Thực hiện phép tính: a) 5/6 + 2/3 − 0 , 5 .b) − √ 4/49 ⋅ ( 5/13 − 9/15 ) − 2/7 ⋅ √ ( − 8/13 )^2 .
Hướng dẫn giải
a) \(\frac{5}{6} + \frac{2}{3} - 0,5\) \( = \frac{5}{6} + \frac{4}{6} - \frac{1}{2}\) \( = \frac{9}{6} - \frac{3}{6}\) \( = \frac{6}{6}\) \( = 1\). | b) \( - \sqrt {\frac{4}{{49}}} \cdot \left( {\frac{5}{{13}} - \frac{9}{{15}}} \right) - \frac{2}{7} \cdot \sqrt {{{\left( {\frac{{ - 8}}{{13}}} \right)}^2}} \) \[ = - \sqrt {{{\left( {\frac{2}{7}} \right)}^2}} \cdot \left( {\frac{5}{{13}} - \frac{9}{{15}}} \right) - \frac{2}{7} \cdot \left| {\frac{{ - 8}}{{13}}} \right|\] \( = - \frac{2}{7} \cdot \left( {\frac{5}{{13}} - \frac{9}{{15}}} \right) - \frac{2}{7} \cdot \frac{8}{{13}}\) \( = - \frac{2}{7} \cdot \left( {\frac{5}{{13}} - \frac{9}{{15}} + \frac{8}{{13}}} \right)\) \( = - \frac{2}{7} \cdot \left( {\frac{5}{{13}} + \frac{8}{{13}} - \frac{9}{{15}}} \right)\) \( = - \frac{2}{7} \cdot \left( {\frac{{13}}{{13}} - \frac{9}{{15}}} \right)\)\( = - \frac{2}{7} \cdot \left( {1 - \frac{9}{{15}}} \right)\) \( = - \frac{2}{7} \cdot \frac{6}{{15}} = \frac{{ - 4}}{{35}}.\) |