# Equivalent fractions

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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 hands-on 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. 12 = 36

## Fraction Lesson: Equivalent Fractions

This short lesson discusses equivalent 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 Introducing Fractions Equivalent Fractions Common Denominators Adding and Subtracting Fractions Simplifying Fractions Mixed Numbers and Improper 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.

Here is half of a pie.
 1 2
Here is two fourths of a pie
 2 4
Here is four eighths of a pie.
 4 8
These are equal fractions of the pie.

So these are 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:

 2 3
Multiply top and bottom by 4
 2 3
 x 4 x 4
=
 8 12
 2 3
are equivalent to
 8 12

 5 6
Multiply top and bottom by 3
 5 6
 x 3 x 3
=
 15 18
 5 6
are equivalent to
 15 18

 8 10
Divide top and bottom by 2
 8 10
 ÷ 2 ÷ 2
=
 4 5
 8 10
are equivalent to
 4 5

 3 4
Multiply top and bottom by 10
 3 4
 x 10 x 10
=
 30 40
 3 4
are equivalent to
 30 40

 25 100
Divide top and bottom by 25
 25 100
 ÷ 25 ÷ 25
=
 1 4
 25 100
are equivalent to
 1 4

### 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.

 4 5
=
 ? 25
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

 4 5
=
 20 25

 45 81
=
 ? 9
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

 45 81
=
 5 9

 3 4
=
 18 ?
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

 3 4
=
 18 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.