Fractions – The Basics Everyone Should Know
Lots of people really don’t like fractions, but with a little bit of work everyone can learn to love (or at least like) fractions. You will find GCSE maths much easier once you’re confident working with fractions.
In this post we’re going to go through the basics. We’ll talk about:
- what fractions actually are;
- how to compare fractions;
- simplifying fractions; and
- links to some further learning and questions for you to try.
What is a fraction?
A fraction represents a given number of equal parts. For example if I split something into four equal parts and select three of them then my fraction is 3/4. The fraction line literally means divide, so for example 4/2 means 4 divided by 2, which of course equals 2.
The number above the line is called the numerator and the number below the line is called the denominator.
A fraction with the numerator smaller than the denominator is less than one, for example: 2/3
If the numerator and denominator are the same then the fraction is equal to one, for example: 3/3 = 1
When the numerator is bigger than the denominator then the fraction is bigger than one, for example: 4/3
Fractions with a numerator greater than the denominator are called improper fractions.
You will often need to compare two or more different fractions to find out which is bigger or smaller. To do this you need to find a common denominator (make the bottom number the same on each fraction).
Let’s compare 2/3 with 3/5. First we need to get a common denominator, by finding a common multiple (a number in both the 3 and 5 times tables). Remember that whatever you multiply the denominator by, you must do the same to the numerator otherwise the fraction will change value. 15 is the lowest common multiple of 3 and 5 so we use that. Here’s how it works:
2×5/3×5 = 10/15 and 3×3/5×3 = 9/15
Once the denominators are the same, you can simply compare the numerators. So, 2/3 is just a bit bigger than 3/5
Fractions usually need to be written in their simplest form. You’ve probably seen lots of questions finish with the line: ‘leave your answer in its simplest form’. To simplify a fraction you need to divide the numerator and denominator by a common factor (a number that divides into both). If necessary you need to keep doing this until nothing else can divide into the numerator and denominator.
Let’s simplify 12/16.
Start by thinking of common factors of 12 and 16. You could start by dividing by 2 and then divide by 2 again. However, a quicker way is to spot that the highest common factor is 4. Using the highest common factor means you can get to the final answer in fewer steps.
Dividing 12 by four gives us 3, and dividing 16 by 4 gives us 4. So our answer is 3/4.
And there you go, 3/4 is 12/16 written in it’s simplest form.
You’ll be pleased to know that this is only the very beginning of what there is to know about fractions. There’s plenty more fun to be had from adding, subtracting, multiplying and dividing fractions to switching between fractions, percentages and decimals. Check out our resources page for more guides and questions on working with fractions.
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