Thực hiện các phép tính (Tính hợp lí nếu có thể): a) \(\frac{5}{9}.\frac{6}{{13}} + \frac{5}{9}.\frac{7}{{13}} - \frac{2}{9} + \frac{2}{{11}}.\) b) \(\frac{1}{4} - \left( {\frac{1}{4} + 4\fra

a) \(\frac{5}{9}.\frac{6}{{13}} + \frac{5}{9}.\frac{7}{{13}} - \frac{2}{9} + \frac{2}{{11}}.\)

\( = \frac{5}{9}.\left( {\frac{6}{{13}} + \frac{7}{{13}}} \right) - \frac{2}{9} + \frac{2}{{11}}\)

\( = \frac{5}{9}.1 - \frac{2}{9} + \frac{2}{{11}}\)

\( = \frac{5}{9} - \frac{2}{9} + \frac{2}{{11}}\)

\( = \frac{3}{9} + \frac{2}{{11}}\)

\( = \frac{{33}}{{99}} + \frac{{18}}{{99}} = \frac{{51}}{{99}} = \frac{{17}}{{33}}\).

b) \(\frac{1}{4} - \left( {\frac{1}{4} + 4\frac{1}{2}} \right) + 9:\frac{{27}}{2} - 1\)

\( = \frac{1}{4} - \left( {\frac{1}{4} + \frac{9}{2}} \right) + 9.\frac{2}{{27}} - 1\)

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

\( = - \frac{9}{2} + \frac{2}{3} - 1\)

\( = - \frac{{27}}{6} + \frac{4}{6} - \frac{6}{6}\)

\( = - \frac{{29}}{6}\).