Fractions can be simplified when the numerator and denominator have a common factor in them. If both the numerator and denominator have common factors, then we can cancel these factors out. For example, in the fraction 8/12, 4 is a common factor of both 8 and 12.
Since this is the case, we can simplify the fraction by canceling the 4 from both the numerator and denominator of the fraction. Canceling is equivalent to dividing both the numerator and denominator by the same number.
The key to simplifying a fraction is to find all the common
factors between the numerator and denominator and to eliminate
them. The easiest way to be sure you have eliminated all the common
factors of the numerator and denominator is to find the prime
factors of each and then cancel them out.
To simplify a fraction, you should follow four steps:
Let's look at an example of this entire process:
Find the simplest form of the fraction 10/24.
The simplest form of 10/24 is 5/12. Let's work through the
steps for doing this.
As we can see, finding prime factors is important for simplifying fractions. Once we find the prime factors, it is merely a matter of canceling out common prime factors. Work through the practices for this section to be sure you understand how to do this.