Properties of Addition

Understanding the important properties of addition is quite simple. The term ‘addition’ involves adding up 2 different values to get a final entity. This is said to be the sum. Now, when there is a defined set of rule (s) on how to add 2 different things, then it is a property for addition. In the context of mathematics, addition and its properties involve suggesting different methods to add a given set of integers. Everybody uses addition in their day-to-day life and considering its significance, we are about to learn the characteristics and properties of addition with examples. 

A Few Basic things to Know about the 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 value, 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. 

FAQ (Frequently Asked Questions)

1. How to Remember the Commutative Property of Addition Easily?

As per general English, commute means to travel from 1 region to another. Put the same meaning in the place of numbers. When 2 integers are intermixed in their order of addition, still the answer will be the same. 3 +  4 is same as 4 + 3 (7 for both the conditions).

2. Among the 4 Properties of Addition, which Involves the Use of Multiplication Operation?

The Distributive Property of Addition involves multiplication operation among the rest of the laws. As per this condition, when the 1st two numbers are added and multiplied by a 3rd number then the answer will be the same even if the  1st number is multiplied with the 2nd and added with the multiplication of the 3rd. It is represented as A × (B + C) = A × B + A × C.

3. Considering a Number Line, in which Direction will Adding Numbers Take Place?

Expect for 0, any other number (s) that is being added on a number line will always shift to the right direction only. 

4. Define the Standard Closure Property of the Addition Operation?

According to the standard closure property of the addition operation, The addition of 2 or more numbers of whole digits will always result in a whole number only. That is Whole Number + Whole Number = Whole Number. Consider 2 number 4 and 2. Adding 2 + 4 or 4 + 2 will both give 6 as the result, which is also a whole number respectively. Note that the addition of 2 different values will always give a result which is a bigger whole number, except for 0, as the same number is the solution.

5. How are the Properties of Addition Used in Real-life Applications? Mention at Least 3. 

The 4 properties of addition play a significant role in various industries such as shopping, banking, placing food orders, literature and arts, construction, designing, online services and even for marking the birthday of someone.