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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It is not always helpful.Some people may find it helpful when comparing fractions. By converting them into percentages they are made into like fractions: all with the denominator 100.
The larger fraction is the one with the smaller denominator, when the numerators are the same.
Since they are all based on a common denominator of 100, some people find them easier for comparing fractions.
well it depends on what you comparing it to, for instance if I'm 19 minutes compared to an hour is 19/60
To simplify fractions, it is necessary to divide the numerator and the denominator by their GCF. You can find their GCF by comparing their prime factorizations. You can find their prime factorizations through the use of factor trees.