Cancelling down fractions to their simplest form

Topic guide

What this worksheet practises

This worksheet provides practice on cancelling down fractions to their simplest form. Simplifying fractions is a fundamental mathematical skill; almost all fraction questions in an exam require you to leave your final answer in its simplest form.

Key method

To cancel down a fraction, you must find a common factor that divides equally into both the numerator (the top number) and the denominator (the bottom number).

• Identify a number that goes into both the top and the bottom without leaving a remainder.
• Divide both the numerator and the denominator by this number.
• Check the new fraction to see if it can be divided again. Repeat the process until the only common factor left is 1.
• If you can spot the highest common factor (HCF) immediately, you can simplify the fraction in a single step.

Worked example

Simplify the fraction 24/36 fully.

Step 1: Notice that both numbers are even, so they can be halved (divided by 2).

24 ÷ 2 = 12, and 36 ÷ 2 = 18. This gives 12/18.

Step 2: Both are still even, so halve them again.

12 ÷ 2 = 6, and 18 ÷ 2 = 9. This gives 6/9.

Step 3: 6 and 9 are both in the 3 times table. Divide by 3.

6 ÷ 3 = 2, and 9 ÷ 3 = 3. This gives 2/3.

There are no more common factors, so the simplest form is 2/3.

(Alternatively, dividing immediately by the HCF, which is 12: 24 ÷ 12 = 2, and 36 ÷ 12 = 3).

Common mistakes to avoid

A frequent mistake is stopping too early. Students often divide by 2 or 3 once and assume the fraction is fully simplified. Always check your resulting fraction to guarantee no further common factors exist.

How to check your answer

Look closely at your final numerator and denominator. If they are both even, you definitely haven't finished. If one is a prime number (like 2, 3, 5, or 7), check if it divides into the other number. If it doesn't, your fraction is fully simplified.