I was only listening to the radio with half an ear.

我只是顺便听着收音机.

《简明英汉词典》

You can't fly with half a wing; you can't hear with half an ear.

你不能只用一只翅膀飞, 你不能只用一只耳朵听(不专心听).

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I was only listening to the radio with half an ear, while preparing some food.

我正在做吃的, 没太留心听收音机.

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