Maths GCSE Revision - Lesson #7 – Multiplying and Dividing Fractions
This lesson from the ‘Number’ section of GCSE Maths is all about Multiplying and Dividing Fractions (transcript below video).
First we are looking at multiplying fractions together. To do this, we just need to multiply the top and bottom numbers together. This will then give you your new numerator and denominator. In this example (4/11 x 3/4), we need to multiply our numerators together (4 x 3 = 12), and multiply our denominators together (11 x 4 = 44). We now have a fraction of 12/44. Lastly, we have to simplify this fraction. We can divide both 12 and 44 by 4, leading to a new fraction of 3/11, which is our final answer.
Let’s have a look at dividing fractions now. The method is very similar to multiplying fractions, with an extra step at the start. Here we have, 4/5 divided by 2/7. The first step is to flip the second fraction (2/7 in our example, giving us 7/2). We can now multiply our two fractions together (4/5 x 7/2), using the same method as before.
4/5 x 7/2 = 28/10 = 14/5
We could also convert our final answer, 14/5, to a mixed number. We have looked at how to do this in a previous lesson, and using that method we get an answer of 2 and 4/5.
Now we’re going to look at an example exam question: Work out 2/3 divided by 7/9, giving your answer in it’s simplest form. This is typical of the types of questions you might get on fractions in an exam. As before, the first step is to flip the second fraction, and change the division sign to a multiplication sign.
This will lead to: 2/3 x 9/7 = 18/21.
To simplify our fraction, we can divide our numerator and denominator both by 3. Our final answer then becomes 6/7.
Before we finish, we’re going to look at one last exam question on fractions: 1 and 2/3 divided by 3/4.
Firstly, we need to convert our mixed number to an improper fraction (this method has been covered in a previous lesson). Following this method, our mixed number can be written as 5/3 (giving us 5/3 divided by 3/4). Now we must flip our second fraction, as before, leading to 5/3 x 4/3 = 20/9. This fraction is already in it’s simplest form, as 20 and 9 do not have any common factors other than 1, so we can write 20/9 as our final answer.
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