• Key Stage 2 • Fractions
Simplifying a fraction means writing it with the smallest possible numbers, without changing its value. For example, 12/18 simplifies to 2/3. Children learn to simplify fractions using common factors in Year 6. This guide gives a step-by-step method, worked examples, quick tricks and practice questions with answers.
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The Quick Answer
- To simplify a fraction, divide the numerator and the denominator by the same number.
- Dividing by the highest common factor (HCF) simplifies it in one step: 12/18 ÷ 6 on top and bottom = 2/3.
- A fraction is in its simplest form when the only number that divides into both the numerator and the denominator is 1.
- Children learn to use common factors to simplify fractions in Year 6.
How to Simplify Fractions: Step by Step
- Find the highest common factor of the numerator and the denominator. This is the biggest number that divides into both.
- Divide the numerator and the denominator by it.
- Check that no number other than 1 divides into both new numbers.
Example: simplify 18/24. The factors of 18 are 1, 2, 3, 6, 9 and 18. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The highest common factor is 6. 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so 18/24 = 3/4.
Can’t Find the HCF? Divide in Small Steps
You do not have to find the highest common factor straight away. Keep dividing by any common factor until you cannot go any further.
Example: simplify 24/36.
- Both numbers are even, so divide by 2: 12/18.
- Both are still even, so divide by 2 again: 6/9.
- Both are in the 3 times table, so divide by 3: 2/3.
Nothing else divides into 2 and 3, so the simplest form is 2/3.
Tip: quick checks for common factors. If both numbers are even, divide by 2. If both end in 0 or 5, divide by 5. If the digits of both numbers add up to a multiple of 3, divide by 3.
Worked Examples
| Fraction | Divide top and bottom by | Simplest form |
|---|---|---|
| 6/8 | 2 | 3/4 |
| 9/12 | 3 | 3/4 |
| 10/15 | 5 | 2/3 |
| 12/16 | 4 | 3/4 |
| 14/21 | 7 | 2/3 |
| 16/40 | 8 | 2/5 |
| 20/30 | 10 | 2/3 |
| 25/100 | 25 | 1/4 |
| 35/42 | 7 | 5/6 |
Simplifying Improper Fractions and Mixed Numbers
Improper fractions (where the numerator is bigger than the denominator) simplify in the same way. 14/4 ÷ 2 on top and bottom = 7/2. As a mixed number, 7/2 = 3 1/2.
Mixed numbers. Leave the whole number alone and simplify the fraction part. 2 6/8 = 2 3/4.
Common Mistakes
- Dividing only one number. Both the numerator and the denominator must be divided by the same number.
- Stopping too early. 12/18 ÷ 2 gives 6/9, but 6 and 9 can both be divided by 3. The simplest form is 2/3.
- Subtracting instead of dividing. Taking the same number away from the top and bottom changes the value of the fraction.
Simplifying Fractions Practice Questions
- 4/6
- 5/10
- 8/12
- 15/20
- 12/30
- 21/28
- 24/36
- 45/60
- Simplify 18/4 and write it as a mixed number.
- 3 10/12
Show the answers
- 2/3
- 1/2
- 2/3
- 3/4
- 2/5
- 3/4
- 2/3
- 3/4
- 9/2 = 4 1/2
- 3 5/6
Frequently Asked Questions
How do you simplify a fraction?
Divide the numerator and the denominator by the same number. Keep going until no number other than 1 divides into both.
What is the simplest form of a fraction?
A fraction is in its simplest form when its numerator and denominator have no common factor other than 1. For example, 2/3 is in its simplest form but 4/6 is not.
What year do children learn to simplify fractions?
Using common factors to simplify fractions is a Year 6 requirement. The curriculum guidance suggests children start simplifying simple fractions such as 6/9 = 2/3 in Year 4, using what they know about equivalent fractions.
What is 12/18 simplified?
2/3. The highest common factor of 12 and 18 is 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
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Sources: Department for Education, National curriculum in England: mathematics programmes of study. Practice questions written by Monster Learning.
