Fractions are in simplest form when 1 is the only common factor for both numerator and
denominator.
Fractions need to be written in the simplest form since the simplest form is easier to understand.
For example
1
127
is easier to understand than
.
2
254
Another good reason for simplifying fraction is to make operations like multiplying or dividing
fractions easier since both numerator and denominator are smaller after the simplification.
Simplifying fractions is also known as reducing fractions.
The best way to simplify a fraction is to find the greatest common factor (GCF) and divide both
numerator and denominator by the GCF. Please refer to GCF link on how to find GCF.
Example: Simplify
18
30
The GCF of 18 and 30 is 6
Let’s divide both the numerator and denominator by 6:
18 18  6 3


30 30  6 5
So, the simplest form of
18 3
is .
30 5
Another way to simplify fractions is to divide both numerator and denominator by the same
number until we get the simplest form.
From the above example, both 18 and 30 are even numbers so we know that they are divisible by
2. So, let’s divide both numerator and denominator by 2:
18 18  2 9


30 30  2 15
Additional tricks on divisibility can be found in divisibility link.
From the tricks on divisibility, we realize that both numbers 9 and 15 are divisible by 3:
9 93 3


15 15  3 5
Here, we also showed that the simplest form of
18 3
is .
30 5
Both methods gave the same result (they should!). The GCF method is more effective when both
numerator and denominator are big numbers.