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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