V- 아/어다가

V- 아/어다가 is a combination of 아- and –다가. It is a conjunction that is used to express an activity that occurs in two places or continues from one place to another, and expresses doing something as the* result/product of a previous action after the previous action....

For example:
햄버거 가게에서 햄버거를 사서 그걸 (= 산 햄버거)집에서 먹었어요.
I bought a hamburger at the hamburger shop, and then I ate it(a hamburger I bought) at home.

햄버거 사다가 (그걸= 산 햄버거) 먹었어요.
I bought a hamburger and ate it.

Since –아다가 is used, the listener understands that the place is where the hamburger was bought and the place where it was eaten are different even if they are not mentioned.

However, this is not the case with -아 and –아서. These two conjunctions indicate a sequence of actions. If the place of these actions is not mentioned, the listener will not know if the actions occurred in one place or not.

뒷뜰에서 꽃병에 꽃을 꽂아서/꽂아 그 꽃병(=꽂은 꽃병)을 내방 책상위에 놓았다
I put the flowers from the backyard into a flower vase, and then I put the vase on my desk in my room.

꽃병에 꽃을 꽂아서/꽂아 책상위에 놓았다
I put the flowers in a vase and put (it) on top of the desk.

In this case, the listener is not be sure where the activities of "putting the flowers in a vase" and "putting the vase on a desk" took place. All he knows is that one took place before the other.

If the listener understand an activity that occurs in two places , 아/어, 아/어서, or -아/어 가지고 is used instead of -아/어다가... 아/어다 is short for 아/어다가

도서관에서 책을 빌려/빌려서/빌려 가지고/ 빌려다/ 빌려다가 (빌린 책을) 읽으세요..