How To Simplify Fractions - BBC Bitesize

Jump to

1. Introduction
2. Activity
3. Explanation
4. Examples

Simplifying fractions

Some fractions can be made 'simpler'.

Simplifying means that the numerator and denominator can be smaller numbers.

But the overall value of the fraction is not changed.

Back to top

Activity: simplifying fractions

Complete this interactive activity to learn more about simplifying fractions and then put your knowledge to the test with a quiz.

Back to top

Simplifying a fraction

Some fractions can be made 'simpler'.

This means that the numerator and denominator can be smaller numbers, but the overall value of the fraction is not changed.

For example, the fraction \(\frac{4}{8}\) has the same value as \(\frac{2}{4}\), which has the same value as \(\frac{1}{2}\).

When you are simplifying fractions, you are looking for a number that you can divide the numerator and the denominator by.

Sometimes, you will be able to simplify a fraction into a unit fraction (a fraction with a numerator of one), but not always.

Back to top

Example 1

What can you divide \(\frac{2}{10}\) by to simplify the fraction?

Show answer

✓ You can divide the numerator and the denominator by 2.

So, 2 divided by 2 is 1 and 10 divided by 2 is 5.

\(\frac{2}{10}\) is equivalent to \(\frac{1}{5}\).

\(\frac{1}{5}\) has the same value as \(\frac{2}{10}\), it's just written in a simpler form.

Back to topExample 2

Can you simplify the fraction \(\frac{6}{9}\)?

Show answer

✓ You can divide the numerator and the denominator by 3.

This gives you the fraction \(\frac{2}{3}\).

\(\frac{2}{3}\) is equivalent to \(\frac{6}{9}\) but it's in a simpler form.

Back to topExample 3

You can simplify using more than one step.

How can you simplify the fraction \(\frac{18}{24}\)?

Show answer

✓ You can divide 18 and 24 by 2.

This will give you the fraction \(\frac{9}{12}\).

You can then simplify that further and divide the numerator and denominator by 3, to give \(\frac{3}{4}\).

Or, in one step you can divide the numerator and the denominator by 6.

Either way, the simplest form of \(\frac{18}{24}\) is \(\frac{3}{4}\).

Back to top

NEW! Play Guardians: Defenders of Mathematica - the winter update. gameNEW! Play Guardians: Defenders of Mathematica - the winter update

It's Mathematica as you’ve never seen it before, with all-new festive backgrounds and costumes. Available for a limited time only. Use your maths skills to save the day before it's too late!

Back to top

More on Fractions

Find out more by working through a topic

• Divide fractions by integers

  • count17 of 17
  

• What are fractions?

  • count1 of 17
  

• Order simple fractions

  • count2 of 17
  

• Finding a third

  • count3 of 17