is 5/9 bigger than 7/12

Multiply the top and bottom of 5/9 by 12 and the top and bottom of 7/12 by 9 to get:

5*12/(9*12)   and  7*9/(12*9)

The bottom of both are now the same, so just compare the tops, which are:

5*12 = 60  and 7*9 = 63

5*12 is smaller than 7*9 so 5/9 is smaller than 7/12

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7/12 is bigger