Thực hiện phép tính (tính hợp lý nếu có thể):
a) \(\frac{7}{3} + \frac{{ - 8}}{{12}} + \frac{5}{4}.\)
b) \({\left( {\frac{{ - 2}}{3}} \right)^2}.\frac{{67}}{4} + \frac{{ - 7}}{4}.{\left( {\frac{{ - 2}}{3}} \right)^2}.\)
c) \(\left( {\frac{6}{{23}} - \frac{6}{{33}}} \right) - \left( {\frac{{27}}{{33}} - \frac{{17}}{{23}}} \right) + 2\frac{4}{7}.\)
Dựa vào quy tắc tính với số hữu tỉ, lũy thừa với số mũ tự nhiên.
a) \(\frac{7}{3} + \frac{{ - 8}}{{12}} + \frac{5}{4}\)
= \(\frac{{28}}{{12}} + \frac{{ - 8}}{{12}} + \frac{{15}}{{12}}\)
= \(\frac{{35}}{{12}}.\)
b) \({\left( {\frac{{ - 2}}{3}} \right)^2}.\frac{{67}}{4} + \frac{{ - 7}}{4}.{\left( {\frac{{ - 2}}{3}} \right)^2}\)
\( = {\left( {\frac{{ - 2}}{3}} \right)^2}.\left( {\frac{{67}}{4} + \frac{{ - 7}}{4}} \right)\)
\( = \frac{4}{9}.\frac{{60}}{4}\)\( = \frac{{60}}{9} = \frac{{20}}{3}.\)
c) \(\left( {\frac{6}{{23}} - \frac{6}{{33}}} \right) - \left( {\frac{{27}}{{33}} - \frac{{17}}{{23}}} \right) + 2\frac{4}{7}\)
\( = \frac{6}{{23}} - \frac{6}{{33}} - \frac{{27}}{{33}} + \frac{{17}}{{23}} + 2\frac{4}{7}\)
\( = \left( {\frac{6}{{23}} + \frac{{17}}{{23}}} \right) + \left( {\frac{{ - 6}}{{33}} + \frac{{ - 27}}{{33}}} \right) + 2\frac{4}{7}\)
\( = 1 + \left( { - 1} \right) + 2\frac{4}{7}\)\( = 2\frac{4}{7}\)