



 
Firstly, two of these are equal, so trying to give them a definite order will be hard! There are various ways to order positive fractions. Here are some, in roughly increasing order of difficulty: (1) a/b > c/b if a>c: so 3/7 > 2/7 (2) a/b < a/c if b>c: so 3/7 < 3/5 Subtracting results in (2) from 1 we get (3) (ba)/b > (ca)/c if b>c; so 4/7 > 2/5 Renaming: ka/kb = a/b, so ka/kb > c/d if a/b > c/d Transitivity: if a/b > c/d and c/d > e/f then a/b > e/f: A special case of this is "benchmarking" when the middle term is something obvious: 6/11 > 1/2 > 3/7 The "big hammer" that always works but needs some arithmetic: a/b > c/d if and only if ad > bc
Good Hunting! RD  


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