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

Tính:

$$\begin{gathered} a) \frac{2}{15} + (\frac{-5}{24}); \\ b) \left(\frac{-5}{9}\right) - (-\frac{7}{27}); \\ c) (\frac{-7}{12}) + 0,75; \\ d) \left(\frac{-5}{9}\right) - 1,25; \\ e) 0,34.(\frac{-5}{17}); \\ g) \frac{4}{9}:\left(\frac{-8}{15}\right); \\ h) (1\frac{2}{3}):(2\frac{1}{2}); \\ i) \frac{2}{5}.(-1,25); \\ k) (\frac{-3}{5}).(\frac{15}{-7}).3\frac{1}{9}; \end{gathered}$$

Hướng dẫn giải:

$$\begin{gathered} a) \frac{2}{15} + (\frac{-5}{24}) = \frac{16}{120} + (\frac{-25}{120}) = \frac{-9}{120}=\frac{-3}{40} \\ b) \left(\frac{-5}{9}\right)-(-\frac{7}{27})=\left(\frac{-15}{27}\right)-(-\frac{7}{27})=\frac{(-15)-(-7)}{27}=\frac{-8}{27} \\ c) (\frac{-7}{12}) + 0,75=(\frac{-7}{12}) + \frac{75}{100}=(\frac{-7}{12}) + \frac{9}{12}=\frac{2}{12}=\frac{1}{6} \\ d) \left(\frac{-5}{9}\right) - 1,25 = \left(\frac{-5}{9}\right) - \frac{125}{100} = \left(\frac{-5}{9}\right) - \frac{5}{4} = \left(\frac{-20}{36}\right) - \frac{45}{36} = \frac{-65}{36} \\ e) 0,34.(\frac{-5}{17})=\frac{34}{100}.(\frac{-5}{17})=\frac{17}{50}.(\frac{-5}{17})=\frac{-5}{50}=\frac{-1}{10}. \\ g) \frac{4}{9}:\left(\frac{-8}{15}\right) =\frac{4}{9}.\left(\frac{-15}{8}\right) = \frac{4.(-15)}{9.8} = \frac{-5}{3.2}=\frac{-5}{6} \\ h) (1\frac{2}{3}):(2\frac{1}{2}) = (\frac{1.3+2}{3}):(\frac{2.2+1}{2}) = \frac{5}{3}:\frac{5}{2}=\frac{5}{3}.\frac{2}{5}=\frac{2}{3} \\ i) \frac{2}{5}.(-1,25) =\frac{2}{5}.\frac{-125}{100} = \frac{2}{5}.\frac{-5}{4} = \frac{-1}{2} \\ k) (\frac{-3}{5}).(\frac{15}{-7}).3\frac{1}{95} = (\frac{-3}{5}).(\frac{15}{-7}).\frac{28}{9} = \frac{(-3).15.28}{5.(-7).9} = \frac{(-3).3.5.7.4}{5.(-7).9}=4 \end{gathered}$$