The identity element #o# for a set and a binary operation is the element such that #o@a=a@o=o# for all #a# in the set, where #@# is the binary operator.
The inverse #b# of a number #a# under a binary operator #@# is the number such that #a@b=b@a=o#, where #o# is the identity element.
The additive inverse for a number #a# is a number #b# such that #a+b=b+a=0# (since #0# is the identity element for addition under the reals).
The multiplicative inverse for a number #a# is a number #b# such that #a*b=b*a=1# (since #1# is the identity element for addition under the reals).
The additive inverse of the number #-11/5# is the number #b# such that #b+(-11/5)=0#. Add #11/5# to both sides to get #b=11/5#.
The multiplicative inverse of the number #-11/5# is the number #b# such that #b*(-11/5)=1#. Multiply #-5/11# to both sides to get #b=-5/11#.
