Hãy sắp xếp theo thứ tự tăng dần ​\( - \frac{{31}}{{24}}; - 1\frac{1}{{12}};\frac{{12}}{{100}};5\frac{1}{2};23{\rm{\% }}\) ta được:

Ta có: \( 23{\rm{\% }} = \frac{{23}}{{100}};\)

Ta chia thành hai nhóm phân số là:

\( \frac{{23}}{{100}};\frac{{12}}{{100}};\frac{{11}}{2}\) và \( - \frac{{13}}{{12}}; - \frac{{31}}{{24}}\)

Nhóm 1:

\( \frac{{12}}{{100}} < \frac{{23}}{{100}} < 1 < \frac{{11}}{2}\)

Nhóm 2:  \(\begin{array}{l} - \frac{{13}}{{12}}; - \frac{{31}}{{24}}\\ - \frac{{13}}{{12}} = \frac{{ - 26}}{{24}} > \frac{{ - 31}}{{24}} \end{array}\) nên \( - \frac{{13}}{{12}} > - \frac{{31}}{{24}}\)

Vậy: \(\begin{array}{l} - \frac{{31}}{{24}} < - \frac{{13}}{{12}} < \frac{{12}}{{100}} < \frac{{23}}{{100}} < \frac{{11}}{2}\\ \Leftrightarrow - \frac{{31}}{{24}} < - 1\frac{1}{{12}} < \frac{{12}}{{100}} < 23\% < 5\frac{1}{2} \end{array}\)