Fractions can be simplified, if needed, by dividing the numerator and denominator by the same number. This will yield a fraction with smaller numbers. However, this "smaller looking" fraction has the same value as the original (see "...But Before You Start, Know This").
Example 1: A Fraction with Small Numbers
The fraction 2/4 can be simplified.
Both the numerator (2) and the denominator (4) are divisible by 2. So we can divide.
Dividing both numerator and denominator by 2 will yield a new "smaller looking" fraction 1/2, but still equivalent and proportional.
"Simplifying fractions can be thought of as trimming all the fat off." - Latreil Jackson
Example 2: A Fraction with Larger Numbers
The fraction 12/20 can be simplified. Try to look for that one number that can divide both numbers. With bigger numbers come bigger divisors.
Both the numerator (12) and the denominator (20) are divisible by 4. So we can divide.
Dividing both numerator and denominator by 4 will yield a new "smaller looking" fraction 3/5, but still equivalent and proportional.
Example 3: Cannot Be Simplified
Let's look at the factors of 11 and 18.
11 = 1 x 11 18 = 1 x 18
2 x 9
3 x 6
Now try to find a number they have in common out of the factors. All I see is the number 1.
So, 11 and 18 have 1 as a common factor that divides them. Well we know that any number divided by 1 is itself, nothing changes.
Therefore, nothing changes with this fraction meaning it cannot be simplified any further.