All of the numbers which are elements of the set 

{x | 1/2 < x < 5/8}

3/8 is wrong because 1/2 = 4/8. So 3/8 is less than 1/2


Consider 1/2 as 8/16 and 5/8 as 10/16.

Then 9/16 will be between them.

You can consider 1/2 as 16/32 and 5/8 as 20/32.

Then any of these fractions will be between them:

17/32, 18/32, 19/32.

18/32 reduces to 9/16.

Or you can consider 1/2 as 32/64 and 5/8 as 40/64.

Then any of these fractions will be between them:

33/64, 34/64, 35/64, 36/64, 37/64, 38/64, 39/64

Notice that 34/64, 36/64, and 38/64 reduces to

17/32, 9/16, and 19/32.

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The idea is to rewrite 1/2 and 5/8 with the same
denominator which is the largest denominator among the
answers, reduce the ones that will reduce, and
the numbers between them will have numerators between
the numerators of what 1/2 and 5/8 are rewritten as.


Edwin