Four Key Properties to Consider in Properties of Addition with Examples

To know the significant properties of addition is not a daunting task. Once you are fully aware of the formula and basics of the properties of addition, then there is no point in not understanding this. When this about knows the ‘addition’, this is very simple for everyone to understand. The term ‘addition’ mainly involves only adding up two different values to get the concluding entity. Now, adding two values is the basic factor, but you can add more than two values. It is known as the ‘sum’.

Now, you can understand that here is the defined rule on the right way to add two different things, called property for addition. If you consider this from a mathematical perspective, you will know that addiction and its properties include recommending various methods for adding a particular set of numbers. We all use addition in our daily lives rather addition or sum is one of the major aspects of our routine. This is why; you cannot ignore its significance. Being fully aware of the additions and sums is important, and you need to know the properties and characterise of addition with instances.

Which are the basic facts about addition?

To get the final value, you need to add two or more numbers, which is the procedure of addition. In the field of statics and mathematics, addition plays an important role. You need to be completely aware of the formula of addition to getting your final value of numbers. The plus symbol (+) signifies an addition operation. Then the numerical get added as are considered as the addends.

To know the subsequent value, when you go through the summation step, this is called sum. Any number or digit can be summated and added. Whether this is a fractional number or a decimal value, it can be easily simplified using the process of addition.

The 4 major key Properties of Addition

When you want to know about the properties of addition, you will have to learn that there are four major classifications of a system.

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

Brief about Additive Identity

A lot of people want to know why are addition properties important. But the significance of sum is very much important, and knowing the formula is also imperative. A comparison of the four properties of addition and the additive identity is very simple. This denotes the fact that in any number, there is a pre-existing unique real value that by adding the value gives the same number.

For example, 0 is a unique and real number that gives the integer when added to an integer. You can denote this as X + 0 = X or 0 + X = X.

Take X as 4

X + 0 = 5 + 0 = 5

And, 0 + 5 = 5

RHS= LHS (5 = 5)

Consequently, addition follows the additive identity property.

Knowing about Commutative Property of Addition

Considering the formula of the commutative property of addition and the right order to add two or more statistics can vary, the results obtain absolutely the same. It is known as a property that is common to the formula of multiplication too. This specific property is easily explained in a certain form of X + Y = Y + X. For your better understanding, here is a simple example to consider.

Take X as a representative of 2 and Y as a representative of 3; (X = 2 and Y = 3)

Now, you will have to add X and Y. X +Y that is 2 + 3 = 5

Here, add Y and X. Y + X that is 3 + 2 = 5

Here is the proof of the commutative law of addition.

Learn the Distributive Property

As per the distributive property formula, the addition of two specific numbers, when these get multiplied by another 3rd number, comes as an equal number to the sum of the other two numbers are multiplied with the 3rd number. It is represented as A × (B + C) = A × B + A × C. here is an instance for better learning.

Take A = 1, B = 2, and C = 3

Now, you will have to pick the LHS – A × (B + C) = 1 × (2 + 3) = 5

After that, the RHS – A × B + A × C = 1 × 2 + 1 × 3 = 5

LHS = RHS (5 = 5)

Therefore, the theory of distributive property is proved.

What do you understand by Associative Property Mean?

The associative Property of Addition is a bit different from the other two formulas. Here, when you add three integers, the obtained outcome will not be affected by a specific pattern of the addition, which has been followed. Eventually, the ultimate pattern is not going to affect the summation result overall.

Now, for your better understanding, you will need to know a simple equation.

Again, take three integers, X, Y and Z. So, an instance on X+(Y+Z) = (X+Y) +Z.

Take A = 4, B = 6 and C = 8

Along with A+ (B+C), you need to take, 4 + (6 + 8) = 18. Now, you can simply consider the formula as LHS (left-hand side)

When you move to Right Hand Side (RHS), then you will get the solution to be (A+B) +C that is (4 + 6) + 8 = 18

L.H.S = R.H.S (18 = 18)

Here is the proof of the associative property of addition.


To get a final result of two numbers, you will have to ensure that you add two numbers. The main four properties of addition to be like: associative, additive, distributive, and commutative identity. Once you are fully aware of the four different formulas, you will not have to face any sort of difficulty in solving the issue at all. You just need to ensure that you keep the formulas in mind.

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