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

a) \(\frac{2}{{11}} - \frac{3}{8} + \frac{4}{{11}} - \frac{6}{{11}} - \frac{5}{8}\);

b) $\frac{-5}{7}\cdot \frac{2}{11}+\frac{-5}{7}\cdot \frac{9}{11}+\frac{5}{7}$;

c) (15,25 + 3,75).4 + (20,71 + 5,29).5;

d) \[\left( {4 - \frac{{12}}{{10}}} \right):2 + 30\% \]

Hướng dẫn giải:

a) \(\frac{2}{{11}} - \frac{3}{8} + \frac{4}{{11}} - \frac{6}{{11}} - \frac{5}{8}\)

\( = \left( {\frac{2}{{11}} + \frac{4}{{11}} - \frac{6}{{11}}} \right) + \left( { - \frac{3}{8} - \frac{5}{8}} \right)\)

\( = \frac{0}{{11}} + \frac{{ - 8}}{8}\)

= – 1.

b) \(\frac{{ - 5}}{7} \cdot \frac{2}{{11}} + \frac{{ - 5}}{7} \cdot \frac{9}{{11}} + \frac{5}{7}\)

\( = \frac{{ - 5}}{7}\left( {\frac{2}{{11}} + \frac{9}{{11}}} \right) + \frac{5}{7}\)

\( = \frac{{ - 5}}{7}.\frac{{11}}{{11}} + \frac{5}{7}\)

\( = \frac{{ - 5}}{7} \cdot 1 + \frac{5}{7}\)

\( = \frac{{ - 5}}{7} + \frac{5}{7}\)

= 0.

c) (15,25 + 3,75).4 + (20,71 + 5,29).5

= 19.4 + 26.5

= 76 + 130

= 206

d) \[\left( {4 - \frac{{12}}{{10}}} \right):2 + 30\% \]

\[ = \left( {4 - \frac{6}{5}} \right):2 + \frac{{30}}{{100}}\]

\( = \left( {\frac{{20}}{5} - \frac{6}{5}} \right):2 + \frac{3}{{10}}\)

\( = \frac{{14}}{5}.\frac{1}{2} + \frac{3}{{10}}\)

\( = \frac{{14}}{{10}} + \frac{3}{{10}}\)

\( = \frac{{17}}{{10}}\).