How do you find the additive and multiplicative inverse of -8?

1 Answer
Mar 26, 2017

Answer:

Additive inverse, #+8#
Multiplicative inverse, #-1/8#

Explanation:

For a number #a#, it's multiplicative inverse #b# is such that #a*b = 1# which is the multiplicative identity.

For a number #a#, it's additive inverse #c# would be such that # a + c = 0# where #0# is additive identity.

Thus, for #a = -8#
It's additive inverse be #c#.

Then #-8 + c = 0#

Now, adding #8# to both sides,

#c = 8#.

Let the multiplicative inverse be #b#.

Then #a*b = 1#
#implies -8*b = 1#

Multiplying both sides with #-1/8#

#b = -1/8#