Finding Equivalent Fractions

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.

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:

1 2 =   2 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 2 =   2 4 =   3 6

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

1 2 =   2 4 =   3 6 =   4 8 =    5  10

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

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 4 pieces shaded instead of 2, and we now have 6 parts making the whole instead of 3.

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 3 =   4 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 3 =   4 6 =   6 9 =    8  12 =   10 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 3

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

4 6

These two fractions are equivalent.

Example 4) Take the fraction

4 8

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

2 4

These two fractions are equivalent.

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.

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.

All the Equivalent Fractions sheets in this section support the Elementary Math Benchmarks for 4th Grade.

• Equivalent Fractions Worksheets

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

• Learning Fractions

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