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Properties of Addition
The properties of addition are the set of rules that are used while adding two or more numbers. These properties are applicable to integers, fractions, decimals, and algebraic expressions. Using the properties of addition makes calculation easier and helps to solve complex problems in Math. Let us learn more about the properties of addition in this article.
1.  What are the Properties of Addition? 
2.  Commutative Property of Addition 
3.  Associative Property of Addition 
4.  Identity Property of Addition 
5.  FAQs on Properties of Addition 
What are the Properties of Addition?
The properties of addition are useful when we add 2 or more values to get their sum. As we add the given values, we come across different rules that make the calculation easier. These rules are known as the properties of addition. Let us learn about the various types of properties that are used in addition.
Commutative Property of Addition
The commutative property of addition states that even when the order of the addends is changed, the sum remains the same. This means that changing the order of the addends does not change the value of the sum. For example, 12 + 7 = 19, and 7 + 12 = 19. Here, it can be seen that even after we changed the order of the addends, 12 and 7, the sum remains to be 19.
Associative Property of Addition
The associative property of addition states that the manner in which three or more numbers are grouped does not change the sum. In other words, while adding a given set of numbers, we can group them in any combination, the sum will remain the same. For example, if we add 4 + (8 + 9) we get the sum as 21. Now, if we group the numbers as (4 + 8) + 9, even then we get the sum as 21.
Identity Property of Addition
The identity property of addition states that when 0 is added to any number, the sum is the number itself. In other words, the addend does not change its identity when it is added to zero. For example, 27 + 0 = 27; or 0 + 76 = 76.
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Examples of Properties of Addition

Example 1: Fill in the missing number using the properties of addition: 34 + (21 + 45) = (34 + 21) + __
Solution: Using the associative property of addition, we can conclude that the missing number is 45 because according to this property. when we add a set of numbers, their sum remains the same even if they are grouped in any combination.

Example 2: Choose the correct number to fill in the missing number: 42765 + _ = 42765
a.) 1
b.) 2
c.) 0
Solution: Using the identity property of addition, we can say that the missing number is 0 because when a number is added to zero, the sum is the number itself. Therefore, the correct option is (c) 0

Example 3: Fill in the missing number using the properties of addition: 23876 + 1256 + 98734 = 98734 + 1256 + _____
Solution: According to the commutative property of addition, the missing number is 23876, because we know that even if the order of the addends is changed, their sum remains the same.
FAQs on Properties of Addition
What are the Properties of Addition?
The properties of addition are a certain set of rules that are used while adding numbers. These rules are known as the properties of addition. There are three basic properties of addition that are used while adding numbers  the Associative property, the Commutative property, and the Identity property of addition.
How to Use the Properties of Addition?
The properties of addition can be used while adding integers, fractions, or decimals. For example, the commutative property of addition can help us understand that changing the order of the addends does not change the sum, therefore, numbers can be added in any order. Another example is that of the identity property of addition which tells us that any number added to zero will result in the number itself.
How many Properties of Addition are there?
There are three main properties of addition  the Associative property, the Commutative property, and the Identity property of addition. Each property has its own features which help in making calculations easier.
What is the Difference between the Commutative and Associative Properties of Addition?
The Commutative property of addition says that the order in which the addends are added does not have an effect on the sum of the addends. For example, 43 + 67 = 67 + 43 = 110. The Associative property of addition says that the way in which numbers are grouped does not change their sum. For example, 54 + (89 + 10) = (54 + 89) + 10 = 153
Give some Examples of the Properties of Addition.
There can be many examples of the different properties of addition. For example, the associative property of addition can be seen in 3 + (4 + 7) = (3 + 4) + 7 = 14; where the grouping of the numbers does not change the sum. The commutative property of addition can be seen in 45 + 20 = 20 + 45 = 6, where the order of the addends does not affect the sum.
What is the Zero Property of Addition?
The zero property of addition is also known as the identity property of addition. According to this property, if any number is added to 0, the sum is the number itself. For example, 7845 + 0 = 7845.
What is the Distributive Property of Addition?
The distributive property is a property of multiplication that is used in addition and subtraction. It states that when we multiply the sum of two or more addends by a number, it will give the same result if we multiply each addend individually by the number given outside the brackets. The distributive property is applied to addition when the sum of numbers is multiplied by a common number. For example, if we need to solve 6(4 + 3), this can be solved as 6 × 7 = 42, where we first solved the expression inside the bracket and then multiplied it with the number outside it. Now, if we apply the distributive law, we can multiply 6 with 4 and 3 individually and then add their products together. This means, 6(4 + 3) = (6 × 4) + (6 × 3) = 24 + 18 = 42. This is called the distributive property.
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