Annoying children with black rodents (5)

I believe the answer is:

brats

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'annoying children' is the definition.
'brats' can be an answer for 'children' (brat is a kind of child). I'm not sure about the 'annoying' bit.

'with black rodents' is the wordplay.
'with' means one lot of letters go next to another.
'black' becomes 'b' (as in pencil classifications).
'rodents' becomes 'rats' (rat is a kind of rodent).
'b' next to 'rats' is 'BRATS'.

Can you help me to learn more?

(Another definition for brats that I've seen is " naughty kids".)

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