Đáp án:
$\begin{array}{l}
a)\dfrac{{ - 1}}{5}.\dfrac{4}{7} + \dfrac{{ - 1}}{5}.1\dfrac{3}{7} + {\left( {\dfrac{{ - 2}}{5}} \right)^3}\\
= - \dfrac{1}{5}.\left( {\dfrac{4}{7} + 1\dfrac{3}{7}} \right) + \dfrac{{ - 8}}{{125}}\\
= - \dfrac{1}{5}.\left( {\dfrac{4}{7} + \dfrac{{10}}{7}} \right) + \dfrac{{ - 8}}{{125}}\\
= - \dfrac{1}{5}.2 + \dfrac{{ - 8}}{{125}}\\
= \dfrac{{ - 50}}{{125}} + \dfrac{{ - 8}}{{125}}\\
= \dfrac{{ - 58}}{{125}}\\
b){\left( {\dfrac{{ - 1}}{2}} \right)^3}:1\dfrac{3}{8} - 25\% .\left( { - 6\dfrac{2}{{11}}} \right)\\
= \dfrac{{ - 1}}{8}:\dfrac{{11}}{8} - \dfrac{1}{4}.\dfrac{{ - 68}}{{11}}\\
= \dfrac{{ - 1}}{8}.\dfrac{8}{{11}} + \dfrac{{17}}{{11}}\\
= \dfrac{{ - 1}}{{11}} + \dfrac{{17}}{{11}}\\
= \dfrac{{16}}{{11}}\\
c)\left( {4\dfrac{5}{{23}} - 2\dfrac{2}{5} + 7\dfrac{7}{{13}}} \right) - \left( {3\dfrac{5}{{23}} - 6\dfrac{6}{{13}}} \right)\\
= 4\dfrac{5}{{23}} - 3\dfrac{5}{{23}} + 7\dfrac{7}{{13}} + 6\dfrac{6}{{13}} - 2\dfrac{2}{5}\\
= 4 + \dfrac{5}{{23}} - 3 - \dfrac{5}{{23}} + 7 + \dfrac{7}{{13}} + 6 + \dfrac{6}{{13}} - \dfrac{{12}}{5}\\
= 1 + 13 + \dfrac{{13}}{{13}} + \dfrac{{12}}{5}\\
= 15 + \dfrac{{12}}{5}\\
= \dfrac{{87}}{5}\\
d)\dfrac{3}{{1.3}} + \dfrac{3}{{3.5}} + \dfrac{3}{{5.7}} + ... + \dfrac{3}{{199.201}}\\
= \dfrac{3}{2}.\left( {\dfrac{2}{{1.3}} + \dfrac{2}{{3.5}} + \dfrac{2}{{5.7}} + ... + \dfrac{2}{{199.201}}} \right)\\
= \dfrac{3}{2}.\left( {1 - \dfrac{1}{3} + \dfrac{1}{3} - \dfrac{1}{5} + \dfrac{1}{5} - \dfrac{1}{7} + ... + \dfrac{1}{{199}} - \dfrac{1}{{201}}} \right)\\
= \dfrac{3}{2}.\left( {1 - \dfrac{1}{{201}}} \right)\\
= \dfrac{3}{2}.\dfrac{{200}}{{201}}\\
= \dfrac{{100}}{{67}}
\end{array}$
