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 a and b, 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, and c, (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 a and b, –(a + b) = (–a) + (–b) The opposite of a sum of real numbers is equal to the sum of the opposites. 