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

a) \(\frac{5}{6} + \frac{{ - 11}}{{30}} + \frac{7}{5}.\)       

b) \[{\left( {\frac{{ - 4}}{5}} \right)^2} \cdot \frac{{57}}{2} + \frac{{ - 7}}{2} \cdot {\left( {\frac{{ - 4}}{5}} \right)^2}.\] 

c) \(\left( {\frac{7}{{25}} - 1\frac{2}{9}} \right) - \left( {\frac{{23}}{{54}} - \frac{{18}}{{25}}} \right) + \frac{{ - 31}}{{54}}.\)

a \(\frac{5}{6} + \frac{{ - 11}}{{30}} + \frac{7}{5}\)

\( = \frac{{25}}{{30}} + \frac{{ - 11}}{{30}} + \frac{{42}}{{30}}\)

\( = \frac{{56}}{{30}} = \frac{{28}}{{15}}\)

 b \[{\left( {\frac{{ - 4}}{5}} \right)^2} \cdot \frac{{57}}{2} + \frac{{ - 7}}{2} \cdot {\left( {\frac{{ - 4}}{5}} \right)^2}\]

 \[ = {\left( {\frac{{ - 4}}{5}} \right)^2} \cdot \left( {\frac{{57}}{2} + \frac{{ - 7}}{2}} \right)\]

\[ = \frac{{16}}{{25}} \cdot \frac{{50}}{2} = 16.\]

 c \(\left( {\frac{7}{{25}} - 1\frac{2}{9}} \right) - \left( {\frac{{23}}{{54}} - \frac{{18}}{{25}}} \right) + \frac{{ - 31}}{{54}}\)

 \[ = \frac{7}{{25}} - 1\frac{2}{9} - \frac{{23}}{{54}} + \frac{{18}}{{25}} + \frac{{ - 31}}{{54}}\]

\[ = \left( {\frac{7}{{25}} + \frac{{18}}{{25}}} \right) + \left( {\frac{{ - 31}}{{54}} + \frac{{ - 23}}{{54}}} \right) - 1\frac{2}{9}\]

\[ = 1 + \left( { - 1} \right) - \frac{{11}}{9}\]\[ = \frac{{ - 11}}{9}\].