103 LearnersLast updated on July 10th, 2025
Commutative Property of Addition
The commutative property of addition is a basic math rule. It states that changing the order of the numbers when adding will not change the result. In this article, we will explore the commutative property of addition with more examples.
What is the Commutative Property of Addition?
The commutative property of addition states that swapping the positions of numbers does not make any difference in the answer. The commutative property is applicable for addition and multiplication, but not for subtraction and division.
What is the Formula for the Commutative Property of Addition?
The formula for the commutative property of addition is a + b = b + a, where a and b can be any real numbers. Here, the rearrangement of the operands ‘a’ and ‘b’ will not change the sum of a and b. Let us explore some examples:
In the following example, we see that adding 4 apples to 2 apples or adding 2 apples to 4 apples will not make any difference, as the result is 6 apples. This explains how the commutative property of addition works.
In the following example, we can see the working of the commutative property of addition.
For example, 5 + 4= 9, in the image the number 4 is in blue color and 5 is in red color. When we observe the result of adding 4 and 5 or 5 and 4, we get the same answer, 9. Hence, we can prove that changing the order of the numbers in the addition process will not affect their sum.
Real-Life Applications of Commutative Property of Addition
Commutative property of addition is applicable to many daily life situations. It can be used in scenarios such as shopping, budgeting, cooking, keeping scores in games, and task planning.
Counting objects:
When counting objects, the order of adding doesn't affect the result. For example, if you have 5 black pens, 2 red pens, and 5 blue pens, to find the total number of pens, the order you add won't affect the result, that is, 5 + 5 + 2 = 5 + 2 + 5 = 2 + 5 + 5 = 12.
Planning For a Trip
When going for a trip, we usually count the clothes while packing. If you are packing 4 shirts and 6 trousers or 6 trousers and 4 shirts, the total count will be 10 items. This helps track the number of items quickly. The commutative property is also helpful in packing items.
Cost Calculation While Shopping:
While shopping, you can add your prices of items that you bought in any order, which does not affect the total price of items. For example, you bought a bag for $100 and a book for $30. If you calculate $100 + $30 or $30 + $100 to get the total cost, the total cost will still be $130. This shows the application of the commutative property in shopping.
Common Mistakes and How to Avoid Them in Commutative Property of Addition
Children might make mistakes while applying the rule of the commutative property of addition. They can also make errors while learning the concept. Let us highlight some mistakes made by children while applying the property to the problems.
Mistake 1
Not Applying Property to Large Numbers
Children might have a misconception that the commutative property is only applicable to single-digit numbers, but not for large numbers. For example, they should practice the property with large numbers, such as 321 + 468 = 468 + 321. The commutative property applies to larger numbers.
Mistake 2
Not Using the Property In Word Problems
In word problems, students sometimes face difficulty recognizing the commutative property. They might forget to use the property while solving word problems. For example, children may not recognize the concept in some word problems like “You have $10 and Ziya has $20” vs “Ziya has $20, and you have $10”. By practicing regularly with worksheets, children understand the concept of commutative problems.
Mistake 3
Misplacing the Numbers While Reordering
Children might mistakenly swap the positions of individual digits in a number instead of the entire number. For example, 12 + 34 = 34 + 21, which is not a correct way of applying the commutative property. Students should remember that the entire numbers should be swapped, like 12 + 34 = 34 + 12, but not the digits.
Mistake 4
Confusing Commutative with Associative
Children might confuse the commutative and associative properties because both involve changes in the number arrangement. For example, (2 + 3) + 4 = 2 + (3 + 4) is commutative. But this is an example of the associative property of addition. Children should be taught that the commutative property is about reordering and the associative property is about grouping the numbers.
Mistake 5
Misunderstanding the Role of Zero
Students sometimes think that zero cannot be added to a number, that is, it will change the number’s value. As the zero is the additive identity, that is, the sum of adding any number to 0 results in the number itself. For example, 0 + 3 = 3 + 0 = 3.
Solved Examples of Commutative Property of Addition
Problem 1
Check whether 230 + 340 = 340 + 230.
Yes, the sum of 230 and 340 is 570 in both cases.
Explanation
Given, 230 + 340 = 340 + 230. First, we will calculate 230 + 340, which is equal to 570, and then calculate 340 + 230, which is also equal to 570. Hence, 230 + 340 = 340 + 230.
Problem 2
If Ravi pays an amount of $40 for a shirt and an amount of $30 for a tie, does the order affect the total bill?
No, the order does not affect the total bill.
Explanation
Whether we add the cost of a shirt to the cost of a tie or vice versa, the total amount will be the same. Here, we can see how it will be the same: $40 + $30 = $70 and $30 + $40 = $70.
Problem 3
A juice contains 100ml of kiwi and 10ml of water. Is 100 + 10 equal to 10 + 100?
Yes, 100 + 10 = 10 + 100.
Explanation
When we add 100ml and 10ml, we get 110ml, and when we add 10ml and 100ml, we get 110ml. Hence, 100 + 10 = 10 + 100.
Problem 4
Reema studies mathematics for 20 minutes and science for 30 minutes. Will the total study time change if we reorder the schedule?
No, the total of studying will not be affected by changing the order of the subjects.
Explanation
The total time will remain the same because 20 minutes + 30 minutes = 50 minutes and 30 minutes + 20 minutes = 50 minutes.
Problem 5
Verify: 20 + 12 = 12 + 20.
Yes, 20 + 12 = 12 + 20.
Explanation
To check if 20 + 12 = 12 + 20, we first find the sum of 20 and 12
20 + 12 = 32
Finding the sum of 12 and 20, 12 + 20 = 32
So, 20 + 12 = 12 + 20
Hence, the order of the numbers does not affect their sum.
FAQs on Commutative Property of Addition
1.Does the commutative property apply to subtraction?
2.Why is the property called “commutative”?
3.Do negative numbers follow the commutative property of addition?
4.Give an example of the commutative property of addition.
5.Can fractions use the commutative property?
6.How can children in Vietnam use numbers in everyday life to understand Commutative Property of Addition ?
7.What are some fun ways kids in Vietnam can practice Commutative Property of Addition with numbers?
8.What role do numbers and Commutative Property of Addition play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve Commutative Property of Addition skills?
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
