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Simplest Form 

How do you know if a fraction is in simplest form? 

Goal:

Goal:

Illustration with a pencil and blue circle with the text made it simple. The greatest common factor is useful for other areas in mathematics, especially when it comes to fractions. A fraction is in simplest form when the numerator and denominator cannot be divided by any common values. So, why simplify fractions?

Simplifying fractions makes them easier to use. For example, you can measure an object to the closest 1/4 of an inch, but it is hard to measure to the nearest 5/20 of an inch. 

To begin, like with all other math, it is important to always start out with your work neat and organized. Next, you will use the greatest common factor to find the simplest form of a fraction.

Consider the fraction.

Eight sixteenths.

What is the simplest form of this fraction?

In order to determine how to find the simplest form of this fraction, work through the slides below. 

Find the Greatest Common Factor 

Simplifying fractions is another way to use equivalent fractions; you are actually creating an equivalent fraction with smaller numbers. 
First, find the GCF for both the numerator and denominator.
The factors of 8 and 16 are: 
8: 1, 2, 4, 8
16 : 1, 2, 4, 8, 16 
You can see that the greatest common factor for 8 and 16 is 8.
This means that they can both be evenly divided by 8. 

Simplify 

Now that you have identified the GCF, you are ready to simplify the fraction.   
To simplify the fraction, you need to divide both the numerator and denominator by the GCF, like this: 

Two equations stacked on top of one another. Equation one: eight divided by eight equals one. Equations two: Sixteen divided by eight equals two.

This new fraction is the simplified fraction:
 \(\mathsf{ \frac{8}{16} }\) was simplified to \(\mathsf{ \frac{1}{2} }\). 

Try it for yourself! Use the steps you have learned to simplify the fractions below. Click the box to check your answers when you are finished.