v. phr. , informal To have any interest or liking; care. Used also with other words in the place of "hang", such as "damn", "rap", "straw"; usually used in the negative. You can quit helping me if you want to. I don't give a hang. Some people don't care a rap about sports. Bruce never goes to the dances; he does not care a straw about dancing.
GIVE A HANG
Meaning of GIVE A HANG in English
American idioms English vocabulary. Английский словарь американских идиом. 2012