How do you say 一边......一边...... in English?
我一边看电视，一边吃东西。
I am eating while watching TV. is it?

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You can say that or you can say I am watching telly and eating dinner.

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Like you said: I´m eating while watching TV.
Another example is a little bit different:
一边吃一边说: ... half chewing, half speaking.... (but at the same time).

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while I was doing ***** I was also doing ******
I am doing **** at the same time I'm doing *****

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Doing two things at the same time, Or, While I was eating I was watching TV. As Beth said