not give a monkey's

:  to make a present of

:  to grant or bestow by formal action

:  to accord or yield to another

:  capacity or tendency to yield to force or strain :  flexibility

:  the ability of a material to bend or stretch

:  a nonhuman primate mammal with the exception usually of the lemurs and tarsiers

:  any of the smaller longer-tailed catarrhine or platyrrhine primates as contrasted with the apes

:  a person resembling a monkey

:  mimic, mock

:  to act in a grotesque or mischievous manner

:  fool, trifle