How do you find the additive and multiplicative inverse of -5/8?

Question

13279 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-26T19:38:42

Additive inverse, #5/8#
Multiplicative inverse, #-8/5#

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 = -5/8#
It's additive inverse be #c#.

Then #-5/8 + c = 0#

Now, adding #5/8# to both sides,

#c = 5/8#.

Let the multiplicative inverse be #b#.

Then #a*b = 1#
#implies -5/8*b = 1#

Multiplying both sides with #-8/5#

#b = -8/5#