The Inverse Properties


Additive Inverse Property

 (or negative)
 

Inverse Property for Addition:

a + (-a) = 0   and     –a + a = 0

Additive inverses are called opposites.


When you add a number to its additive inverse, the result is 0.

Other terms that are synonymous with additive inverse are negative and opposite.

Example:   Write the opposite (or additive inverse) of -3.


                      The opposite of -3 is 3, since -3 + 3 = 0.

 

Example:      Write the opposite (or additive inverse) of 1/5.

                      The opposite of 1/5 is -1/5, since 1/5 + (-1/5) = 0.



Multiplicative Inverse Property
(or reciprocal)

Inverse Property for Multiplication:

Multiplicative inverses are called reciprocals.



When you multiply a number by its multiplicative inverse the result is 1.

A multiplicative inverse or reciprocal of a real number a (except 0) is found by “flipping” a upside down.

The numerator of a becomes the denominator of the reciprocal of a and the denominator of a becomes the numerator of the reciprocal



Example: Write the reciprocal (or multiplicative inverse) of -3.



The reciprocal of -3 is -1/3,      since -3(-1/3) = 1.
 


Example : Write the reciprocal (or multiplicative inverse) of 1/5.



The reciprocal of 1/5 is 5,       since 5(1/5) = 1.