Simplifying fractions: what children learn
A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. Year 6 pupils use common factors to simplify fractions, and common multiples to give fractions the same denominator. For example, 12/18 simplifies to 2/3 because 12 and 18 can both be divided by 6.
In this quiz, each question shows a fraction to simplify, with four choices. Watch out: sometimes one of the wrong choices is equal in value but only partly simplified (such as 6/9 for 12/18). It is a fair fraction, but not the simplest form, so it is not the answer.
This topic covers the Year 6 statutory requirement in the National Curriculum in England (Number – fractions (including decimals and percentages)): pupils should be taught to “use common factors to simplify fractions; use common multiples to express fractions in the same denomination”. Year 6 pupils are usually aged 10–11.
For families following US standards, the closest Common Core standard is 4.NF.A.1, which is taught in Grade 4. Common Core covers equivalent fractions but does not name 'simplest form' as a separate standard.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 120-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Find a common factor. Look for a number that divides both the numerator and the denominator. 12 and 18 are both even, so 2 is a common factor.
- Divide both numbers by it. 12 ÷ 2 = 6 and 18 ÷ 2 = 9, so 12/18 = 6/9.
- Keep going until you can't. 6 and 9 share the factor 3: 6/9 = 2/3. 2 and 3 have no common factor except 1, so 2/3 is the simplest form.
- Or use the highest common factor. The highest common factor (HCF) of 12 and 18 is 6. Dividing both by 6 gets to 2/3 in one step.
Worked examples
Example 1: Simplify 15/20.
Working: Both are in the 5 times table: 15 ÷ 5 = 3, 20 ÷ 5 = 4.
Answer: 3/4
Example 2: Simplify 24/36.
Working: HCF is 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3. (Dividing by 2 first gives 12/18, which still simplifies.)
Answer: 2/3
Example 3: Simplify 7/21.
Working: 7 is a factor of both: 7 ÷ 7 = 1, 21 ÷ 7 = 3.
Answer: 1/3
Common mistakes and how to fix them
- Stopping too early: 24/36 simplified to 12/18. After each step, check whether the new numbers still share a factor.
- Dividing the numerator and denominator by different numbers. Both must be divided by the same number, or the value of the fraction changes.
- Subtracting instead of dividing (thinking 5/8 simplifies to 2/5 by taking 3 from each). Simplifying only ever uses division by a common factor.
Activities to try at home
- Look at fractions in recipes or measurements: is 4/8 of a cup the same as ½?
- Fold paper to show that 2/4, 3/6 and 4/8 cover the same area as ½.
- Play 'snap' with equivalent fraction cards.
Ideas for the classroom
- Use fraction walls to show families of equivalent fractions.
- Ask pupils to list the factors of the numerator and denominator and circle the highest common factor.
- Link to adding fractions with different denominators, where simplifying the answer is the last step.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
What does simplest form mean?
The numerator and denominator have no common factor other than 1. For example, 2/3 is in simplest form, but 4/6 is not.
Is a fraction wrong if it isn't simplified?
It isn't wrong in value, but Year 6 questions often ask for answers in simplest form, so it is a good habit.
What is the US equivalent?
The closest Common Core standard is 4.NF.A.1 (Grade 4) on equivalent fractions. It does not set out 'simplest form' as a separate standard.