Addition is the process of combining two or more numbers to find their total or sum. It is one of the basic arithmetic operations in math. Some of common properties of addition:
Let's discuss each property in detail.
Closure Property of Addition
According to closure property of addition, "adding two real numbers the result is always a real number."
For example, if we add 2 and √2, we will get 2 + √2, which is a real number as well.
Commutative Property of Addition
According to the Commutative Property of Addition, for any two real numbers p and q, their sum is always commutative, i.e. ,
a + b = b + c.
For example, if we add 2 and 3 or 3 and 2, in both cases we will get 5 as answer.
Associative property of Addition
According to Associative property of Addition, for three real numbers a, b, and c their sum in any order is equal, i.e.,
The sum of (a + b) + c = a + (b + c).
Identity Property of Addition
According to the Identity Property of Addition, for real numbers, we have an identity element in addition that always give the original number as a result of addition, i.e. the sum of any real number say p, and the identity element zero (0) is the number p.
a + 0 = a
Inverse Property of Addition
According to the Inverse Property of Addition, for real numbers, we have an inverse element of each element such that the addition of these two elements always gives the result to be zero. i.e.
a + (-a) = 0
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