Bài 5 (Trang 38 SGK Toán lớp 6 Tập 2 - Bộ Cánh diều):

Tính một cách hợp lí :

$$\begin{gathered} a, \frac{27}{13}-\frac{106}{111}+\frac{-5}{111} \\ b,\frac{12}{11}-\frac{-7}{19}+\frac{12}{19} \\ c, \frac{5}{17}-\frac{25}{31}+\frac{12}{17}+\frac{-6}{31} \end{gathered}$$

Hướng dẫn giải:

$$\begin{gathered} a) \frac{27}{13} - \frac{106}{111} + \frac{-5}{111} = \frac{27}{13} + (\frac{-106}{111} + \frac{-5}{111}) \\ = \frac{27}{13} + (-\frac{111}{111}) = \frac{27}{13} +\hspace{0.17em}(-1) = \frac{27}{13} - \frac{13}{13} \\ = \frac{27 - 13}{13} = \frac{14}{13}. \end{gathered}$$

$$\begin{gathered} b) \frac{12}{11} - \frac{-7}{19} + \frac{12}{19} = \frac{12}{11} + \frac{7}{19} + \frac{12}{19} \\ =\frac{12}{11} + \frac{19}{19} = \frac{12}{11} +\hspace{0.17em}1 = \frac{12}{11} + \frac{11}{11} \\ = \frac{23}{11} \end{gathered}$$

$$\begin{gathered} c) \frac{5}{17} - \frac{25}{31} + \frac{12}{17} + \frac{-6}{31} \\ = (\frac{5}{17} +\hspace{0.17em}\frac{12}{17}) + (\frac{-25}{31} + \frac{-6}{31}) \\ = (\frac{5 +\hspace{0.17em}12}{17}) + (\frac{-25 - 6}{31}) = \frac{17}{17} +\hspace{0.17em}\frac{-31}{31} \\ = 1 + (-1) = 0 \end{gathered}$$