Commutative Property
2026-02-28 13:07 Diff
https://brightchamps.com/en-us/math/numbers/commutative-property

1381 Learners

Last updated on December 3, 2025

Arithmetic operations follow different properties, including the commutative, associative, distributive, and identity properties. 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?

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

The commutative property is a basic math rule. It states that when adding or multiplying any numbers. This 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, \(A \times B = B \times A\) and \(A + B = B + A\), so the order of the operands does not impact the result in addition and multiplication. For example, \(5 + 7 = 7 + 5 = 12. \)
 

Commutative Property vs 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.

Commutative Property Associative Property

The commutative property states that changing the order of numbers in addition and multiplication does not affect the result.

The associative property states that the way numbers are grouped in addition and multiplication does not affect the result.

Commutative property formula:\(A + B = B + A\)

\(A × B = B × A\)

Associative property formula:\(A + (B + C) = (A + B) + C \)

\(A \times (B \times C) = (A \times B) \times C\)

The commutative property requires only two numbers Associative property requires at least three numbers

For example, 8 + 4 = 4 + 8 = 12

For example, 8 + (5 + 2) = (8 + 5) + 2 = 15

Commutative Property Formula

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
 

  • \(A + B = B + A\)
     
  • \(A \times B = B \times A\)

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, \(A \times B = B \times A.  \)

For example, 

\(12 \times 15 = 180 \)

\(15 × 12 = 180 \)

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, \(A ÷ B ≠ B ÷ A\)

Explore Our Programs

Tips and Tricks to Master Commutative Property

Commutative property helps students solve problems faster, check answers easily, and perform mental math with confidence. Use these simple tips and tricks to understand and apply them in your daily math practice. 

  • To enhance mental math skills, students can use the commutative property to rearrange the numbers for easier calculations. For example, 19 + 6 + 1 can be rearranged to \(19 + 1 + 6 = 20 + 6 = 26\).
     
  • Always remember that the commutative property does not apply to subtraction and division. The commutative property is applicable only to addition and multiplication. 
     
  • Use visual aids like blocks to understand the commutative property. For example, when adding \(2 + 3 + 1\), students can arrange 2 blocks, 3 blocks, and 1 block; the way of arranging the blocks does not change the result.
     
  • Use the commutative property in real life to add expenses, count, and multiply. 
     
  • The commutative property is applicable to algebraic expressions to simplify or rearrange the terms in an expression. 
     
  • Parents can create games in which children rearrange numbers or objects to find sums or products more quickly. This makes learning fun and reinforces the concept.
     
  • Teachers can provide worksheets with problems that specifically highlight the commutative property, helping students spot patterns and build confidence.
     
  • Teachers can show how the commutative property works alongside the associative and distributive properties to build a stronger foundation in mathematics.

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. 
 

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 simplify the recipe.
     
  • For mental math, students can use the commutative property for easy calculation. 
     
  • In finance, the commutative property is used to add the deposit or interest from multiple accounts, as the order doesn't matter.
     
  • To calculate the total score in different levels of a game, we use the commutative property. As the order of the score does not change the total score. 

Problem 1

John has 5 apples, and Sarah gives him 8 more. How many apples does John have?

Okay, lets begin

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 \(= 5 + 8 = 13\)
 

Well explained 👍

Problem 2

A photographer arranges 5 photo albums, each containing 18 photos. How many photos are there in total?

Okay, lets begin

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 \(= 18 × 5 = 90\).
 

Well explained 👍

Problem 3

A train has 33 passengers in one compartment and 27 in another. How many passengers are there in total?

Okay, lets begin

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 \(= 33 + 27 = 60\).
 

Well explained 👍

Problem 4

Find the missing value: 150 + 275 = ___ + 150

Okay, lets begin

Here, the missing value is 275.
 

Explanation

Commutative property states that \(A + B = B + A\)


So, \(150 + 275 = 275 + 150\)
 

Well explained 👍

Problem 5

A school has 9 classes, and each class has 25 students. How many students are in the school?

Okay, lets begin

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 \(= 25 \times 9 = 225\)
 

Well explained 👍

FAQs on Commutative Property

1.What is commutative property?

According to the commutative property, changing the order of numbers in addition or multiplication does not change the result. 
 

2.What is the formula for the commutative property?

The formula for the commutative property is \(A + B = B + A\) and \(A \times B = B \times A\).
 

3.What is the commutative property of 3 + (- 4)?

The commutative property of \(3 + (-4) = (-4) + 3\).
 

4.What property is 8 + (- 3) = (- 3) + 8?

This is commutative, as the order of the numbers has changed, but the sum remains the same. 
 

5.What is the commutative property of 9 × 7?

The commutative property of \(9 × 7\) is \(7 × 9\).
 

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.