Q: I often find myself engaged in conversations in public places and others come up to talk with me. I don’t know how to break away from one conversation to just acknowledge a comment from those who come up to me without being rude to the person I am speaking with and the person in waiting. I want to be proper without being rude.
A: Yes, this is a common situation that always feels awkward! The person doing the interrupting just thinks he is being friendly, and doesn’t realize that he is putting you on the spot.
You can always simply say to the person you are with and loud enough for the interrupting party to hear, “excuse me for one moment,” or “pardon me for just a quick moment”. This way you can acknowledge the new person and the fact that you are engaged in a conversation that is not yet finished. Say a quick “Hello, I’ll catch up with you later,” and get back to your conversation.
Sometimes, when interrupted, it is possible that you can handle the situation non-verbally, making quick eye contact with the interrupter and giving a little wave or sign to acknowledge them, and then try to have a conversation with them later.