II. PHẦN TỰ LUẬN

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

a) \[\frac{2}{3} + \frac{{ - 3}}{5}\];                                                           b) \[\frac{2}{9} - \left( {\frac{1}{{20}} + \frac{2}{9}} \right)\];

c) \(\frac{{25}}{6}:\frac{5}{3} - \left( {\frac{{ - 1}}{4}} \right)\);        d) \[\frac{{11}}{{23}}.\frac{{12}}{{17}} + \frac{{11}}{{23}}.\frac{5}{{17}} + \frac{{12}}{{23}}\].

a) \[\frac{2}{3} + \frac{{ - 3}}{5} = \frac{{10}}{{15}} + \frac{{ - 9}}{{15}} = \frac{1}{{15}}\];

b) \[\frac{2}{9} - \left( {\frac{1}{{20}} + \frac{2}{9}} \right) = \frac{2}{9} - \frac{1}{{20}} - \frac{2}{9} =  - \frac{1}{{20}}\];

c) \(\frac{{25}}{6}:\frac{5}{3} - \left( {\frac{{ - 1}}{4}} \right) = \frac{{25}}{6}.\frac{3}{5} + \frac{1}{4}\)\( = \frac{5}{2} + \frac{1}{4} = \frac{{11}}{4}\);

d) \(\frac{7}{{19}}.\frac{8}{{11}} + \frac{7}{{19}}.\frac{3}{{11}} + \frac{{12}}{{19}} = \frac{7}{{19}}\left( {\frac{8}{{11}} + \frac{3}{{11}}} \right) + \frac{{12}}{{19}}\)

 \( = \frac{7}{{19}} \cdot \frac{{11}}{{11}} + \frac{{12}}{{19}} = \frac{7}{{19}} \cdot 1 + \frac{{12}}{{19}} = \frac{{19}}{{19}} = 1\).