Bài 4 (Trang 15, SGK Toán 7, Tập 1, Bộ Chân trời sáng tạo)

Tính:

$$\begin{gathered} a) \frac{3}{7}.(\frac{-1}{9}) + \frac{3}{7}.(\frac{-2}{3}); \\ b) \left(\frac{-7}{13}\right).\frac{5}{12} + \left(\frac{-7}{13}\right).\frac{7}{12} + \left(\frac{-6}{13}\right); \\ c) [\left(\frac{-2}{3}\right) + \frac{3}{7}]:\frac{5}{9} + (\frac{4}{7} - \frac{1}{3}):\frac{5}{9}; \\ d) \frac{5}{9}:(\frac{1}{11} - \frac{5}{22}) + \frac{5}{9}:(\frac{1}{15} - \frac{2}{3}); \\ e) \frac{3}{5} + \frac{3}{11} - (\frac{-3}{7}) + (\frac{-2}{97}) - \frac{1}{35} -\frac{3}{4} + (\frac{-23}{44}). \end{gathered}$$

Hướng dẫn giải:

$$\begin{gathered} a) \frac{3}{7}.(\frac{-1}{9}) + \frac{3}{7}.(-\frac{2}{3}) \\ =\frac{3}{7}.[\left(\frac{-1}{9}\right) + (-\frac{2}{3})] \\ =\frac{3}{7}.[\left(\frac{-1}{9}\right) + \left(\frac{-6}{9}\right)] \\ =\frac{3}{7}.(\frac{-7}{9})=\frac{-1}{3}. \\ b) \left(\frac{-7}{13}\right).\frac{5}{12} + \left(\frac{-7}{13}\right).\frac{7}{12} + \left(\frac{-6}{13}\right) \\ =\left(\frac{-7}{13}\right).(\frac{5}{12}+\frac{7}{12}) + \left(\frac{-6}{13}\right) \\ =\left(\frac{-7}{13}\right).\frac{12}{12} + \left(\frac{-6}{13}\right)= \frac{-13}{13} = -1 \end{gathered}$$

$$\begin{gathered} c) [\left(\frac{-2}{3}\right)+\frac{3}{7}]:\frac{5}{9} + (\frac{4}{7} - \frac{1}{3}):\frac{5}{9} \\ =[\left(\frac{-2}{3}\right) + \frac{3}{7}].\frac{9}{5} + (\frac{4}{7} - \frac{1}{3}).\frac{9}{5} \\ =\frac{9}{5}.[\left(\frac{-2}{3}\right) - \frac{1}{3} + \frac{3}{7} + \frac{4}{7}] \\ =\frac{9}{5}.(-1 + 1) = 0 \\ d) \frac{5}{9}:(\frac{1}{11} - \frac{5}{22}) + \frac{5}{9}:(\frac{1}{15} - \frac{2}{3}) \\ =\frac{5}{9}:(\frac{2}{22} - \frac{5}{22}) + \frac{5}{9}:(\frac{1}{15} - \frac{10}{15}) \\ =\frac{5}{9}.\frac{-22}{3} + \frac{5}{9}.\frac{-15}{9} \\ =\frac{5}{9}.(\frac{-22}{3} + \frac{-5}{3}) = \frac{5}{9}.(-9) = -5 \\ e) \frac{3}{5} + \frac{3}{11} - (\frac{-3}{7}) + (\frac{-2}{97}) - \frac{1}{35} - \frac{3}{4} + (\frac{-23}{44}) \\ =[\frac{3}{5} - \left(\frac{-3}{7}\right) - \frac{1}{35}] + [\frac{3}{11} - \frac{3}{4} + \left(\frac{-23}{44}\right)] + (\frac{-2}{97}) \\ =[\frac{21}{35} - \left(\frac{-15}{35}\right) - \frac{1}{35}] + [\frac{12}{44} - \frac{33}{44} + \left(\frac{-23}{44}\right)] + (\frac{-2}{97}) \\ =1 + (-1) + (\frac{-2}{97}) = \frac{-2}{97} \end{gathered}$$