Support Page

Welcome to our Finding Equivalent Fractions support page.

Here you will find some helpful support in learning what an equivalent fraction is and how to find equivalent fractions.

We also have an equivalent fraction worksheets page to help you practice and show your understanding of this concept.

Here you will find some simple advice and support to help you learn to find equivalent fractions.

Towards the bottom of this page, there are also three printable resource sheets which explain about equivalent fractions in a little more detail.

Being able to find equivalent fractions is really important to know before you start trying to add or subtract fractions with different denominators.

So what is an equivalent fraction?

If two fractions are *equivalent*, it means that
they are equal, or represent the same value.

How do I find an equivalent fraction?

A good way to learn equivalent fractions is by looking at fraction strips.

Let us look at the fraction strips for a half.

A half is worth half of a whole. If we split each of the halves into two equal pieces, we end up with fourths or a whole split up into 4 equal parts.

Each half has been split into two-fourths (as there are two parts out of 4 parts shaded), so we have the equivalent fraction:

One half is equivalent to (or equal to) two-fourths.

In other words, \[ {1 \over 2} = {2 \over 4} \]

If we split each half into three equal pieces instead of 2, we get 3 strips shaded (the numerator) out of a total of 6 strips (the denominator), giving the fraction three-sixths.

This gives us: \[ {1 \over 2} = {2 \over 4} = {3 \over 6} \]

We can repeat this by splitting the same half into 4, 5, 6, etc. pieces, ending up with:

\[ {1 \over 2} = {2 \over 4} = {3 \over 6} = {4 \over 8} = {5 \over 10} \]

This series of fractions equivalent to a half could be continued for ever.

It also makes sense in context, for example, if you got 5 out of 10, or five-tenths, in a spelling test correct, then you would have got half the answers correct and half wrong.

This process can be repeated for any fraction.

Let us look at the fraction two-thirds.

If we split each of the thirds into two equal parts, we get a total of 6 pieces with 4 pieces shaded, so we now have 4 out of 6 shaded instead of 2 out of 3 shaded.

In other words, we have doubled the number of shaded parts (numerator) and also doubled the number of total parts (denominator).

So now we have: \[ {2 \over 3} = {4 \over 6} \]

Again, this can be repeated and the fraction two-thirds could be split into any number of equal parts.

This gives us the equivalent fraction sequence: \[ {2 \over 3} = {4 \over 6} = {6 \over 9} = {8 \over 12} = {10 \over 15} \]

Each time the fraction is split, both the denominator and the numerator are multiplied by the split. This gives us an equivalent fraction.

In other words, if you multiply the numerator and denominator by the same number, you get the same (or equivalent) fraction.

And by using the same logic, if we divide the numerator and denominator by the same number, you get an equivalent fraction.

Example 3) Take the fraction \[ {2 \over 3} \]

If we multiply the numerator and denominator both by 2, we get

\[ {2 \times 2 \over 3 \times 2} = {4 \over 6} \]

These two fractions are equivalent.

Example 4) Take the fraction \[ {4 \over 8} \]

If we divide the numerator and denominator both by 2, we get

\[ {4 \div 2 \over 8 \div 2} = { 2 \over 4 } \]

These two fractions are equivalent.

We have found out that if you multiply or divide the numerator and denominator of a fraction by the same number, you get an equivalent fraction.

If you would like to see this all in a little more detail, please print out the 3 sheets below which will tell you all you need about equivalent fractions.

Using Equivalent Fraction Strips is a great way to learn your Fraction facts and help you to understand exactly how much fractions are worth in a visual way.

Using these fraction strips will help your child to:

- understand Fraction as lengths;
- understand equivalent fractions;
- understand visually how much each fraction is worth.

Here you will find a selection of Equivalent Fractions worksheets designed to help your child practice their equivalent fraction facts.

This is a key learning step your child needs to be confident with before they start learning to add and subtract fractions with different denominators.

Using these sheets will help your child to:

- apply their understanding of equivalent fractions.

This interactive explorer is an app created by:

PhET Interactive Simulations University of Colorado Boulder https://phet.colorado.edu

It is a great way of exploring equivalent fractions in a visual way.

You can either explore different fraction equivalences in the Equality Lab, or test your knowledge of equivalent fractions using the Game area.

Here you will find the Math Salamanders free online Math help pages about Fractions.

There is a wide range of help pages including help with:

- fraction definitions;
- equivalent fractions;
- converting improper fractions;
- how to add and subtract fractions;
- how to convert fractions to decimals and percentages;
- how to simplify fractions.

How to Print or Save these sheets

Need help with printing or saving?

Follow these 3 easy steps to get your worksheets printed out perfectly!

How to Print or Save these sheets

Need help with printing or saving?

Follow these 3 easy steps to get your worksheets printed out perfectly!

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

## New! Comments

Have your say about the Math resources on this page! Leave me a comment in the box below.