# Math fractions

What are math fractions?

Let’s think of an example to make things clear from the start. Jacob and Sophia share a pizza.

Now consider what is a fraction? It’s part of a 'whole' - for instance, part of Jacob and Sophia's pizza.

It can be expressed

or

### numerator/denominator

We'll stick to numerator/denominator here but you can use either way - they mean the same thing.

The denominator is the total number of pieces which make up the 'whole'. The numerator is the number of pieces taken from the 'whole'.

Going back to our example, the fairest and simplest way for Jacob and Sophia to share their pizza would be to slice it straight down the middle and each take a large piece!

## So what fraction of the pizza does Jacob take?

The pizza's been divided into two pieces or slices, so the denominator is 2.

Jacob takes one piece or slice of the pizza - the numerator for the fraction of the pizza he takes is therefore 1.

So the fraction of the pizza taken by Jacob is

1/2

otherwise known as a half or one half.

## And what fraction of the pizza does Sophia take?

As above, the pizza’s been divided into two slices - the denominator is 2.

Sophia also takes one slice of the pizza – so the numerator for the fraction of the pizza she takes is 1.

Therefore the fraction of pizza taken by Sophia is also

1/2

In other words, Jacob and Sophia each take one half of the pizza.

## But what if Sophia isn't as hungry as Jacob?

Let's say in this case the friends decide to divide the pizza into 3 equal slices.

Because Sophia’s less hungry, she takes just one slice. The denominator is 3 (because the pizza’s been cut into three) and the numerator is 1 (because Sophia takes one slice). So the fraction of the pizza taken by Sophia is

1/3

- a third or one third.

Jacob takes the rest of the pizza, that's two slices. Again the denominator is 3 (remember the pizza’s been cut into three) but the numerator is 2 (because Jacob takes two slices). So the fraction of the pizza taken by Jacob is

2/3

- two thirds.

## Are you ready for more math fractions?

Hopefully from the example above you can see that learning math fractions can be fun - and don’t worry, there’ll be plenty of other worked examples on how to do fractions!

For more on fractions click:

Equivalent fractions

Simplifying fractions

How to subtract fractions

Multiplying fractions

How to divide fractions

Improper fractions

Mixed fractions (mixed numbers)

Comparing fractions

Ordering fractions

Fraction to decimal chart

Decimal to fraction

Fraction to percent