II. PHẦN TỰ LUẬN

Thực hiện phép tính (tính nhanh nếu có thể):

a) \(\frac{1}{2} - \frac{{ - 3}}{4}\);                                                            b) \[\frac{{12}}{{11}} - \frac{{ - 7}}{{19}} + \frac{{12}}{{19}}\];

c) \(11\frac{3}{{13}} - \left( {2\frac{4}{7} + 5\frac{3}{{13}}} \right)\);        d) \[\frac{{ - 5}}{7} \cdot \frac{2}{{11}} + \frac{{ - 5}}{7} \cdot \frac{9}{{11}} + \frac{5}{7}\].

a) \(\frac{1}{2} - \frac{{ - 3}}{4} = \frac{{1.2}}{{2.2}} - \frac{{ - 3}}{4} = \frac{2}{4} - \frac{{ - 3}}{4} = \frac{5}{4};\)

b) \[\frac{{12}}{{11}} - \frac{{ - 7}}{{19}} + \frac{{12}}{{19}} = \frac{{12}}{{11}} + \frac{7}{{19}} + \frac{{12}}{{19}} = \frac{{12}}{{11}} + \left( {\frac{7}{{19}} + \frac{{12}}{{19}}} \right)\]

\[ = \frac{{12}}{{11}} + 1 = \frac{{12}}{{11}} + \frac{{11}}{{11}} = \frac{{23}}{{11}};\]

c) \(11\frac{3}{{13}} - \left( {2\frac{4}{7} + 5\frac{3}{{13}}} \right) = \left( {11 + \frac{3}{{13}}} \right) - \left[ {\left( {2 + \frac{4}{7}} \right) + \left( {5 + \frac{3}{{13}}} \right)} \right]\)

\( = 11 + \frac{3}{{13}} - \left[ {7 + \frac{4}{7} + \frac{3}{{13}}} \right] = 11 + \frac{3}{{13}} - 7 - \frac{4}{7} - \frac{3}{{13}} = 4 - \frac{4}{7} = \frac{{24}}{7}\);

d) \[\frac{{ - 5}}{7} \cdot \frac{2}{{11}} + \frac{{ - 5}}{7} \cdot \frac{9}{{11}} + \frac{5}{7} = \frac{{ - 5}}{7}\left( {\frac{2}{{11}} + \frac{9}{{11}}} \right) + \frac{5}{7} = \frac{{ - 5}}{7} \cdot 1 + \frac{5}{7} = 0\].