Chatting away is like waffling on (British slang) or yammering on (American slang). Those are probably not helpful to you, but they're a way to vary the language you use. Other words are 'babbling' or "nattering"- again, unless you know the meaning these alternative words are probably not helping you. Basically, "chatting away" is just a way of saying talking, but it kind of suggests excitement or even being carefree, and if you're chatting away, you're probably not talking about anything serious it's likely to be small talk or fairly light hearted. Use "chatting away" like "We were chatting away for what seemed like hours" or "The bell rang, but they just continued chatting away, unaware of the fact that the teacher was staring right at them". Therefore, if you're "chatting away" you're immersed in conversation, but it's not likely to be a serious or sad topic. It's kind of hard to explain but I hope this helped.

Often, it will be used to indicate someone is "casually talking without paying attention to what is going on around them." It is often used as mild to moderate criticism. Example: "She was just chatting away while everyone else was busy working." This isn't a synonym for "chatting away", but to describe the person doing it, you could use the word "oblivious."

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