Factorising

Both answers are correct.  Don't fret over it   

I liked the way you asked your questions.   

You are here to learn not just to garnish answers from us.

We like that.

Thank you.     

Thanks Melody.

Definite yes to learning. I have no interest in just getting the answers right unless I understand how I got them and can get them again. It's sort of cheating otherwise.

I'm glad my answer was also correct but I still can't understand how their's was stating the HCF was 1/2 from 1/2 and 1/4 as obviously they both have 1/4 in them but only 1/2 has 1/2 so can't be common to both?

I'm completely home study relying entirely on publicly available resources on the net such as this so I'd really appreciate it if you could explain this to me as I have no tutor to ask.

Thanks

1/2x+1/4

Well, I have only ever thought of a HCF as being a whole number so to me the question is a bit strange.

I do not think that your answer is any less correct than theirs.

BUT

1/2 is bigger than 1/4  

Depending on the problem either could be the best way to go.

For nice presentation at the end of a question, your way is nicest.  You can also present it as an entire fraction if you want which often looks nice.      (2x+1)/4

BUT

when you are working on a problem it can be nice to have 1 as the coefficient of x.  So   1/2(x+1/2)

can also be very useful.

I really do not thing that there is a correct answer to your problem.  Although I will come back to my original assertion that  1/2 is bigger than 1/4

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