How do you find the additive and multiplicative inverse of 2.5?

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Answer 1 · 2017-03-26T19:46:50

Additive inverse, #- 5/2# or #-2.5#
Multiplicative inverse, #2/5# or #0.4#

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 = 2.5 = 5/2#
It's additive inverse be #c#.

Then #5/2 + c = 0#

Now, adding #-5/2# to both sides,

#c = -5/2#.

Let the multiplicative inverse be #b#.

Then #a*b = 1#
#implies 5/2*b = 1#

Multiplying both sides with #2/5#

#b = 2/5#