Equivalent fractions

Before learning about equivalent fractions, please make sure you've read the primer on fractions.

Now let’s say you’re going to eat some candy and you have a ‘whole’ or total of two pieces of candy. So the denominator of the fraction is 2.

You decide to eat one piece of candy, making the numerator of the fraction 1.

The fraction of the candy you take is therefore


- a half or one half.

Here's your candy fraction!

Your friend on the other hand has a ‘whole’ or total of four pieces of candy. So here the denominator of the fraction is 4.

She decides to eat two pieces of candy, making the numerator 2 and the fraction of the candy she takes


- two fourths or two quarters.

You can see that while you and your friend have different amounts of candy at the start, both of you take the same proportion of the candy available to you - you each eat one piece of candy for every two pieces you have. You've taken fractions of candy which are equal in value, although it may not feel like it as your friend has eaten one more piece of candy than you!

So what exactly are equivalent fractions?

They're fractions that look different but have the same value.

You can show that 1/2 is equal in value to 2/4 (that is a half is equal to two quarters) by multiplying numerator and denominator by 2

Similarly, you can show that 2/4 is equal in value to 1/2 (that is two quarters is equal to a half) by dividing numerator and denominator by 2

How about another example?

If your friend starts out with five pieces of candy and decides to eat three pieces, the denominator would be 5 and the numerator 3, making the fraction of candy she takes


- three fifths,

whereas if you have ten pieces of candy and eat six pieces, the denominator would be 10 and the numerator 6, with the fraction of candy you take being


- six tenths.

However, by either multiplying or dividing by 2 it can be seen that these are another example of fractions which are equivalent or equal in value - three fifths is equal in value to six tenths, and six tenths is equal in value to three fifths. Again, you and your friend are each taking the same proportion of candy available to you at the start - in this case three in every five pieces.

Over to you!

Now try thinking of a few examples of equivalent fractions yourself!

For more on fractions click:

What is a fraction?

Simplifying fractions

Adding fractions

How to subtract fractions

Multiplying fractions

How to divide fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal

Fraction to decimal chart

Decimal to fraction

Fraction to percent

Percent to fraction

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