\(\begin{array}{l}
(\frac{{ - 8}}{{25}}).\frac{{15}}{4} = \frac{{( - 2).4.3.5}}{{5.5.4}} = \frac{{( - 2).3}}{5} = \frac{{ - 6}}{5}\\
8.(\frac{{ - 3}}{2}) = \frac{{8.( - 3)}}{2} = \frac{{2.4.( - 3)}}{2} = 4.( - 3) =  - 12\\
( - 11)(\frac{{ - 5}}{{121}}) = \frac{{( - 11).( - 5)}}{{121}} = \frac{{11.5}}{{11.11}} = \frac{5}{{11}}\\
(\frac{{ - 1}}{2}).(\frac{3}{5} - \frac{{14}}{3} + \frac{2}{3}).\frac{{18}}{{55}} = (\frac{{ - 1}}{2}).(\frac{3}{5} + \frac{{ - 14 + 2}}{3}).\frac{{18}}{{55}}\\
 = (\frac{{ - 1}}{2})(\frac{3}{5} + \frac{{ - 12}}{3}).\frac{{18}}{{55}}\\
 = (\frac{{ - 1}}{2}).(\frac{3}{5} - 4).\frac{{18}}{{55}}\\
 = (\frac{{ - 1}}{2}).\frac{{3 - 20}}{5}.\frac{{18}}{{55}}\\
 = (\frac{{ - 1}}{2}).(\frac{{ - 17}}{5}).\frac{{18}}{{55}}\\
 = \frac{{1.17.2.9}}{{2.5.55}} = \frac{{153}}{{275}}
\end{array}\)