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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.
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