Commutative Property of Multiplication
The commutative property of multiplication states that the product of two or more numbers remains the same irrespective of the order in which they are placed. For example, 3 × 4 = 4 × 3 = 12. Let us study more about the commutative property of multiplication in this article.
What is the Commutative Property of Multiplication?
According to the commutative law of multiplication, if two or more numbers are multiplied, we get the same result irrespective of the order of the numbers. Here, the order of the numbers refers to the way in which they are arranged in the given expression. Observe the following example to understand the concept of the commutative property of multiplication.
5 × 6 = 6 × 5
30 = 30
Here, we can observe that even when the order of the numbers is changed, the product remains the same. This means 5 × 6 = 30; and 6 × 5 = 30.
Commutative Property of Multiplication Formula
The commutative property formula for multiplication shows that the order of the numbers does not affect the product. The commutative property of multiplication applies to integers, fractions, and decimals.
The Commutative property multiplication formula is expressed as:
A × B = B × A
According to the commutative property of multiplication, the order in which we multiply the numbers does not change the final product.
This can be applied to two or more numbers and the order of the numbers can be shuffled and arranged in any way.
Example: 5 × 3 × 2 × 10 = 10 × 2 × 5 × 3 = 300. We can see that even after we shuffle the order of the numbers, the product remains the same.
Commutative Property of Multiplication and Addition
The commutative property is applicable to multiplication and addition.
 For Addition: The Commutative law for addition is expressed as A + B = B + A. For example, (7 + 4) = (4 + 7) = 11. This shows that even after we change the order of the numbers, 7 and 4, the sum remains the same.
 For Multiplication: The Commutative law of multiplication is expressed as A × B = B × A. For example, (7 × 4) = (4 × 7) = 28. Here, we can see that the product of the numbers remains the same even when the order of the numbers is changed.
It should be noted that the Commutative property of multiplication is not applicable to subtraction and division.
Tips on the Commutative Property of Multiplication:
Here are a few important points related to the Commutative property of multiplication.
 The commutative property of multiplication and addition is only applicable to addition and multiplication. It cannot be applied to division and subtraction.
 The commutative property of multiplication and addition can be applied to 2 or more numbers.
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Examples of Commutative Property of Multiplication

Example 1: Fill in the missing number using the commutative property of multiplication: 6 × 4 = __ × 6.
Solution:
According to the commutative property of multiplication formula, A × B = B × A. So, let us substitute the given values in this formula and check.
(6 × 4) = (4 × 6) = 24. Hence, the missing number is 4. 
Example 2: Shimon's mother asked him whether p × q = q × p is an example of the commutative property of multiplication. Can you help Shimon to find out whether it is commutative or not?
Solution:
We know that the commutative property for multiplication states that changing the order of the multiplicands does not change the value of the product.
pq = qp
So, we see that changing the order will not alter the product value.
So this is an example of the commutative property.Answer: p q = q p is an example of the commutative property of multiplication.

Example 3: Which of the expressions follows the commutative property of multiplication?
a.) 7 × 8 × 5 × 6
b.) 4 × ( 2)
Solution:
a.) Let us find the product of the given expression. It comes to 7 × 8 × 5 × 6 = 1680.
Now, let us reverse the order of the numbers and find the product of the numbers. It comes to 6 × 5 × 8 × 7 = 1680.
Both the products are the same. Therefore, the given expression follows the commutative property of multiplication because it shows that even when we changed the order of the numbers the product remains the same.
b.) Let us find the product of the given expression, 4 × ( 2) = 8. Now, let us reverse the order of the numbers and check, ( 2) × 4 = 8. This shows that the given expression follows the commutative property of multiplication.
FAQs on Commutative Property of Multiplication
What is the Commutative Property of Multiplication?
The commutative law of multiplication states that the product of two or more numbers remains the same, irrespective of the order of the operands. For multiplication, the commutative property formula is expressed as (A × B) = (B × A). The commutative property of multiplication applies to integers, fractions, and decimals.
How do you find the Commutative Property of Multiplication?
The commutative property of multiplication states that if 'a' and 'b' are two numbers, then a × b = b × a. If the product of the values on the Lefthand side (LHS) and the product of the values on the righthand side (RHS) terms is equal, then it can be said that the given expression follows the commutative property of multiplication.
What is an Example of Commutative Property of Multiplication?
An example of the commutative property of multiplication can be seen as follows. We know that (A × B) = (B × A). Let us substitute the value of A = 8 and B = 9. On substituting these values in the formula we get 8 × 9 = 9 × 8 = 72. Hence it is proved that the product of both the numbers is the same even when we change the order of the numbers. This means, if we have expressions such as, 6 × 8, or 9 × 7 × 10, we know that the commutative property of multiplication will be applicable to it.
What is the Commutative Property of Multiplication for the Numbers 7 and 6?
Let us arrange the given numbers as per the general equation of commutative law that is (A × B) = (B × A). Here A = 7 and B = 6. After substituting the values in the formula, we get 7 × 6 = 6 × 7 = 42. Hence, 6 × 7 follows the commutative property of multiplication.
What is the Commutative Property of Multiplication for Rational Numbers?
The commutative property of multiplication for rational numbers can be expressed as (P × Q) = (Q × P). Here the values of P, Q are in form of a/b, where b ≠ 0.
What is the Commutative Property of Multiplication for Fractions?
The commutative property of multiplication for fractions can be expressed as (P × Q) = (Q × P). Let us substitute the values of P, Q in the form of a/b. For example, if, P = 7/8 and Q = 5/2. On substituting the values in (P × Q) = (Q × P) we get, (7/8 × 5/2) = (5/2 × 7/8) = 35/16. Hence, the commutative property of multiplication is applicable to fractions.
What is the Commutative Property of Multiplication for Integers?
The commutative property of multiplication for integers can be expressed as (P × Q) = (Q × P). For example, let us substitute the value of P = 3 and Q = 9. On substituting the values in the formula, we get (3 × 9) = (9 × 3) = 27. Hence, the commutative property of multiplication is applicable to integers.
What is the Difference between the Associative and Commutative Property of Multiplication?
The associative property of multiplication states that the product of the numbers remains the same even when the grouping of the numbers is changed. The associative property of multiplication is expressed as (A × B) × C = A × (B × C). The commutative property of multiplication states that the product of two or more numbers remains the same even if the order of the numbers is changed. The commutative property of multiplication is expressed as A × B × C = C × B × A.
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