Tính a) 3/7 . (-1/9) + 3/7 . (-2/3); b) (-7/13) . 5/12 + (-7/13)

* Hướng dẫn giải

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

$$\begin{gathered} b) \left(\frac{-7}{13}\right)\cdot \frac{5}{12}+\left(\frac{-7}{13}\right)\cdot \frac{7}{12}+\left(\frac{-6}{13}\right) \\ =\left(\frac{-7}{13}\right)\cdot \left(\frac{5}{12}+\frac{7}{12}\right)+\left(\frac{-6}{13}\right) \\ =\left(\frac{-7}{13}\right)\cdot \frac{12}{12}+\left(\frac{-6}{13}\right) \\ =\left(\frac{-7}{13}\right)+\left(\frac{-6}{13}\right)=\frac{-13}{13}=-1 \end{gathered}$$

$$\begin{gathered} c) \left[\left(\frac{-2}{3}\right)+\frac{3}{7}\right]:\frac{5}{9}+\left(\frac{4}{7}-\frac{1}{3}\right):\frac{5}{9}=\left[\left(\frac{-2}{3}\right)+\frac{3}{7}\right]\cdot \frac{9}{5}+\left(\frac{4}{7}-\frac{1}{3}\right)\cdot \frac{9}{5} \\ =\frac{9}{5}\cdot \left[\left(\frac{-2}{3}\right)+\frac{3}{7}+\frac{4}{7}-\frac{1}{3}\right]=\frac{9}{5}\cdot \left[\left(\frac{-2}{3}\right)-\frac{1}{3}+\frac{3}{7}+\frac{4}{7}\right] \end{gathered}$$

$$\begin{gathered} d) \frac{5}{9}:\left(\frac{1}{11}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{2}{3}\right)=\frac{5}{9}:\left(\frac{2}{22}-\frac{5}{22}\right)+\frac{5}{9}:\left(\frac{1}{15}-\frac{10}{15}\right) \\ =\frac{5}{9}:\left(\frac{-3}{22}\right)+\frac{5}{9}:\left(\frac{-9}{15}\right)=\frac{5}{9}\cdot \frac{-22}{3}+\frac{5}{9}\cdot \frac{-15}{9}=\frac{5}{9}\cdot \left(\frac{-22}{3}+\frac{-5}{3}\right)=\frac{5}{9}\cdot (-9)=-5 \end{gathered}$$

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