The addition is the basic arithmetic operation in mathematics. It adds two or more numbers together. The properties of addition define the way of adding two or more numbers. It defines the various rules and condition for addition. In this section, we will learn four basic properties of addition along with other properties.

The four basic addition properties are:

• Commutative Property
• Associative Property
• Distributive Property
• Identity Property

### Commutative Property

The commutative property states that the order of addends does not affect the result when we add two numbers. It allows us to add numbers in any order.

a+b=b+a

For example, if we add 45 and 23 or 23 and 45 both give the same result, i.e.68.

45+23=23+45=68

### Associative Property

The associative property states that if we change the group of addends, it does not affect the addition.

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

For example:

(5+8)+3=5+(8+3)=16

### Distributive Property

The distributive property is different from the other two. The property states that if the sum of two numbers is multiplied by the third number is equal to the sum when each of the two numbers is multiplied to the third number.

a×(b+c)=a×b+a×c

For example:

5×(6+3)=5×6+5×3=45

### Identity Property

The identity property states that add any number to 0, the sum is always that number. Zero is known as an additive identity.

a+0=0+a=a

For example:

6+0=0+6=6

Let's see some other properties of addition.

### Closure Property

The closure property states that if a and b are two whole numbers then the sum two numbers will be a whole number.

a+b=c

Where a, b, and c are whole numbers.

For example:

6+9=15

### Property of Opposites

The opposites property states that the sum of a real number a, and its opposite real number -a is always 0. It is known as additive inverse. In other words, for any real number a, there exist a unique real number -a such that:

a+(-a)=0 or (-a)+a=0

For example:

9+(-9)=0 or (-9)+9=0
Or
9-9=0 or-9+9=0

### Property of Opposite of a Sum

It states that the opposite of the sum of two whole numbers is equal to the sum of opposites whole numbers.

Suppose, a and b are two whole numbers, and their opposites are -a and -b, respectively then according to the above statement:

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

For example:

-(7+2)=(-7)+(-2)
Or
-(9)=-7-2
Or
-9=-9

### Successor Property

The successor property states that we get the successor of the number if we add 1 to the sum of a number. Suppose, a is any whole number then:

a+1=(a+1)

Where (a+1) is the successor of a.

For example:

38+1=39

It means, 39 is the successor of 38.