Properties of Addition

The following are the properties of addition for real numbers. Some textbooks list just a few of them, others list them all. They may have slightly different names in your textbook.

PROPERTIES OF ADDITION
Identity Property

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.

Commutative Property

For all real numbers aandb ,

a+b=b+a

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

Associative Property

For all real numbers a,b,andc ,

( a+b )+c=a+( b+c )

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

Property of Opposites

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

a+( a )=0 and ( a )+a=0

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

Property of Opposite of a Sum

For all real numbers aandb ,

( a+b )=( a )+( b )

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