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Introduction

QUICK LINKS


Introduction

Simplifying Fractions

To help us better understand fractions, we like to imagine them as pizzas or legos.

Pick whichever you vibe with more:

INTRO
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A simplified (or reduced) fraction is a fraction written in simplest form, meaning the only number that evenly divides into both the top and bottom is .
In pizza terms, when we simplify a fraction, we want to determine the fewest number of equal slices we can cut a portion of pizza into without changing the amount of pizza.
Simplifying a fraction does not change its value, meaning the simplified fraction is equivalent to the original fraction. Check out equivalent fractions below by dragging the blue line:
Check out our
Calculator
or explore our
Lesson
and
Practice
sections to learn more about how to simplify fractions and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

CALCULATOR
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Simplifying Fractions Calculator


Step 1. Divide the top and bottom by the same number.

The number should be a common factor, or a number that divides evenly into both the top and bottom.
Since the only common factor here is , this fraction is already completely simplified.
KEY STEPS
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How to Simplify Fractions

Step 1. Divide the top and bottom by the same number.

The number should be a common factor, or a number that divides evenly into both the top and bottom.

Step 2. Repeat Step 1 until the only common factor left is .

Keep dividing the top and bottom by a common factor until the only one left is .
We can also just find the greatest common factor, and divide both the top and bottom by it. This guarantees us the most simplified version of the fraction.
LESSON
β€” Simplifying Fractions

Simplifying Fractions

Simplifying (or reducing) a fraction means making the top and bottom as small as possible without changing the value of the fraction.

We can do this by dividing the top and bottom of the fraction by common factors until the only common factor left is .

What is a common factor?

A common factor is a number that evenly fits into two or more given numbers.
And remember, factors always come in pairs consisting of the factor and the number of times it fits evenly into the given number.
Factors of :
Factors of :
The common factors of and are and .
Now that we know our basics, let’s check out some examples of how to simplify fractions using common factors!

EXAMPLE 1

Let's start by simplifying:

Step 1. Divide the top and bottom by the same number.

The number should be a common factor, or a number that divides evenly into both the top and bottom.
This simplifies our fraction. In pizza terms, we’re changing the size of the slice, which also changes the number of slices, keeping the amount the same:

Step 2. Repeat Step 1 until the only common factor left is .

The only common factor left is , so we're done!
So our answer is
.

EXAMPLE 2

Nice work! Now let's try a harder one. Let's simplify:

Step 1. Divide the top and bottom by the same number.

The number should be a common factor, or a number that divides evenly into both the top and bottom.
This simplifies our fraction. In pizza terms, we’re changing the size of the slice, which also changes the number of slices, keeping the amount the same:

Step 2. Repeat Step 1 until the only common factor left is .

Keep dividing the top and bottom by a common factor until the only one left is .
So our answer is
.
Awesome! If you’d like to practice additional problems simplifying fractions, expand the
Practice
below before closing out this lesson! ⚑
PRACTICE
β€” Simplifying Fractions

Practice: Simplifying Fractions

Question 1 of 3: Simplify .

Step 1. Divide the top and bottom by the same number.

The number should be a common factor, or a number that divides evenly into both the top and bottom.


This simplifies our fraction. In pizza terms, since we’re changing the size of the slice and also the number of slices, the amount stays the same.

Step 2. Repeat Step 1 until the only common factor left is .

Keep dividing the top and bottom by a common factor until the only one left is .

Now that the only common factor left is , we're done!
Awesome job! The simplified version of is Β 
.

CONCLUSION
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Incredible job, look at you go! Thanks for checking out this lesson β˜ΊοΈπŸ™. Where to next?
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