How do you find the additive and multiplicative inverse of -1 1/5?

1 Answer
Apr 9, 2017

Answer:

Additive inverse: #11/5#
Multiplicative inverse: #-5/11#

Explanation:

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#.