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How to simplify fractions

Home > By Subject > Fractions > Simplifying Fractions

Common fractions are most often written in their simplest form. This is also known as expressing or writing fractions using the lowest terms.

Common fractions can be simplified to their lowest terms by applying the concept of equivalent fractions.

If necessary, review equivalent fractions with your child before working on simplifying common fractions.

Fraction Lesson: How To Simplify Fractions

This short lesson shows two different methods for simplifying fractions.

The above lesson includes audio (so remember to switch on your speakers). Use the play/ pause button if you need to stop and start the lesson.

Related Fractions Lessons

Lesson 1: Introducing Fractions Lesson 2: Equivalent Fractions Lesson 3: Common Denominators Lesson 4: Adding and Subtracting Fractions Lesson 5: Simplifying Fractions Lesson 6: Mixed Numbers and Improper Fractions
Introducing Fractions Equivalent Fractions Common Denominators Adding and Subtracting Fractions Simplifying Fractions Mixed Numbers and Improper Fractions

The methods shown in the above lesson are also illustrated below .

Equivalent Fractions: Recap

Look at the four fractions below. They are all equivalent to each other.

circle showing one half arrow circle showing two fourths arrow circle showing four eighths arrow circle showing eight sixteenths
1
2
x
2
2
2
4
x
2
2
4
8
x
2
2
8
16

Note how the numerator and denominator both increase by a factor of 2 each time.

Multiplying or dividing both the numerator and denominator by the same number does not change the amount the fraction represents; it only changes how the fraction is written.

Here is another example of equivalent fractions.

bar showing 6/15
arrow
bar showing 2/5
6
15
÷
3
3
2
5

In this case the numerator and denominator both decrease by a factor of 3

 

Simplifying fractions: using common factors

Simplifying fractions means dividing the top and bottom by the same number so that the top and bottom become as small or as simple as possible.

To simplify a common fraction we can find the greatest common factor for the numerator and the denominator and then use it to divide both. The steps below show an example of how to do this:

What is the fraction?
16
20
Find the factors of 16 (the numerator) 1 , 2 , 4 , 8 , 16
Find the factors of 20 (the denominator) 1 , 2 ,4 , 5 , 10 , 20
Find the common factors 1 , 2 , 4
Find the greatest common factor 4
Divide 16 (the numerator) by 4 16 ÷ 4 = 4
Divide 20 (the denominator) by 4 20 ÷ 4 = 5
Write the fraction in simplest form
4
5

Simplifying fractions: trial and error, exploration

When simplifying fractions you can use a trial and error method as an alternative to the greatest common factor one that is shown above .

  1. Ask yourself, what is the largest whole number that you can think of that both the top and bottom (numerator and denominator) are divisible by.
  2. Divide both by this number.
  3. Keep asking yourself the same question until the only number that both are divisible by is 1

The following examples show how this trial and error method can be used while simplifying fractions.

Example: Simplifying 16/24

Simplify 16/24
Question/ Step Try   Simplified?
What number are the top and bottom both divisible by? 2 Divide top and bottom by 2 to get 8/12

Not yet..keep going..

Same question as above 2 Divide top and bottom by 2 to get 4/6 Not yet..keep going..
Same question as above 2 Divide top and bottom by 2 to get 2/3 Yes
If we had tried dividing by 4 or even 8 on our first try we would have simplified the fraction sooner. Not to worry though, we got there in the end!

Example: Simplifying 48/60

Simplify 48/60
Question/ Step Try   Simplified?
What number are the top and bottom both divisible by? 6 Divide top and bottom by 6 to get 8/10

Not yet..keep going..

Same question as above 2 Divide top and bottom by 2 to get 4/5 Yes

Example: Simplifying 60/100

Simplify 60/100
Question/ Step Try   Simplified?
What number are the top and bottom both divisible by? 10 Divide top and bottom by 10 to get 6/10

Not yet..keep going..

Same question as above 2 Divide top and bottom by 2 to get 3/5 Yes

Common error when simplifying fractions

The example below shows a fairly common error made by students when showing fractions in their simplest form.

common error example showing fraction only partially simplified.

In fairness to those that make the "error" above, if just asked to "simplify a fraction" then the answer above is not wrong - it is just not as good an answer as the correct one!

Use the worksheet generator icon Simplifying Fractions Worksheet Generator to get as much practice as you need.

The worksheet below will also provide practice on simplifying fractions..

Here is a very nice and simple explanation of simplifying fractionslink to external site from Math is Fun.

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