# Inverse Property of Addition

**Inverse property of addition**:

`huge color(purple)(a+(-a)=(-a)+a=0) `

`-a` is called the **additive inverse** of `a`.

Inverse property is true for any real number `a`.

Notice, that we wrote, that `a+(-a)=(-a)+a`. This is true, according to the commutative property of addition.

**Example 1**. Additive inverse of `5/3` is `-5/3`, because `5/3+(-5/3)=0`.

**Example 2**. Additive inverse of `-sqrt(2)` is `sqrt(2)`, because `(-sqrt(2))+sqrt(2)=0`.

**Example 3**. `2.57+(-2.57)=(-2.57)+2.57=0`.

**Conclusion**. Additive inverse of the number (`a`) is a number, that has the same value as `a`, but different sign, i.e. `-a`.