Equivalent fractions
Operating with fractions
will be extremely difficult for your child unless they can grasp the
concept of equivalent fractions.
Teaching equivalent fractions
Explain to your child why equivalent fractions are important. They
may not yet have tried addition or subtraction with fractions
but you can introduce equivalency by comparing fractions.
Use handson activities. For example, take a pizza, cut it in half then cut one half
into three equal slices. The single half and the half cut into three
should appear equal. 1⁄2 = 3⁄6
Fraction Lesson: Equivalent Fractions
This short lesson discusses equivalent fractions.
The concepts and methods from the above lesson are also shown below in text and graphic form.
The example below uses a pie, cut into equal pieces, to show equivalent fractions.
How to find equivalent fractions
Look at the pie example above. Notice how the top and bottom (numerator and denominator) of the fraction is increasing by a factor of 2. In other words, they are both being multiplied by 2.
Multiplying or dividing both the numerator and denominator of a fraction will result in an equivalent fraction. Here are some more examples:
 Multiply top and bottom by 4 

 = 

 are equivalent to 


 Multiply top and bottom by 3 

 = 

 are equivalent to 


 Divide top and bottom by 2 

 = 

 are equivalent to 


 Multiply top and bottom by 10 

 = 

 are equivalent to 


 Divide top and bottom by 25 

 = 

 are equivalent to 

Do the same to both the numerator and the denominator
Questions often require equivalent fractions to be written when only the numerator or denominator are given. The examples below show how these questions can be answered.
 = 
 What was done to the denominator to get to 25?
 It was multiplied by 5
So do the same to the numerator.
4 x 5 = 20 
 = 


 = 
 What was done to the denominator to get to 9?
 It was divided by 9
So do the same to the numerator.
45 ÷ 9 = 5 
 = 


 = 
 What was done to the numerator to get to 18?
 It was multiplied by 6
So do the same to the denominator.
4 x 6 = 24 
 = 

Remember: Only use multiplication or division when finding equivalent fractions. Do not use addition or subtraction.
Before moving on to work with fractions it is important that your
child understands equivalency with fractions. Be sure he or she can
accurately determine larger and smaller equivalent fractions. Ask him
or her to describe what they are doing to determine equivalent fractions?
Worksheets
Practice working with equivalent fractions using the worksheets below.
You can use this fraction
bar to help illustrate equivalency of fractions.
Online Fraction Games
The two fraction games below will help with practicing equivalent fractions.
You will also find some more fraction games here.
Understanding equivalent fractions is important when learning
how to add fractions.