Giải Bài 5 trang 38

Đề bài

Tính một cách hợp lí:

a)     $\frac{27}{13}-\frac{106}{111}+\frac{-5}{111}$

b)    $\frac{12}{11}-\frac{-7}{19}+\frac{12}{19}$

c)     $\frac{5}{17}-\frac{25}{31}+\frac{12}{17}+\frac{-6}{31}$

Lời giải chi tiết

a)$\frac{27}{13}-\frac{106}{111}+\frac{-5}{111}=\frac{27}{13}+(\frac{-106}{111}+\frac{-5}{111})$$=\frac{27}{13}+\frac{-111}{111}=\frac{27}{13}+(-1)$$=\frac{27}{13}+\frac{-13}{13}=\frac{14}{13}$

b)$\frac{12}{11}-\frac{-7}{19}+\frac{12}{19}=\frac{12}{11}+(\frac{7}{19}+\frac{12}{19})$$=\frac{12}{11}+\frac{19}{19}=\frac{12}{11}+1$$=\frac{12}{11}+\frac{11}{11}=\frac{23}{11}$

c) $\frac{5}{17}-\frac{25}{31}+\frac{12}{17}+\frac{-6}{31}=(\frac{5}{17}+\frac{12}{17})+(\frac{-25}{31}+\frac{-6}{31})$$=\frac{17}{17}+\frac{-31}{31}=1+(-1)=0$