Giải thích các bước giải:
a) Ta có:
$\begin{array}{l}
\dfrac{7}{{13}} = 1 - \dfrac{6}{{13}} = 1 - \dfrac{{30}}{{65}}\\
\dfrac{{11}}{{21}} = 1 - \dfrac{{10}}{{21}} = 1 - \dfrac{{30}}{{63}}
\end{array}$
Mà lại có:
$\begin{array}{l}
\dfrac{{30}}{{65}} < \dfrac{{30}}{{63}}\\
\Rightarrow 1 - \dfrac{{30}}{{65}} > 1 - \dfrac{{30}}{{63}}\\
\Rightarrow \dfrac{7}{{13}} > \dfrac{{11}}{{21}}
\end{array}$
b) Xét phân số:
$\begin{array}{l}
\dfrac{{121}}{{25}} < \dfrac{{125}}{{25}} = 5\\
\dfrac{{100}}{{11}} > \dfrac{{100}}{{20}} = 5\\
\Rightarrow \dfrac{{100}}{{11}} > \dfrac{{121}}{5}\\
\Rightarrow \dfrac{1}{{\dfrac{{100}}{{11}}}} < \dfrac{1}{{\dfrac{{121}}{5}}}\\
\Rightarrow \dfrac{{100}}{{11}} < \dfrac{{25}}{{121}}
\end{array}$
