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Simplifying Fractions

In one line: Simplifying a fraction means dividing the top number and the bottom number by the same number, so the fraction uses smaller numbers but stays exactly the same size.

Why it works

Simplified fractions are easier to read, compare and work with. It is much quicker to see that 2/3 is two thirds than to picture 24/36. Answers in maths are usually expected in simplest form, which means the top number (the numerator) and the bottom number (the denominator) cannot both be divided by any whole number except 1. Simplifying is also a key step when adding, subtracting, multiplying and dividing fractions later on.

Think of it like: Imagine a pizza cut into 8 equal slices, and you eat 4 of them. That is 4/8 of the pizza. Now imagine the same pizza had been cut into just 2 big slices, and you ate 1 of them. That is 1/2. You ate exactly the same amount of pizza either way. Simplifying 4/8 to 1/2 is like swapping lots of small slices for fewer, bigger slices without changing how much pizza you have. (Where this breaks: The pizza picture shows why the amount stays the same, but it does not tell you which number to divide by. With fractions you must divide the top and bottom by the same whole number that goes into both exactly, and some fractions, such as 7/9, cannot be put into bigger slices at all because they are already in simplest form.)

Worked example

Simplify 24/36.

  1. List the factors of 24 (numbers that divide into it exactly): 1, 2, 3, 4, 6, 8, 12, 24.
  2. List the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
  3. Find the highest common factor (HCF), the biggest number in both lists: 12.
  4. Divide the top and the bottom by 12: 24 ÷ 12 = 2 and 36 ÷ 12 = 3.
  5. Check: 2 and 3 share no common factor except 1, so the fraction is in simplest form.

Answer: 24/36 = 2/3

Common mistakes

  • Dividing the top and bottom by different numbers (for example 6/8 becoming 3/2) changes the fraction's size, so always divide both by the same number.
  • Stopping too early, such as turning 18/24 into 9/12 and leaving it, is a common slip, so always check whether the new top and bottom still share a factor.
  • Subtracting the same number from top and bottom (such as 6/8 becoming 4/6) does not keep the fraction equal, so only ever divide.
  • Thinking a simplified fraction is smaller than the original is wrong, because 4/8 and 1/2 are exactly the same amount, just written with smaller numbers.

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Simplify 6/8.

Questions parents ask

What year do kids learn simplifying fractions?

Children usually meet equivalent fractions first, around Year 3 to 4 in the UK and Australia or Grades 3 to 4 in the US. Simplifying fractions using common factors is typically taught and practised from about Year 5 to Year 7 in the UK and Australia, and around Grades 4 to 6 in the US.

How can I help my child with simplifying fractions at home?

Make sure your child knows their times tables well, because spotting common factors depends on them. Use real objects like pizza slices, chocolate squares or egg cartons to show that 2/4 and 1/2 are the same amount, then practise a few fractions together and always ask, 'Can both numbers still be divided by the same number?'

Does simplifying a fraction change its value?

No. A simplified fraction is exactly equal to the original one; only the numbers used to write it change. For example, 10/20, 5/10 and 1/2 all describe the same amount.

What is the highest common factor, and is it the same as the greatest common factor?

The highest common factor (HCF) is the biggest whole number that divides exactly into two or more numbers. In the US it is usually called the greatest common factor (GCF), but it means the same thing. Dividing by the HCF simplifies a fraction in one step, though dividing by smaller common factors several times also works.