Properties of addition define in what ways we can add the given integers. “Addition” is one of the basic arithmetic operations in Mathematics. The addition is the process of adding things together. To add the numbers together, a sign “+” is used. The numbers which are going to add is called “addends” and the result which we are going to obtain is called “sum”. Addition process involves two or more addends which can be any digit number. Addends can be any numbers such as positive integer, a negative integer, fractions and so on.
Also read: Properties of Multiplication
What are the four Properties of Addition?
Properties of addition are defined for the various conditions and rules of addition. These properties also indicate the closure property of the addition. In fact, like for addition, properties for subtraction, multiplication and division are also defined in Mathematics. But for each operation, the properties might vary. There are basically four Maths properties defined for addition.
Commutative Property of Addition
According to this property, when two numbers or integers are added, the sum remains the same even if we change the order of numbers/integers. This property is also applicable in the case of multiplication. It can be represented as;
- A + B = B + A
Let us take A = 10 and B = 5
10 + 5 = 5 + 10
15 = 15
Associative Property of Addition
As per this property or law, when we add three numbers, the association of numbers in a different pattern does not change the result. We can represent this property as;
- A+(B+C) = (A+B)+C
Let us take A = 2, B = 4 and C = 6
L.H.S =A+(B+C) = 2 + (4 + 6)
R.H.S = (A+B)+C = (2 + 4) + 6
L.H.S = R.H.S
12 = 12
Distributive Property of Addition
This property is completely different from Commutative and Associative property. In this case, the sum of two numbers 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
Here A is the monomial factor and (B+C) is the binomial factor.
Let us take A = 2, B = 3 and C = 5
L.H.S =A × (B + C)= 2 × (3+5)
= 2 × 8
R.H.S = A × B + A × C = 2 × 3 + 2 × 5
L.H.S = R.H.S
16 = 16
Additive Identity Property of Addition
This property states, for every number, there is a unique real number, which when added to the number gives the number itself. Zero is the unique real number, which is added to the number to generate the number itself. Hence, zero is called here the identity element of addition.
- A + 0 = A or 0 + A = A
9 + 0 = 9 (or)
0 + 9 = 9
Some More Properties of Addition
Property of Opposites: In this case, if A is a real number then there exist a unique number -A such that;
- A + (-A) = 0 or (-A) + A = 0
Since the result of the addition of two numbers is zero, therefore they both are called additive inverses.
Sum of Opposite of Numbers: Let the two numbers are A and B, then their opposites will be -A and -B. Then according to the property;
- -(A + B) = (-A) + (-B)
Example 1: Prove: – (3+7) = (-3)+(-7)
-(10) = -3-7
-10 = -10
L.H.S = R.H.S
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