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Commutative Property: The property of commutative explains that the order of terms doesn’t matter while performing a mathematics operation. The commutative property is otherwise called Commutative Law.
On this page, we will provide you with all the necessary information about commutative property meaning, definition, formulas. Read on to find out more.
Commutative Property Definition: “Any mathematics operation is commutative if changing the order of the operands does not change the result”.
The commutative property is applicable for Addition and Multiplication. The commutative property of Division and Subtraction doesn’t apply while performing mathematics operations.
Let’s understand the topic in details by checking out this example of communicative property.
If 2 + 3 = 6, we can change the order of the operands to check if the results are the same.
Example 1: Commuative Property of Addition
2 + 3 = 6
3 + 2 = 6
Which means 2 + 3 = 3 + 2
Example 2: Commuative Property of Mulitiplication
2 x 3 = 6
3 x 2 = 6
Which means 2 x 3 = 3 x 2
Commutative Property Meaning: Commutative is originated from the French word “Commute” which means switch or move around. Whereas the word “ative” which is the suffix of commutative means “tend to“. The word commutative means that we can switch the positions of integers while performing an operation and the resultant product will be the same.
The sum of 2 numbers will be the same in whatever order they are added.
| A + B = B + A |
Example:
2 + 3 = 3 + 2 = 5
5 + 6 = 6 + 5 = 11
7 + 8 = 8 + 7 = 15
The product of 2 numbers will be the same in whatever order they are multiplied.
| A.B = B.A |
Example:
2 x 3 = 3 x 2 = 6
3 x 9 = 9 x 3 = 27
7 x 4 = 4 x 7 = 28
As discussed above, the commutative property is not applicable for Division and Subtraction problems.
The difference between 2 numbers will not be the same if they are subtracted in a different order.
Example:
2 – 3 = -1 Whereas 3 – 2 = 1
5 – 9 = – 4 ≠ 9 – 5 = 4
9 – 6 = 3 ≠ 6 – 9 = -3
The quotient and the remainder will not be the same if we perform division operation by changing the order of the numbers.
8 ÷ 2 = 4 which is not equal to 2 ÷ 8 = 0.25
6 ÷ 2 = 3 ≠ 2 ÷ 6 = 1/3
The formulas of commutative property are given below:
| A + B = B + A A × B = B × A |
Question 1: Does 12 x 3 satisfies commutative law?
Answer: Yes, 12 x 3 satisfies the commutative law. Because when 12 multiplied by 3, the result is 36 and when 3 multiplied by 13, the product is 36.
12 x 3 = 3 x 12 = 36.
Question 2: Does 4 + 20 obey the commutative laws?
Answer: Yes, 4 + 20 obey’s commuatative law.
4 + 20 = 20 + 4 = 24.
Question 3: Does 4 – 5 statisfiees commutative law?
Answer: No, commutative law does not obey subtraction.
Question 4: Which of the following obeys commutative law?
1. 34 + 5
2. 8 ÷ 6
3. 4 x -5
4. 3 – 6
Answer: The commutative law obeys only while performing multiplication and addition operations. Thus only option 1 and option 3 provided above obeys commutative law.
Also, Check:
| Trigonometry Formulas | Algebra Formula |
| Mensuration Formulas | Differentiation Formulas |
| Factorisation Formulas | BODMAS Rules |
The frequently asked questions on Commutative Property are given below:
| Q. Is commutative for whole numbers? A. Yes, Commutative property is applicable for the Whole number. |
| Q. Why is there no commutative property for division? A. The commutative property of division is not applicable since the order matters while performing division operation. |
| Q. Are integers commutative under subtraction? A. No Integers are not communicative under subtraction, because while performing subtraction operation of integers if the order gets changed even the results will get changed. |
| Q. What is another name for the commutative property? A. The other name of the commutative property is “Commutative Law”. |
| Q. What is the formula of commutative property? A. The formulas of Commutative property is: Commutative Property of Addition: A + B = B + A Commutative Property of Subtraction: A × B = B × A |
Students can also make use of Embibe’s Mathematics Study page which covers almost all the Mathematical Concepts right from Grade 11 and Grade 12. All these concepts come with video lectures which can be accessed for. Also, solve and take Maths Mock Tests on Embibe:
Now that you are provided with all the necessary information about Commutative Property and we hope this article is helpful to you. If you have any queries on Commutative Law, ping us through the comment section below and we will get back to you as soon as possible.
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