Sắp xếp theo thứ tự tăng dần $23\% ;\,\dfrac{{12}}{{100}}; - 1\dfrac{1}{{12}}; - \dfrac{{31}}{{24}};5\dfrac{1}{2}$  ta được

Ta có: $23\%  = \dfrac{{23}}{{100}};$ $- 1\dfrac{1}{{12}} =  - \dfrac{{13}}{{12}};$ $5\dfrac{1}{2} = \dfrac{{11}}{2}$

Ta chia thành hai nhóm phân số là: $\dfrac{{23}}{{100}};\dfrac{{12}}{{100}};\dfrac{{11}}{2}$ và $- \dfrac{{13}}{{12}}; - \dfrac{{31}}{{24}}$

Nhóm 1:

$\dfrac{{12}}{{100}} < \dfrac{{23}}{{100}} < 1 < \dfrac{{11}}{2}$ nên $\dfrac{{12}}{{100}} < \dfrac{{23}}{{100}} < \dfrac{{11}}{2}$

Nhóm 2: $- \dfrac{{13}}{{12}}; - \dfrac{{31}}{{24}}$

$- \dfrac{{13}}{{12}} = \dfrac{{ - 26}}{{24}} > \dfrac{{ - 31}}{{24}}$ nên $- \dfrac{{13}}{{12}} >  - \dfrac{{31}}{{24}}$

Vậy $- \dfrac{{31}}{{24}} <  - \dfrac{{13}}{{12}} < \dfrac{{12}}{{100}} < \dfrac{{23}}{{100}} < \dfrac{{11}}{2}$ hay $- \dfrac{{31}}{{24}} <  - 1\dfrac{1}{{12}} < \dfrac{{12}}{{100}} < 23\%  < 5\dfrac{1}{2}$