What is Common Numerator?
A nonzero number that is a multiple of the numerators of two or more fractions is called their common numerator.
For example, consider the fractions ^{4}⁄_{5 }and ^{6}⁄_{7 }. Both the fractions have different numerators. To find their common numerator, we find the common multiples of the numerators 4 and 6.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, ...
Common multiples of 4 and 6: 12, 24, 36, …
So, common numerators for ^{4}⁄_{5 }and ^{6}⁄_{7 }can be 12, 24, 36, …
If we want the common numerator to be 12, we need to multiply both the numerator and denominator as shown:
Now, we have two fractions with a common numerator.
Comparing fractions with common numerator
We can easily compare two or more fractions when their numerators are common or like.
For example, let us compare ^{3}⁄_{7 }and ^{3}⁄5
As fifths are greater than sevenths, threefifths are greater than threesevenths.
Therefore, ^{3}⁄_{7 }< ^{3}⁄_{5}
So, in general:
If two or more fractions have a common numerator then the fraction with the smallest denominator is the greatest.
Fun Facts
