B. TỰ LUẬN (3,0 điểm)

Câu 25-26. (1,5 điểm)

1) Thực hiện phép tính (tính hợp lí nếu có thể):

a) \(\frac{2}{5} \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 9}}{{13}}} \right) - \frac{2}{5} \cdot \left( {\frac{8}{{13}} - \frac{5}{{12}}} \right):2.\)                                b) \[\frac{{ - 1}}{4} \cdot \left( {12\frac{3}{4} - 7,75} \right) - 25\% \cdot 3\frac{1}{2}.\]

1) a) \(\frac{2}{5} \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 9}}{{13}}} \right) - \frac{2}{5} \cdot \left( {\frac{8}{{13}} - \frac{5}{{12}}} \right):2\)

\( = \frac{1}{5} \cdot 2 \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 9}}{{13}}} \right) - \frac{2}{5} \cdot \left( {\frac{8}{{13}} - \frac{5}{{12}}} \right) \cdot \frac{1}{2}\)

\( = \frac{1}{5} \cdot \left( {\frac{{ - 10}}{{12}} + \frac{{ - 18}}{{13}}} \right) - \frac{1}{5} \cdot \left( {\frac{8}{{13}} - \frac{5}{{12}}} \right)\)

\[ = \frac{1}{5} \cdot \left( {\frac{{ - 10}}{{12}} + \frac{{ - 18}}{{13}} - \frac{8}{{13}} + \frac{5}{{12}}} \right)\]

\[ = \frac{1}{5} \cdot \left[ {\left( {\frac{{ - 10}}{{12}} + \frac{5}{{12}}} \right) + \left( {\frac{{ - 18}}{{13}} - \frac{8}{{13}}} \right)} \right]\]

\[ = \frac{1}{5} \cdot \left( {\frac{{ - 5}}{{12}} + \frac{{ - 26}}{{13}}} \right) = \frac{1}{5} \cdot \left[ {\frac{{ - 5}}{{12}} + \left( { - 2} \right)} \right]\]

\[ = \frac{1}{5} \cdot \frac{{ - 29}}{{12}} = \frac{{ - 29}}{{60}}.\]

b) \[\frac{{ - 1}}{4} \cdot \left( {12\frac{3}{4} - 7,75} \right) - 25\% \cdot 3\frac{1}{2}\]

\[ = \frac{{ - 1}}{4} \cdot \left( {12,75 - 7,75} \right) - \frac{{25}}{{100}} \cdot \frac{7}{2}\]

\[ = \frac{{ - 1}}{4} \cdot 5 - \frac{1}{4} \cdot \frac{7}{2}\]

\[ = \frac{{ - 5}}{4} - \frac{7}{8}\]

\[ = \frac{{ - 10}}{8} - \frac{7}{8}\]

\[ = \frac{{ - 17}}{8}.\]