Properties of Addition

The addition is a process of adding or summing up 2 or more integers to get the final value. The addition is one of the highly important and common operations in the fields of mathematics and statistics. The Plus (+) sign denotes the addition operation. The numbers that are to be added are referred to as addends. The resulting value of this summation step is called the sum. Any digit with any number of units can be added and summated. From fractional numbers to decimal values, any type of integer can be simplified using addition, regardless of the nature of its sign.

The List of 4 key Properties of Addition

Speaking of the properties of addition, there are 4 major classifications to this system.

1. Commutative Property

2. Associative Property

3. Distributive Property

4. Additive Identity

These properties will help us in defining the various conditions and norms to be followed while adding a set of numbers. The 4 mentioned properties of addition give an accurate closure to adding things. Note that there are separate mathematical properties for multiplication, subtraction, and division as well. The norms vary across each type of operation. Let us learn each property with brief details as follows.

The Commutative Property of Addition 

As per the Commutative Property of Addition, even if the order of adding 2 or more numbers vary, the results obtained will be the same. This is a property common to multiplication as well. This property can be explained easily in the form of A + B = B + A. let us consider an example for better understanding. 

• Take A as 2 and B as 3. (A = 2 and B = 3) 

• Add A and B. A +B which is 2 + 3 = 5

• Now, add B and A. B + A which is 3 + 2 = 5

• Hence the commutative law of addition is proved.

What does the Associative Property Mean?

The law of Associative Property of Addition means that when 3 different integers are added, the obtained result is not affected by the pattern of addition followed. The pattern will not influence the correct summation result. Again, let us have 3 integers X, Y and Z. As per the property, we have the following example based on X+(Y+Z) = (X+Y)+Z.

• Take A = 4, B = 6 and C = 8

• With A+(B+C), we have, 4 + (6 + 8) = 18. Consider this as the left-hand side (LHS)

• Moving to the RHS (Right-hand side), the solution is (A+B)+C, which is (4 + 6) + 8 = 18

• L.H.S = R.H.S (18 = 18)

• The associative property of addition is hence proved.

Learning the Distributive Property 

According to the Distributive Property of addition, the addition of 2 numbers when multiplied by another 3rd number will be equal to the sum the other two integers are multiplied with the 3rd number. This is represented as A × (B + C) = A × B + A × C. we have an example again for better learning. 

• Take A = 1, B = 2, and C = 3

• Now, pick the LHS - A × (B + C) = 1 × (2 + 3) = 5

• Then, the RHS - A × B + A × C = 1 × 2 + 1 × 3 = 5

• LHS = RHS (5 = 5)

• Hence the distributive property is proved

Defining the Additive Identity Property

On comparing the 4 properties of addition, the additive identity is quite simple. It states that any number,  there is a pre-existing unique real value, which by adding the value gives the same number. For instance, 0 is a real and unique number which when added to any integer gives the integer itself. Also, 1 reason why 0 is deemed to be the addition’s identity element. We can denote this as G + 0 = G or 0 + G = G.

• Take G as 4

• G + 0 = 5 + 0 = 5

• And, 0 + 5 = 5

• LHS = RHS (5 = 5)

• Thus, addition follows the additive identity property

Conclusion

The addition is the process of adding 2 or more numbers to get a final result. The 4 main properties of addition are commutative, associative, distributive, and additive identity.  Commutative refers that the result obtained from addition is still the same if the order changes. Associative property denotes that the pattern of summing up 3 numbers does not influence the result. The distributive property says that adding 2 numbers and multiplying with a 3rd number will have constant answers if the 2nd and 3rd numbers are multiplied and added by the 1st. Additive identity states that any number added to 0 gives the same integer as a result.

Properties of Addition

There are four properties of addition of whole numbers :

• Closure Property

• Commutative Property

• Associate Property

• Additive Property

Addition ” is one of the introductory computation operations in Mathematics. The addition is the process of adding effects together. To add the figures together, the sign “+” is used. The figures which we are going to add are called “ addends” and the result which we're going to gain is called “ sum”. The addition process involves two or further addends, which can be any number. Addends can be any figures similar to a positive integer, a negative integer, fragments and so on. The parcels of addition are used in numerous algebraic equations in order to reduce the complex expressions into a simpler form. These parcels are veritably helpful to the scholars as these parcels observe all kinds of figures.

• Multiplicative Inverse

A multiplicative antipode is a correlative. What's a correlative? A correlative is one of a brace of figures that, when multiplied with another number, equals the number 1. For illustration, if we have the number 7, the multiplicative antipode, or correlative, would be 1/7 because when you multiply 7 and 1/7 together, you get 1!