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Let us say that we have two fractions: 3/4 and 14/18.
Is 3/4 > 14/18 or is 3/4 < 14/18?
It is not immediately apparent which one is greater than the other. However, it is possible to convert the problem of comparing fractions into the problem of comparing integers, which is intuitive to solve.
In order to do so, we must find a common denominator of 3/4 and 14/18. To do so, we multiply the numerator and the denominator by the denominator of the other fraction like so:
(3/4) * (18/18) = (54/72)
and
(14/18) * (4/4) = (56/72)
From the above, it is clear that 56 > 54, which means that 56/72 > 54/72.
We can do this because 18/18 = 1 = 4/4. All we are doing is multiplying each fraction by the number 1. If you recall the Identity Property of multiplication, multiplying any number by 1 does not change the number, so this means:
56/72 > 54/72
14/18 = 56/72 and 3/4 = 54/72
So
14/18 > 3/4
To generalize:
If you have fractions a/b and c/d, convert the problem of comparing a/b and c/d to comparing the integers a*d and c*b. If a*d > c*b then a/b > c/d. If a*d < c*b then a/b < c/d.
Obviously, if a*d = c*b then a/b = c/d
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