One way to order fractions is to convert to approximate decimal:
(3/12=¼) 0.25, (⅖) 0.40, (⅓) 0.33, (4/9) 0.44, (¾) 0.75, (⅝) 0.63, (⅚) 0.83, (⅔) 0.67.
These can now be ordered:
0.25, 0.33, 0.40, 0.44, 0.63, 0.67, 0.75, 0.83, which is:
3/12, ⅓, ⅖, 4/9, ⅝, ⅔, ¾, ⅚.