Thực hiện phép tính (tính hợp lí nếu có thể). (a) − 8 /15 + 1 /25 − 7/ 15 ;

14/18

(2,0 điểm) Thực hiện phép tính (tính hợp lí nếu có thể).

(a) \(\frac{{ - 8}}{{15}} + \frac{1}{{25}} - \frac{7}{{15}}\);

(b) \[\frac{2}{{11}}\,\,.\,\,\frac{{ - 3}}{{17}} - \frac{{14}}{{17}}\,\,.\,\,\frac{2}{{11}} + 3\frac{2}{{11}}\];

(c) \[{\left( {\frac{1}{3}} \right)^{14}}:{\left( {\frac{1}{3}} \right)^{12}} - \left[ {\frac{5}{4} - \left( {\sqrt {16} - \frac{2}{3}} \right)} \right]\];

(d) \(24\,\,.\,\,{\left( {\frac{1}{4}} \right)^2} + \left| {\frac{{ - 2}}{3}} \right|\,\,.\,\,\sqrt {\frac{{81}}{{64}}} - {\left( {\frac{{31}}{{19}}} \right)^0}\).

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Giải thích

a) \(\frac{{ - 8}}{{15}} + \frac{1}{{25}} - \frac{7}{{15}} = \frac{{ - 8}}{{15}} - \frac{7}{{15}} + \frac{1}{{25}} = - 1 + \frac{1}{{25}} = \frac{{ - 24}}{{25}}\);

b) \[\frac{2}{{11}}\,\,.\,\,\frac{{ - 3}}{{17}} - \frac{{14}}{{17}}\,\,.\,\,\frac{2}{{11}} + 3\frac{2}{{11}} = \frac{2}{{11}}\,\,.\,\,\left( {\frac{{ - 3}}{{17}} - \frac{{14}}{{17}}} \right)\, + \frac{{35}}{{11}}\]

\[ = \frac{2}{{11}}\,\,.\,\,\left( { - 1} \right)\, + \frac{{35}}{{11}} = \frac{{ - 2}}{{11}}\, + \frac{{35}}{{11}} = 3\];

c) \[{\left( {\frac{1}{3}} \right)^{14}}:{\left( {\frac{1}{3}} \right)^{12}} - \left[ {\frac{5}{4} - \left( {\sqrt {16} - \frac{2}{3}} \right)} \right] = {\left( {\frac{1}{3}} \right)^2} - \left[ {\frac{5}{4} - \left( {4 - \frac{2}{3}} \right)} \right]\]

\[ = {\left( {\frac{1}{3}} \right)^2} - \left[ {\frac{5}{4} - \left( {4 - \frac{2}{3}} \right)} \right] = \frac{1}{9} - \left( {\frac{5}{4} - \frac{{10}}{3}} \right) = \frac{1}{9} - \frac{{ - 25}}{{12}} = \frac{1}{9} + \frac{{25}}{{12}} = \frac{{79}}{{36}}\];

d) \(24\,\,.\,\,{\left( {\frac{1}{4}} \right)^2} + \left| {\frac{{ - 2}}{3}} \right|\,\,.\,\,\sqrt {\frac{{81}}{{64}}} - {\left( {\frac{{31}}{{19}}} \right)^0} = 24\,\,.\,\,\frac{1}{{16}} + \frac{2}{3}\,\,.\,\,\frac{9}{8} - 1\)

\( = \,\frac{3}{2} + \frac{3}{4} - 1 = \frac{9}{4} - 1 = \frac{5}{4}\).