Tính một cách hợp lí:

a) $A=\frac{-3}{14}+\frac{2}{13}+\frac{-25}{14}+\frac{-15}{13};$

b) $B=\frac{5}{3}.\frac{7}{25}+\frac{5}{3}.\frac{21}{25}-\frac{5}{3}.\frac{7}{25}$.

Giải

a) $A=\frac{-3}{14}+\frac{2}{13}+\frac{-25}{14}+\frac{-15}{13}$

$$\begin{gathered} =\left(\frac{-3}{14}+\frac{-25}{14}\right)+\left(\frac{2}{13}+\frac{-15}{13}\right) \\ =\frac{(-3)+(-25)}{14}+\frac{2+(-15)}{13} \\ =\frac{-(3+25)}{14}+\frac{2+(-15)}{13} \\ =\frac{-28}{14}+\frac{-13}{13} \\ =(-2)+(-1) \\ =-(1+2) \\ =-3 \end{gathered}$$

b) $B=\frac{5}{3}.\frac{7}{25}+\frac{5}{3}.\frac{21}{25}-\frac{5}{3}.\frac{7}{25}$

$$\begin{gathered} =\frac{5}{3}.\left(\frac{7}{25}+\frac{21}{25}-\frac{7}{25}\right) \\ =\frac{5}{3}.\frac{7+21-7}{25} \\ =\frac{5}{3}.\frac{21}{25} \\ =\frac{7}{5} \end{gathered}$$