see under not give a damn.

Also, not give a fig or hang or hoot or rap or shit . Not care about, be indifferent to, as in I don't give a damn about him, or She doesn't give a fig if he comes or not. The nouns in all these terms signify something totally worthless. Although probably in oral use for much longer, damn is first recorded in this negative form in the late 1700s and the worthless item it is used to denigrate is a curse. Fig has denoted something small and worthless since about 1400, and hang since the mid-1800s; hoot has been used for the smallest particle since the later 1800s; rap, also for the smallest particle, since the first half of the 1800s, and shit, for excrement, since about 1920. All but the first of these terms are colloquial and the last (using shit) is vulgar.

Also, not worth a plugged nickel or red cent or bean or hill of beans or fig or straw or tinker's damn . Worthless, as in That car isn't worth a damn, or My new tennis racket is not worth a plugged nickel. As for the nouns here, a damn or curse is clearly of no great value (also see not give a damn); a plugged nickel in the 1800s referred to a debased five-cent coin; a cent denotes the smallest American coin, which was red when made of pure copper (1800s); a bean has been considered trivial or worthless since the late 1300s (Chaucer so used it), whereas hill of beans alludes to a planting method whereby four or five beans are put in a mound (and still are worthless); and both fig and straw have been items of no worth since about 1400. A tinker's dam, first recorded in 1877, was a wall of dough raised around a spot where a metal pipe is being repaired so as to hold solder in place until it hardens, whereupon the dam is discarded. However, tinker's damn was first recorded in 1839 and probably was merely an intensification of "not worth a damn," rather than having anything to do with the dam.