1148 LearnersLast updated on June 6th, 2025
Commutative Property
Different properties are applied to arithmetic operations, such as the commutative, associative, distributive, and identity. The commutative property can be applied to arithmetic operations like multiplication and addition. In this topic, we will learn more about the commutative property.
What is the Commutative Property?
The commutative property is a basic math rule, it states that when adding or multiplying any numbers, the order of the numbers doesn’t affect the result.
That is, a × b = b × a and a + b = b + a, so the order of the operands does not impact the result in addition and multiplication. For example, 5 + 7 = 7 + 5 = 12.
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Difference Between Commutative Property and Associative Property
Commutative and associative properties are the two basic math rules. Now, let’s learn how the commutative and associative properties are different from each other.
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What is the Formula for the Commutative Property?
The commutative property is applicable for both addition and multiplication, which means the order of the values in the addition and multiplication does not affect the result. For the two variables A and B, the formula for the commutative property is
- A + B = B + A
- A × B = B × A
Commutative Property of Addition
The commutative property of addition states that the order of the addends is irrelevant.
So, A + B = B + A.
For example,
15 + 12 = 27
12 + 15 = 27
So, 15 + 12 = 12 + 15
Commutative Property of Multiplication
According to the commutative property of multiplication, the order of the multiplier and multiplicand does not change the product. So, A × B = B × A.
For example,
12 × 15 = 180
15 × 12 = 180
So, 12 × 15 = 15 × 12
Commutative Property of Division and Subtraction
We know that commutative property is applicable only for addition and multiplication. Therefore, A - B ≠ B - A and A ÷ B ≠ B ÷ A.
For example, 8 - 5 = 3
5 - 8 = -3
So, 8 - 5 ≠ 5 - 8
Example 2: 8 ÷ 4 = 2
4 ÷ 8 = 0.5
So, A ÷ B ≠ B ÷ A
Real-world Applications of Commutative Property
The commutative property is used to make the basic arithmetic operations easier. In the real world, we use commutative properties in different fields to make calculations easier.
- In shopping, to calculate the total cost, we use the commutative property as it makes the calculation easier.
- In cooking, to adjust the recipe, we use the commutative property. This helps in simplifying the recipe.
- For mental math, students can use the commutative property for easy calculation.
Common Mistakes and How to Avoid Them in Commutative Property
It is common for students to make errors when working with the commutative property. Here, we will learn some common mistakes and ways to avoid them to master the commutative property.
Mistake 1
Thinking that commutative properties apply to subtraction or division
Students tend to confuse that common property is applicable for both the subtraction and division that is 10 - 5 ≠ 5 - 10, which is wrong. The commutative property is only applicable to multiplication and addition.
Mistake 2
Incorrect usage of signs when applying the commutative property
In the incorrect usage of negative signs, students tend to mistakenly change the sign or misplace it when swapping the order, that is -6 + 3 = 6 - 3 instead of 3 + (-6). So it is important to note that when switching the order of the terms, the signs are a part of the respective number, and the result should be the same. That is -5 + 3 = -2 and 3 + (-5) = -2, which means -5 + 3 = 3 + (-5) = -2.
Mistake 3
Not applying the commutative property for variables
Students tend to believe that the commutativity property is only applicable to numbers, not to algebraic expressions. This is a wrong assumption because a + b = b + a.
Mistake 4
Not applying it in word problems
When working on word problems, students tend to rearrange the terms to simplify the calculations. If not done properly, it can lead to confusion and complexity. So, to avoid these errors, students should understand the concept of commutative problems and try to identify the hints from the word problems.
Mistake 5
Confusion between commutative and associative property
It is easy to get confused between commutative and associative property since both involves order of numbers. We must regularly practice with examples to differentiate between the two properties.
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Solved Examples of Commutative Property
Problem 1
John has 5 apples, and Sarah gives him 8 more. How many apples does John have?
The number of apples John has is 13
Explanation
The number of apples John has = 5
The number of apples Sarah gives John = 8
So, the total number of apples John has = 5 + 8 = 13
Problem 2
A photographer arranges 5 photo albums, each containing 18 photos. How many photos are there in total?
The number of photos in total = 90
Explanation
The number of albums = 5
The number of photos in each album = 18
So, the number of photos in total = 18 × 5 = 90
Problem 3
A train has 33 passengers in one compartment and 27 in another. How many passengers are there in total?
The total number of passengers is 60
Explanation
The number of passengers in the first compartment = 33
The number of passengers in the other compartment = 27
So, the total number of passengers = 33 + 27 = 60
Problem 4
Find the missing value: 150 + 275 = ___ + 150
Here, the missing value is 275
Explanation
Commutative property states that A + B = B + A
So, 150 + 275 = 275 + 150
Problem 5
A school has 9 classes, and each class has 25 students. How many students are in the school?
The number of students in the school = 225
Explanation
The number of students in each class is 25
The total number of classes = 9
So, the total number of students = 25 × 9 = 225
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FAQs on Commutative Property
1.What is commutative property?
2.What is the formula for the commutative property?
3.What is the commutative property of 3 + (- 4)?
4.What property is 8 + (- 3) = (- 3) + 8?
5.What is the commutative property of 9 × 7?
6.How can children in Philippines use numbers in everyday life to understand Commutative Property?
7.What are some fun ways kids in Philippines can practice Commutative Property with numbers?
8.What role do numbers and Commutative Property play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve Commutative Property 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.
