Đáp án:

$\begin{array}{l}
a)\dfrac{{ - 18}}{{17}} < \dfrac{{ - 999}}{{1000}}\\
b) - 0,76 < \dfrac{{ - 19}}{{28}}\\
c)\dfrac{{ - 1941}}{{1931}} < \dfrac{{ - 2011}}{{2001}}\\
d)\dfrac{{ - 1930}}{{1945}} > \dfrac{{ - 1996}}{{2011}}\\
e)\dfrac{{37}}{{59}} < \dfrac{{47}}{{69}}\\
f)\dfrac{{ - 27}}{{100}} < \dfrac{{ - 25}}{{124}}\\
g)\dfrac{{ - 97}}{{201}} > \dfrac{{ - 194}}{{399}}\\
h)\dfrac{{ - 189}}{{398}} < \dfrac{{ - 187}}{{394}}
\end{array}$

Giải thích các bước giải:

$\begin{array}{l}
a)\left\{ \begin{array}{l}
\dfrac{{ - 18}}{{17}} < \dfrac{{ - 17}}{{17}} =  - 1\\
\dfrac{{ - 999}}{{1000}} > \dfrac{{ - 1000}}{{1000}} =  - 1
\end{array} \right.\\
 \Rightarrow \dfrac{{ - 18}}{{17}} < \dfrac{{ - 999}}{{1000}}\\
b) - 0,76 = \dfrac{{ - 19}}{{25}} < \dfrac{{ - 19}}{{28}}\\
 \Rightarrow  - 0,76 < \dfrac{{ - 19}}{{28}}\\
c)\left\{ \begin{array}{l}
\dfrac{{ - 1941}}{{1931}} =  - \dfrac{{1931 + 10}}{{1931}} =  - 1 - \dfrac{{10}}{{1931}}\\
\dfrac{{ - 2011}}{{2001}} =  - \dfrac{{2001 + 10}}{{2001}} =  - 1 - \dfrac{{10}}{{2001}}
\end{array} \right.\\
Do:\dfrac{{10}}{{2001}} < \dfrac{{10}}{{1931}} \Rightarrow  - \dfrac{{10}}{{2001}} >  - \dfrac{{10}}{{1931}}\\
 \Rightarrow \dfrac{{ - 1941}}{{1931}} < \dfrac{{ - 2011}}{{2001}}\\
d)\left\{ \begin{array}{l}
\dfrac{{ - 1930}}{{1945}} =  - \dfrac{{1945 - 15}}{{1945}} =  - 1 + \dfrac{{15}}{{1945}}\\
\dfrac{{ - 1996}}{{2011}} =  - \dfrac{{2011 - 15}}{{2011}} =  - 1 + \dfrac{{15}}{{2011}}
\end{array} \right.\\
Do:\dfrac{{15}}{{1945}} > \dfrac{{15}}{{2011}}\\
 \Rightarrow \dfrac{{ - 1930}}{{1945}} > \dfrac{{ - 1996}}{{2011}}\\
e)\left\{ \begin{array}{l}
\dfrac{{37}}{{59}} = \dfrac{{59 - 22}}{{59}} = 1 - \dfrac{{22}}{{59}}\\
\dfrac{{47}}{{69}} = \dfrac{{69 - 22}}{{69}} = 1 - \dfrac{{22}}{{69}}
\end{array} \right.\\
Do:\dfrac{{22}}{{59}} > \dfrac{{22}}{{69}}\\
 \Rightarrow \dfrac{{37}}{{59}} < \dfrac{{47}}{{69}}\\
f)\dfrac{{ - 27}}{{100}} < \dfrac{{ - 25}}{{100}} < \dfrac{{ - 25}}{{124}}\\
 \Rightarrow \dfrac{{ - 27}}{{100}} < \dfrac{{ - 25}}{{124}}\\
g)\dfrac{{ - 97}}{{201}} = \dfrac{{ - 194}}{{402}} > \dfrac{{ - 194}}{{399}}\\
 \Rightarrow \dfrac{{ - 97}}{{201}} > \dfrac{{ - 194}}{{399}}\\
h)\left\{ \begin{array}{l}
\dfrac{{ - 189}}{{398}} = \dfrac{{ - 1}}{2}.\dfrac{{378}}{{398}} = \dfrac{{ - 1}}{2}\left( {1 - \dfrac{{20}}{{398}}} \right) = \dfrac{{ - 1}}{2} + \dfrac{{10}}{{398}}\\
\dfrac{{ - 187}}{{394}} = \dfrac{{ - 1}}{2}.\dfrac{{374}}{{394}} = \dfrac{{ - 1}}{2}\left( {1 - \dfrac{{20}}{{394}}} \right) = \dfrac{{ - 1}}{2} + \dfrac{{10}}{{394}}
\end{array} \right.\\
Do:\dfrac{{10}}{{398}} < \dfrac{{10}}{{384}}\\
 \Rightarrow \dfrac{{ - 189}}{{398}} < \dfrac{{ - 187}}{{394}}
\end{array}$