Thực hiện phép tính một cách hợp lí: d) − 3/7 ⋅ 12/13 + 3/7 ⋅ ( − 1/13 ) + 5/14 .
Giải thích
d) \( - \frac{3}{7} \cdot \frac{{12}}{{13}} + \frac{3}{7} \cdot \left( { - \frac{1}{{13}}} \right) + \frac{5}{{14}}\)
\( = \frac{3}{7} \cdot \frac{{ - 12}}{{13}} + \frac{3}{7} \cdot \left( { - \frac{1}{{13}}} \right) + \frac{5}{{14}}\)
\[ = \frac{3}{7} \cdot \left[ {\frac{{ - 12}}{{13}} + \left( { - \frac{1}{{13}}} \right)} \right] + \frac{5}{{14}}\]
\[ = \frac{3}{7} \cdot \frac{{ - 13}}{{13}} + \frac{5}{{14}}\]
\[ = \frac{3}{7} \cdot \left( { - 1} \right) + \frac{5}{{14}}\]\[ = \frac{{ - 3}}{7} + \frac{5}{{14}}\]
\[ = \frac{{ - 6}}{{14}} + \frac{5}{{14}} = \frac{{ - 1}}{{14}}.\]