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# Algebraic fraction - making a single fraction watch

1. Hi, I have recently started revision for my GCSE exams next year and I found this question, I understand parts of the answer, however am confused as to why you do 3 x m+3n and then 3 x (m+3n) to make the denominator of the fraction. If anyone could explain why this is so I can understand this question and other similar ones it would be much appreciated.
Many Thanks, Jonathon
2. (Original post by Jrmcooper)
Hi, I have recently started revision for my GCSE exams next year and I found this question, I understand parts of the answer, however am confused as to why you do 3 x m+3n and then 3 x (m+3n) to make the denominator of the fraction. If anyone could explain why this is so I can understand this question and other similar ones it would be much appreciated.
Many Thanks, Jonathon
To add the two fractions we need to put them over a common denominator.

From the first fraction, "3" must be a factor of the common denominator.

From the second fraction, "m+3n" must be a factor of the common denominator.

So, our common denominator wants to be 3(m+3n)

Hence we multiply the top and bottom of the first fraction by "m+3n", and the top and bottom of the second fraction by "3"

3. (Original post by Jrmcooper)
Hi, I have recently started revision for my GCSE exams next year and I found this question, I understand parts of the answer, however am confused as to why you do 3 x m+3n and then 3 x (m+3n) to make the denominator of the fraction. If anyone could explain why this is so I can understand this question and other similar ones it would be much appreciated.
Many Thanks, Jonathon
How do you do ?
4. Firstly, just in case there is any confusion, when you say "am confused as to why you do 3 x m+3n and then 3 x (m+3n)", you should realise that both of these expressions are the same. The m+3n in the first expression should have a bracket around it too.

As to why we do it this way - I am sure that you know that when you add or subtract fractions, they have to have a common denominator. For example, if we have to add 1/2 and 2/3, it is not easy because they have different denomonators - one is one lot of a half, and the other is two lots of a third. But if we multiply the top and bottom of the first fraction by the denominator of the second fraction, we have 3/6 (three lots of one sixth), and then multiply the top and bottom of the other fraction by the denominator of the first, we have 4/6 (four lots of one sixth). So altogether, we have 3+4 = 7 lots of one sixth, or 7/6.

This is probably very easy for you to understand, and I am sure that if I asked you to add 1/2 and 2/3, you would do this without thinking. The important thing to realise is that what is going on in your question is exactly the same. It may look more complicated because of the algebraic expressions, but the idea is the same.

[There isn't always a need to do it exactly this way - sometimes there are shortcuts you can take - but this is guarenteed to always work.]
5. Thank you to everyone for your replies, I have now gone back over the question using your advice and it’s much easier to understand 👍

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Updated: July 23, 2017
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