Giải Bài 6.24 trang 12

Đề bài

Tính một cách hợp lí:

$\begin{array}{c}a)A=\frac{-5}{7}+\frac{8}{11}+(-\frac{2}{7})+\frac{1}{2}+\frac{3}{11};\\ b)B=\frac{11}{17}+(-\frac{8}{19})+(-\frac{3}{4})+\frac{6}{17}-\frac{30}{19}.\end{array}$

Lời giải chi tiết

$\begin{array}{c}a)A=\frac{-5}{7}+\frac{8}{11}+(-\frac{2}{7})+\frac{1}{2}+\frac{3}{11}\\ =[\frac{-5}{7}+(-\frac{2}{7}\left)\right]+(\frac{8}{11}+\frac{3}{11})+\frac{1}{2}\\ =\frac{-7}{7}+\frac{11}{11}+\frac{1}{2}\\ =(-1)+1+\frac{1}{2}\\ =\frac{1}{2}\\ b)B=\frac{11}{17}+(-\frac{8}{19})+(-\frac{3}{4})+\frac{6}{17}-\frac{30}{19}.\\ =(\frac{11}{17}+\frac{6}{17})+\left[\right(-\frac{8}{19})-\frac{30}{19}]+(-\frac{3}{4})\\ =\frac{17}{17}+\frac{-38}{19}+(-\frac{3}{4})\\ =1+(-2)+(-\frac{3}{4})\\ =\frac{-7}{4}\end{array}$