Properties of Addition

There is a unique real number $0$ such that for every real number $a$ ,

$a+0=a$ and $0+a=a$

Zero is called the identity element of addition.

For all real numbers $a\text{and}b$ ,

$a+b=b+a$

The order in which you add two numbers does not change the result.

For all real numbers $a,b,\text{and}c$ ,

$\left(a+b\right)+c=a+\left(b+c\right)$

When you add three real numbers, the grouping (or association) of the numbers does not change the result.

For all real number $a$ , there is a unique real number $-a$ such that

$a+\left(-a\right)=0$ and $\left(-a\right)+a=0$

A number and its opposite are called additive inverses of each other because their sum is zero.

For all real numbers $a\text{and}b$ ,

$-\left(a+b\right)=\left(-a\right)+\left(-b\right)$

The opposite of a sum of real numbers is equal to the sum of the opposites.