Thực hiện phép tính:
a) \(\frac{{ - 7}}{5}.\left( {\frac{{15}}{{14}} + \frac{5}{7}} \right) + \left| {\frac{{ - 7}}{2}} \right|\).
b) \(\frac{1}{{13}} + \left( {\frac{{ - 5}}{{18}} - \frac{1}{{13}} + \frac{9}{{25}}} \right) - \left[ {{{\left( {\frac{3}{5}} \right)}^2} - \frac{{\sqrt {25} }}{{18}} + \frac{{19}}{{11}}} \right]\).
- Sử dụng tính chất của phép nhân.
- Sử dụng định nghĩa giá trị tuyệt đối của một số:
\(\left| x \right| = \left\{ \begin{array}{l}x\,khi\,x \ge 0\\ - x\,khi\,x < 0\end{array} \right.\).
a) \(\frac{{ - 7}}{5}.\left( {\frac{{15}}{{14}} + \frac{5}{7}} \right) + \left| {\frac{{ - 7}}{2}} \right|\)
\(\begin{array}{l} = \frac{{ - 7}}{5}.\frac{{15}}{{14}} + \left( {\frac{{ - 7}}{5}} \right).\frac{5}{7} + \frac{7}{2}\\ = \frac{{ - 3}}{2} + \left( { - 1} \right) + \frac{7}{2} = \left( {\frac{{ - 3}}{2} + \frac{7}{2}} \right) - 1 = 2 - 1 = 1\end{array}\)
b) \(\frac{1}{{13}} + \left( {\frac{{ - 5}}{{18}} - \frac{1}{{13}} + \frac{9}{{25}}} \right) - \left[ {{{\left( {\frac{3}{5}} \right)}^2} - \frac{{\sqrt {25} }}{{18}} + \frac{{19}}{{11}}} \right]\)
\(\begin{array}{l} = \frac{1}{{13}} + \left( {\frac{{ - 5}}{{18}} - \frac{1}{{13}} + \frac{9}{{25}}} \right) - \left[ {\frac{9}{{25}} - \frac{5}{{18}} + \frac{{19}}{{11}}} \right]\\ = \frac{1}{{13}} - \frac{5}{{18}} - \frac{1}{{13}} + \frac{9}{{25}} - \frac{9}{{25}} + \frac{5}{{18}} + \frac{{19}}{{11}}\\ = \left( {\frac{1}{{13}} - \frac{1}{{13}}} \right) + \left( {\frac{5}{{18}} - \frac{5}{{18}}} \right) + \left( {\frac{9}{{25}} - \frac{9}{{25}}} \right) + \frac{{19}}{{11}}\\ = \frac{{19}}{{11}}\end{array}\)