Maths
How do you simplify a fraction?
Quick answer
To simplify a fraction, divide the top and bottom by the same number until you cannot go any further. For example, 12/18 simplifies to 2/3 when you divide both by 6.
In one sentence
Simplifying a fraction means writing it with smaller numbers, by dividing the numerator and denominator by the same number, without changing its value.
Explained
The fractions 4/8, 2/4 and 1/2 are all the same amount: half. We say they are equivalent. In maths, we usually like to write a fraction in its simplest form, also called lowest terms, which is the one with the smallest numbers.
To simplify, find a number that divides exactly into both the top (numerator) and the bottom (denominator). That number is a common factor. Divide both by it. Repeat until the only number that fits both is 1.
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Example: simplify 12/18.
Step by step
- Find a common factor.Both 12 and 18 are even, so use 2.
- Divide top and bottom.12 ÷ 2 = 6 and 18 ÷ 2 = 9, so you get 6/9.
- Check again.6 and 9 are both divisible by 3.
- Divide again.6 ÷ 3 = 2 and 9 ÷ 3 = 3, so you get 2/3.
Now 2 and 3 share no factor other than 1, so 2/3 is the simplest form. You could have jumped there in one step with the highest common factor. The biggest number that divides both 12 and 18 is 6. Dividing by 6 gives 2/3 straight away. To find the highest common factor, list the factors of each number.
Quick tips: if both numbers are even, divide by 2. If both end in 0 or 5, divide by 5. If the digits of both add up to a multiple of 3, divide by 3. You can check with equivalent fractions: multiplying 2/3 by 6/6 brings you back to 12/18.
Examples
| Fraction | Divide by | Simplest form |
|---|---|---|
| 4/8 | 4 | 1/2 |
| 6/9 | 3 | 2/3 |
| 15/25 | 5 | 3/5 |
| 12/18 | 6 | 2/3 |
| 7/11 | none | 7/11 |
Common mistakes
- Stopping too early. 6/12 becomes 3/6, but you can still go on to 1/2.
- Dividing only one number. Always do the same to the top and bottom.
- Subtracting instead of dividing. 8/12 is not 4/8 (subtracting 4). Divide by 4 to get 2/3.
Quick quiz
Simplifying fractions
Check what you know with 4 quick questions.
Question 1 of 4
Simplify 6/8.
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Related topics
Equivalent fractions
Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.
Factors and multiples
Factors are numbers that divide exactly into a number (the factors of 12 are 1, 2, 3, 4, 6 and 12). Multiples are the numbers in its times table (12, 24, 36…).
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Adding and subtracting fractions
To add or subtract fractions, first give them the same denominator. Then add or subtract only the numerators and keep the denominator. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
Improper fractions and mixed numbers
An improper fraction has a numerator bigger than its denominator, like 7/4. A mixed number shows the same amount as a whole number plus a fraction, like 1 3/4.
Comparing fractions
To compare fractions, check whether they share a denominator or a numerator, or rewrite them with a common denominator. The bigger fraction is the one with more of the whole.