x=\frac{-4}{5}+\frac{3}{2} \\ \frac{3}{10}x=\frac{-8}{10}+\frac{15}{10} \\ \frac{3}{10}x=\frac{7}{10} \\ x=\frac{7}{10}:\frac{3}{10} \\ x=\frac{7}{10}.\frac{10}{3} \\ x=\frac{7}{3} \end{gathered}$$

Vậy$x=\frac{7}{3}$

a) $\frac{13}{23}.\frac{7}{11}+\frac{10}{23}.\frac{7}{11}$

$=\frac{7}{11}.\left(\frac{13}{23}+\frac{10}{23}\right)$

$=\frac{7}{11}.\frac{23}{23}=\frac{7}{11}$

b) $\frac{5}{9}.\frac{23}{11}-\frac{1}{11}.\frac{5}{9}+\frac{5}{9}$

$=\frac{5}{9}.\left(\frac{23}{11}-\frac{1}{11}+1\right)$

$=\frac{5}{9}.\left(\frac{22}{11}+1\right)$$=\frac{5}{9}.3=\frac{5}{3}$

c) $\left[\left(-\frac{4}{9}\right)+\frac{3}{5}\right]:\frac{13}{17}+\left(\frac{2}{5}-\frac{5}{9}\right):\frac{13}{17}$

$=\left[\left(-\frac{4}{9}\right)+\frac{3}{5}\right].\frac{17}{13}+\left(\frac{2}{5}-\frac{5}{9}\right).\frac{17}{13}$

$=\frac{17}{13}.\left(-\frac{4}{9}+\frac{3}{5}+\frac{2}{5}-\frac{5}{9}\right)$

$$\begin{gathered} =\frac{17}{13}.\left[\left(\frac{-4}{9}-\frac{5}{9}\right)+\left(\frac{3}{5}+\frac{2}{5}\right)\right] \\ =\frac{17}{13}.\left(-1+1\right)=0. \end{gathered}$$

d) $\frac{3}{16}:\left(\frac{3}{22}-\frac{3}{11}\right)+\frac{3}{16}:\left(\frac{1}{10}-\frac{2}{5}\right)$

$=\frac{3}{16}:\left(\frac{3}{22}-\frac{6}{22}\right)+\frac{3}{16}:\left(\frac{1}{10}-\frac{4}{10}\right)$

$=\frac{3}{16}:\frac{-3}{22}+\frac{3}{16}:\frac{-3}{10}$

$=\frac{3}{16}.\frac{22}{-3}+\frac{3}{16}.\frac{10}{-3}$

$=\frac{3}{16}.\left(\frac{22}{-3}+\frac{10}{-3}\right)$$=\frac{3}{16}.\frac{32}{-3}$$=-2$