Maths GCSE Revision - Lesson #8 – Adding and Subtracting Fractions
This lesson from the ‘Number’ section of GCSE Maths is all about Adding and Subtracting fractions, along with finding common denominators (transcript below video).
The first thing we are going to look at is Common Denominators. To find a common denominator between two fractions, you need to find the lowest common multiple (LCM) of the denominators in question. Let’s look at an example. Here we have to put these three fractions in ascending order. This will be much easier if we have a common denominator for all of our fractions.
Put these in ascending order: 2/3, 3/5, 1/4
The lowest common multiple of 3, 5 and 4 (our denominators) is 60. To get our new numerators, we have to consider how many times our current denominators go in to 60.
3 x 20 = 60
5 x 12 = 60
4 x 15 = 60
We need to multiply our current numerators by the same numbers, to get our new numerators.
2 x 20 = 40
3 x 12 = 36
1 x 15 = 15
Our fractions then become:
2/3 = 40/60
3/5 = 36/60
1/4 = 15/60
Now that our fractions all have a common denominator, it is much easier to put them in ascending order (with 1/4 being the smallest, and 2/3 being the largest). Be careful to write your final answer using the original fractions that you were given in the question (rather than the fractions with a common denominator).
To add fractions, you need to firstly convert any mixed numbers in to improper fractions. Secondly, you need to find common denominators between all of your fractions. Lastly, you can add together your numerators. Here’s an example:
1 and 1/7 + 2 and 1/2
Converting to improper fractions gives us:
8/7 + 5/2
The LCM of 7 and 2 is 14, which will be our common denominator. Using the method described above, we can convert our fractions to:
16/14 + 35/14 = 41/14
As you can see, once you have a common denominator, you can just add your numerators to get your final answer (keeping your denominator as 14).
Here is another example, involving the subtraction of fractions:
3 and 5/6 – 2 and 1/4.
First we convert to improper fractions:
23/6 – 9/4
Our common denominator of 6 and 4 will be 12. Giving us:
46/12 – 27/12 = 19/12
This fraction is in it’s simplest form, so is our final answer. We could also convert this to a mixed number, which would give us 1 and 7/12.
In this last section, we are going to look at a question from an example exam paper. We are going to answer this question using the methods we have covered previously.
2/7 + 1/5 = 10/35 + 7/35 = 17/35
The second part of the question involves division, which you can revise by looking at Lesson #7 in our Maths GCSE ‘Number’ series.
Thanks for watching, and if you have any questions about the topics talked about, or you are stuck on a particular concept, just get in touch and we will get back to you as soon as possible!