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The Collaborative International Dictionary
Not to care a rap

Rap \Rap\, n. [Perhaps contr. fr. raparee.] A popular name for any of the tokens that passed current for a half-penny in Ireland in the early part of the eighteenth century; any coin of trifling value.

Many counterfeits passed about under the name of raps.

Tie it [her money] up so tight that you can't touch a rap, save with her consent.
--Mrs. Alexander.

Not to care a rap, to care nothing.

Not worth a rap, worth nothing.