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.