Please throw out the half-eaten banana. 먹다 만 바나나를(는) 버려 주세요. ==> GOOD I ate the half-cooked noodles. 요리하다 만 국수를 먹었어요. ==> ok but better "덜 익은(삶은) 국수를 먹었어요" (고기, 과일 등) 음식에는 익다 란 표현을 많이 씁니다. I ate the (fully) cooked noodles. ==> (완전히) 삶은(익은) 국수를 먹었어요. or 요리한 국수를 먹었어요. is ok too. 요리했다 만 국수를 먹었어요. ==> does not make sense. 만 means 그만 (멈춘)

This is the link of the question, http://www.italki.com/question/198848 // if somebody stop/quit something, he ought to do something. So, in "stem of verb-다가 말다", the verb ought to/can be an action verb, as you know. for instance, "책을 보-다(가) 말다 ", "그녀는 울-다(가) 말고, 갑자기 미친 듯이 웃기 시작했다". In addition, the connective ending "-다가" has three different meanings according to the context. // By the way, Have you completely understand the difference of between "왔다가 갔다" and "오다가 갔다"? A hint is the "perfect tense", Korean language doesn't have the perfect tense form of a verb, though.

Sometimes there are two different concepts I am trying to understand and I miss the relevance of a previous explanation. 배울 아주 많은 것들이 있어요. 그래서 쉽게 혼란돼요. 넌 질문에 링크가 있나요?

Lately, In a certain question of someone, you asked me a similar thing like this when I answered that "왔다가 갔다". At that time, I thought you could have understood the difference of meanings between "왔-다가 갔다" and "오-다가 갔다".

You're right, I didn't think about it logically at all. I read this: http://www.koreangrammaticalforms.com/entry.php?eid=0000001478 - and thought, hey, I wonder if I can put that together with 말다, without even really thinking it through.