simplifying vectors ???????????

how do you simplify vectors?
i know how to expand them but i do not understand when people get 4/3 b for instance.
can someone please help me understand why AC= 3/2 OA?
1) OA= a-2b
AC= 2b+(a-b)=(1/2a-4b)
2) Which is then simplified as 3/2a-3b=3/2(a-2b) This is what I do not understand. Where did the 3/2a and -3b come from and the brackets???
3)In this question I would have to make sure that AC is a scalar multiple of OA, and this is what the answer is: AC= 3/2 OA
I do not understand how this was achieved

I would be really grateful if someone explained this pleasseeeeeee

Hi! I think I could help you. Have you got any diagram that I can use to help you better.?

I can see where you are confused. When simplifying it down, lets use a as the example. You have 1/2 a and a and you need to add that to simplify it down in to one. As half of a is seen as 1/2, then whole a is seen as 2/2, so when adding these two you would get 3/2 a. If you have a fraction of the vector when simplifiying them down try see them all in fractions if you kind of know what I mean. I feel this is where you got stuck on this question with not being able to simplify the a and b down and the last part you will be able to understand as it is simply just factorising out the 3/2. I hope this helps sorry if it didn't I'm not great at explaining things haha

Hi. Hope this is helpful, as I have gone through and tried to recreate what has happened. If you are still confused let me know.