You clean fish. vs You clean a fish. Which is correct?
Fish is non-countable, and non-countable nouns don't have indefinite article a before themselves. But I saw a phrase like "clean a fish", which makes me confused.

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Since "fish" can be both plural and singular without changing form, "clean fish" means to clean multiple fish, while "clean a fish" means to clean a single fish.

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Yes that phrase means "clean a single fish". Where as "clean fish" could be any amount more than one.

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"Fish" can be singular (a fish), plural (10 fish) or uncountable (I eat fish). When it is uncountable, we mean it as food, ie. the flesh of a fish.  Since the spelling and pronunciation doesn't change, I can understand that this may be confusing for learners.