Expanding fractions

The cake must be enough for everyone!

Remember back when we compared a fraction to a cake: The numerator represented the number of pieces, the denominator indicated in how many pieces the cake was divided.

Imagine you have two large pieces of cake.

2/8 cake

Now you are just four and everyone should get exactly the same amount of the cake. So what do we do?

The two pieces are cut exactly in the middle, so that there are 4 pieces of cake with the same size.

How big are these pieces? If you divide each of the originally eight pieces of cake in this way, you would have exactly twice as many: 16.


2/8 cake    =    4/16 cake

Both the numerator and denominator have been multiplied by the number 2.

formula: Expanding fractions

Expand a fraction by multiplying the numerator and denominator by the same number. The value of the fraction does not change!

Another example:

Expanding fractions - Example

The numerator and denominator have been extended by a factor of 7. Calculate: 6 divided by 3 and 42 divided by 21 both produce the same result 2.

Attention: Frequent error when expanding fractions

Very important: ALWAYS extend the numerator AND the denominator! Otherwise the value of the fraction will change:

3/8 is not equal to 6/8!

Thinking back to the cake, we would have made 6 pieces out of 3 pieces - Oliver would have his joy!

So: If we want to do Oliver this favor anyway, then we are allowed to cut the pieces half the size. On the whole cake we have 16 pieces. Now it fits again:


Online Exercise: Expanding fractions

Here you can practise expanding fractions online:

  1. Expand the fraction with the specified expansion number.
  2. Determine the expansion number and the denominator.
  3. Determine the expansion number and the numerator.
If you have any problems with the exercises, please have a look at the hint and the sample solution first.

Let's continue with: "Simplifying/Reducing fractions"