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Commutative Property of Multiplication – Definition With Examples

Jo-ann Caballes

Updated on January 8, 2024

Dive into the world of mathematics with Brighterly, your trusted guide in children’s learning. Today, we’ll explore the fascinating topic of the Commutative Property of Multiplication. This principle is a cornerstone of math, shaping the way we understand and manipulate numbers. It is the property that tells us the order in which we multiply numbers doesn’t change the result. For instance, multiplying 3 and 5 together, whether it’s 3 × 5 or 5 × 3, will give us the same product, 15. This exciting property introduces children to the flexibility inherent in mathematics, demonstrating that the rigid order is not always required. It’s like a fun puzzle game where you can rearrange the numbers and still reach the same goal. Just imagine, whether you’re juggling three apples or five apples first in a multiplication problem, you’ll still end up with the same amount of apples. Isn’t that intriguing? Let’s dive deeper into this mathematical magic trick that makes learning math at Brighterly a joyful and rewarding experience.

What Is the Commutative Property of Multiplication in Math?

The Commutative Property of Multiplication is a foundational concept in mathematics, enabling us to understand and manipulate numbers with ease. It states that the order in which you multiply numbers does not change the product. In other words, if you are multiplying two numbers together, you can swap their places, and the answer remains the same. For instance, if you’re multiplying 3 and 4 together, 3 × 4 is the same as 4 × 3; both give you the product of 12. This property is exceptionally useful, allowing children to understand that multiplication doesn’t always have to follow a strict order, thereby giving them more flexibility when solving math problems.

Commutative Property of Multiplication Formula

The Commutative Property of Multiplication can be written as a simple formula: a × b = b × a. This formula is a way of expressing the property in mathematical terms. It is easy to remember and understand. For any given numbers ‘a’ and ‘b’, regardless of their values, this property will always hold true. It underscores the idea that the product of two numbers remains constant, irrespective of their order. The formula is not only relevant in basic arithmetic but also in more advanced areas of mathematics, including algebra and calculus. 

Commutative Property of Multiplication and Addition

Just like multiplication, the commutative property also applies to addition. This means that the order in which you add numbers does not affect the sum. For instance, 2 + 5 will give the same result as 5 + 2; both result in 7. Combining these two properties, we can solve more complex arithmetic problems with ease. For instance, the expression (2 + 5) × 3 = 2 × (5 + 3) can be simplified and solved using the commutative properties of both addition and multiplication.

What Is Multiplication?

Multiplication is one of the four basic operations in arithmetic, along with addition, subtraction, and division. It is a faster way of adding the same number multiple times. For instance, instead of adding 2 + 2 + 2 + 2, you can simply multiply 2 × 4 to get the same result, which is 8. Multiplication is a powerful tool, enabling us to solve problems involving groups, arrays, and combinations more efficiently. 

Fact to Remember of Commutative Property of Multiplication

An important fact to remember about the Commutative Property of Multiplication is that it applies only to the operations of addition and multiplication. It does not apply to subtraction and division. This means that the order in which you subtract or divide numbers can affect the result. For instance, 9 ÷ 3 is not the same as 3 ÷ 9. This fact underscores the importance of understanding the properties of different arithmetic operations. 

Solved Examples of Commutative Property of Multiplication

Let’s explore some examples to better understand the Commutative Property of Multiplication:

Example 1: If we multiply 7 × 2, we get the product 14. If we change the order and multiply 2 × 7, we still get 14. Hence, 7 × 2 = 2 × 7.

Example 2: If we multiply 5 × 3 × 4, we can rearrange the numbers in any order because of the commutative property. So, 5 × 3 × 4 = 4 × 5 × 3 = 3 × 4 × 5 = 60.

Practice Problems of Commutative Property of Multiplication

To understand the Commutative Property of Multiplication better, let’s try some practice problems.

1. 6 × 9 = ? × 6
2. 5 × ? = ? × 5
3. If 8 × 7 = 56, then 7 × 8 = ?
4. Rearrange 2 × 3 × 5 to demonstrate the commutative property.
5. If 4 × 9 = 36, what is 9 × 4?

Conclusion

In the journey of mathematics with Brighterly, we have unfolded the magic of the Commutative Property of Multiplication, a fundamental principle that asserts that the product of numbers remains constant, irrespective of their order in multiplication. This property acts like a powerful magic wand that allows children to juggle numbers with greater freedom while ensuring the result remains untouched. This freedom, this flexibility, transforms math from a rigid discipline into a playful exploration, empowering children to approach arithmetic problems with confidence and creativity.

By mastering the Commutative Property of Multiplication, children not only acquire a crucial math skill but also imbibe a broader life lesson – that changing perspectives, swapping positions, or trying different orders can often lead to the same result. It encourages them to be adaptable and versatile in their thinking. It’s not just about learning a mathematical principle; it’s about nurturing a flexible and resilient mindset.

So, whether you’re multiplying apples, oranges, or the number of stars in a constellation, remember the Commutative Property of Multiplication, your loyal companion in the wonderful world of math. With Brighterly, let’s continue to illuminate young minds by making math an enjoyable and meaningful adventure.

Frequently Asked Questions of Commutative Property of Multiplication

Does the Commutative Property of Multiplication apply to more than two numbers?

Yes, the Commutative Property of Multiplication applies to any number of factors. This means if you are multiplying three, four, or even more numbers together, you can rearrange them in any order, and the product will remain the same. For instance, 2 × 3 × 4 = 24, and if you rearrange the numbers, say 4 × 2 × 3, the product is still 24. This property is incredibly useful in calculations as it provides the flexibility to rearrange numbers for ease of computation, especially when dealing with large numbers or multiple factors.

Does the Commutative Property of Multiplication apply to zero?

Absolutely! The Commutative Property of Multiplication applies to zero as well. In multiplication, any number times zero equals zero, irrespective of the order. For instance, 5 × 0 = 0, and similarly, 0 × 5 = 0. This holds true for any number, no matter how large or small, positive or negative. This is because the concept of zero in multiplication is equivalent to having ‘none’ of a certain quantity, and regardless of how many times ‘none’ is taken, the result will still be ‘none’ or zero.

Does the Commutative Property of Multiplication apply to fractions?

Yes, the Commutative Property of Multiplication applies to fractions as well. This means that the order of fractions in a multiplication operation does not affect the product. For example, 1/2 × 2/3 equals 1/3, and if you swap the fractions, i.e., 2/3 × 1/2, the product remains the same, 1/3. This is a powerful property that allows us to manipulate fractions with flexibility, helping in simplifying complex mathematical problems and computations. It’s one of the reasons why understanding the commutative property is so crucial in mastering fractions and other advanced mathematical concepts.

Jo-ann Caballes

5 articles

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.