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\(\begin{array}{l}a)\left( {\frac{2}{3} + \frac{1}{6}} \right):\frac{5}{4} + \left( {\frac{1}{4} + \frac{3}{8}} \right):\frac{5}{2}\\ = \left( {\frac{4}{6} + \frac{1}{6}} \right).\frac{4}{5} + \left( {\frac{2}{8} + \frac{3}{8}} \right).\frac{2}{5}\\ = \frac{5}{6}.\frac{4}{5} + \frac{5}{8}.\frac{2}{5}\\ = \frac{2}{3} + \frac{1}{4}\\ = \frac{8}{{12}} + \frac{3}{{12}}\\ = \frac{{11}}{{12}}\\b)\frac{5}{9}:\left( {\frac{1}{{11}} - \frac{5}{{22}}} \right) + \frac{7}{4}.\left( {\frac{1}{{14}} - \frac{2}{7}} \right)\\ = \frac{5}{9}:\left( {\frac{2}{{22}} - \frac{5}{{22}}} \right) + \frac{7}{4}.\left( {\frac{1}{{14}} - \frac{4}{{14}}} \right)\\ = \frac{5}{9}:\frac{{ - 3}}{{22}} + \frac{7}{4}.\frac{{ - 3}}{{14}}\\ = \frac{5}{9}.\frac{{ - 22}}{3} + \frac{{ - 3}}{8}\\ = \frac{{ - 110}}{{27}} + \frac{{ - 3}}{8}\\ = \frac{{ - 880}}{{216}} + \frac{{ - 81}}{{216}}\\ = \frac{{ - 961}}{{216}}\end{array}\)
139\(\frac{5}{7}:\frac{2}{3}\)-\(138\frac{2}{7}:\sqrt{\frac{4}{9}}\)
=139\(\frac{5}{7}:\frac{2}{3}\)-\(138\frac{2}{7}:\frac{2}{3}\)
=(139\(\frac{5}{7}\)-\(138\frac{2}{7}\)):\(\frac{2}{3}\) =\(1\frac{3}{7}\):\(\frac{2}{3}\) =\(\frac{9}{7}.\frac{3}{2}\) =\(\frac{27}{14}\)=\(\frac{2.2^9.3^9-2^5.2^4.3^8}{2.2^8.3^8}\)
=\(\frac{2^{10}.3^9-2^9.3^8}{2^9.3^8}\)
=\(\frac{2^9.3^8.\left(2.3-1\right)}{2^9.3^8}\)
=\(6-1\)
=5
-4/5 + 1/-5 = -1 => -4/5 + 1/-5 = -1
-13/22 + -7/22 = -10/11 => -13/22 + -7/22 < -8/11 (vì -10 < -8)
2/3 + -1/5 = 7/15 ; 3/5 = 9/15 => 3/5 > 2/3 + -1/5 (vì 9 >7)