Finding Equivalent Fractions

Welcome to the Math Salamanders Finding Equivalent Fractions support page.

Here you will find some helpful support in learning how to find equivalent fractions.

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.

What is an Equivalent fraction?

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.

Example 1

Let us look at the fraction strips for a half.

Finding fractions whole and 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.

Finding fractions quarters

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.

Finding fractions 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.

Example 1

Let us look at the fraction two-thirds.

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.

Fraction four-sixths

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.

Further Examples

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.

So what have we learnt?

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.

How to find Equivalent fractions printable sheets

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.

Equivalent Fractions Worksheets

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.

Learning Fractions Math Help Page

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.

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