Thực hiện phép tính (tính hợp lí nếu có thể): a) 2/ 5 ⋅ ( − 5 /12 + − 9 /13 ) − 2 /5 ⋅ ( 8/ 13 − 5 /12 ) : 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) \(0,25 \cdot \frac{7}{{15}} - 25\% \cdot \frac{{ - 8}}{{15}} + 2,75\)

\( = 0,25 \cdot \frac{7}{{15}} - 0,25 \cdot \frac{{ - 8}}{{15}} + 2,75\)

\( = 0,25 \cdot \left( {\frac{7}{{15}} - \frac{{ - 8}}{{15}}} \right) + 2,75\)

\( = 0,25 \cdot \frac{{15}}{{15}} + 2,75\)

\( = 0,25 \cdot 1 + 2,75\)

\( = 3.\)