The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of numbers while adding or multiplying them does not change the end result. For example, 4 + 5 gives 9, and 5 + 4 also gives 9. The order of numbers being added does not affect the sum. The same concept applies to multiplication too. The commutative property does not hold for subtraction and division, as the end results are completely different in changing the order of numbers. Let us look at all these concepts in detail.
|1.||What is Commutative Property?|
|2.||Commutative Property of Addition|
|3.||Commutative Property of Multiplication|
|4.||FAQs on Commutative Property|
What is Commutative Property?
The word 'commutative' originates from the word 'commute', which means to move around. Hence, the commutative property deals with moving the numbers around. So mathematically, if changing the order of the operands does not change the result of the arithmetic operation then that particular arithmetic operation is commutative. Apart from this, there are other properties of numbers: the associative property, the distributive property, and the identity property. They are different from the commutative property of numbers. Let us discuss the commutative property of addition and multiplication briefly.
Commutative Property of Addition
The commutative property of addition says that changing the order of the addends does not change the value of the sum. There are cases where we need to add more than two numbers. The commutative property is true even when there are more than two numbers being added. For example, 10 + 20 + 30 + 40 = 100, and 40 + 30 + 20 + 10 is also equal to 100. The sum is 100 in both cases even when the order of numbers is changed. If 'A" and 'B' are two numbers, then the commutative property of numbers can be represented as shown in the figure below.
Commutative Property of Multiplication
The commutative property of multiplication says that the order in which we multiply the numbers does not change the final product. Similar to the commutative property of addition, the commutative property holds good if there are more than 2 numbers to be multiplied. For example, 6 × 7 × 8 = 336. The same result is obtained when we multiply 8 × 7 × 6 = 336. The product in both cases is 336. So, it is evident that the order or the position of numbers being multiplied does not change the product. The image given below represents the commutative property of the multiplication of two numbers.
Some key points to remember about the commutative property are given below.
- The Commutative property states that "changing the order of the operands does not change the result."
- The commutative property for addition is A + B = B + A
- The commutative property for multiplication is A × B = B × A
☛Topics Related to Commutative Property
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Examples of Commutative Property
Example 1: Jacky's mother asked him whether x + y = y + x is an example of the commutative property. Can you help Jacky find out whether it is commutative or not?
We know that the commutative property of addition states that changing the order of the addends does not change the value of the sum. In this case, x + y = y + x, is an example of the commutative property which says A + B = B + A.
Example 2: Benny was given a question in his assignment: 3 + 5 + 7 = 15, in which he was asked to check whether the commutative property of addition was applied or not. Can you help Bran with his assignment?
By simple rules of addition, the sum of the given numbers can be calculated as: Sum = 3 + 5 + 7 = 15
Now, we if we change the order of the numbers and add them: Sum = 5 + 3 + 7 = 15
Let us arrange this in another order: Sum = 7 + 5 + 3 = 15
∴ The sum is the same in all the cases. Thus, the commutative property is applied here.
FAQs on Commutative Property
What is the Commutative Property? Give Examples?
The commutative property states that if the order of position of numbers is interchanged while performing addition or multiplication, the sum or the product obtained does not change. It is to be noted that commutative property holds good only for addition and multiplication and not for subtraction and division. For example, 6 + 7 is equal to 13 and 7 + 6 is also equal to 13. Similarly, 6 × 7 = 42, and 7 × 6 = 42.
What is the Commutative Property of Addition?
According to the commutative property of addition, when two numbers are added in any order the sum remains the same. This property applies even when more than two numbers are added, and the order of the numbers is changed, the sum still remains the same. For example, 3 + 4 + 5 is equal to 12, and 4 + 3 + 5 is also equal to 12. In both cases, the sum is the same.
What is the Commutative Property of Multiplication?
According to the commutative property of multiplication, the order of multiplication of numbers does not change the product. For example, 4 × 5 is equal to 20 and 5 × 4 is also equal to 20. Though the order of numbers is changed the product is 20. This property holds true even when more than 2 numbers are multiplied.
Can Commutative Property be Applied for Subtraction and Division? List Out the Reasons.
Commutative property cannot be applied for subtraction and division, because the changes in the order of the numbers while doing subtraction and division do not produce the same result. For example, 5 - 2 is equal to 3, whereas 3 - 5 is not equal to 3. In the same way, 10 divided by 2, gives 5, whereas, 2 divided by 10, does not give 5. Therefore, commutative property is not true for subtraction and division.
What is the Difference Between Commutative Property and Associative Property?
The commutative property states that the change in the order of numbers in an addition or multiplication operation does not change the sum or the product. The commutative property of addition is written as A + B = B + A. The commutative property of multiplication is written as A × B = B × A. The associative property states that the grouping or combination of two or more numbers that are being added or multiplied does not change the sum or the product. The associative property of addition is written as: (A + B) + C = A + (B + C). The associative property of multiplication is written as (A × B) × C = A × (B × C).
What is the Difference Between Commutative Property and Distributive Property?
The commutative property states that the change in the order of numbers for the addition or multiplication operation does not change the result. The commutative property of addition for two numbers 'A' and 'B' is A + B = B + A. The distributive property means multiplying a number with every number inside the parentheses. The numbers inside the parentheses are separated by an addition or a subtraction symbol. The distributive property of addition for two numbers 'A', 'B' is: A(B + C) = AB + AC.
What are Commutative Laws?
Commutative law is another word for the commutative property that applies to addition and multiplication. The commutative law of addition states that the order of adding two or more numbers does not change the sum (A + B = B + A). The commutative property of multiplication states that the order of multiplying two or more numbers does not change the product (A × B = B × A).