How do you find the additive and multiplicative inverse of 1/3?

Question

14235 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-26T19:33:45

Additive inverse, #-1/3#
Multiplicative inverse, #3#

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 = 1/3#
It's additive inverse be #c#.

Then #1/3 + c = 0#

Now, adding #-1/3# to both sides,

#c = -1/3#.

Let the multiplicative inverse be #b#.

Then #a*b = 1#
#implies 1/3*b = 1#

Multiplying both sides with #3#

#b = 3#