The Collaborative International Dictionary
Not worth 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.
--Swift.
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.
Usage examples of "not worth a rap".
I want to make money, without which reputation is not worth a rap.