Which Of The Following Shows Why The Commutative Property - T-Tees - Your Answers Await, Life's Questions Unraveled

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The commutative property applies to the arithmetic operations of addition and multiplication. It means that changing the order or position of two 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 two 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 after changing the order of numbers.

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1. What is Commutative Property? 2. Commutative Property of Addition 3. Commutative Property of Multiplication 4. Commutative Property vs Associative Property 5. FAQs on Commutative Property

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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. Let us discuss the commutative property of addition and multiplication.

Commutative Property Formula

For any two numbers, A and B, the formula of the commutative property of numbers is expressed as follows.

A + B = B + A
A × B = B × A
A – B ≠ B – A
A ÷ B ≠ B ÷ A

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The commutative property formula states that the change in the order of two numbers while adding and multiplying them does not affect the result. However, while subtracting and dividing any two real numbers, the order of numbers are important and hence it can’t be changed.

The commutative property of addition says that changing the order of the addends does not change the value of the sum. If ‘A’ and ‘B’ are two numbers, then the commutative property of addition of numbers can be represented as shown in the figure given below.

Let us take an example of the commutative property of addition and understand the application of the above formula.

Example: Let us check the Commutative property by adding 10 and 13.

Let us add the given numbers 10 and 13. So, 10 + 13 = 23 and 13 + 10 = 23. Therefore, 10 + 13 = 13 + 10 which proves the commutative property of addition.

The commutative property of multiplication says that the order in which we multiply two numbers does not change the final product. The figure given below represents the commutative property of the multiplication of two numbers.

If 4 and 6 are the numbers, then 4 × 6 = 24, and 6 × 4 is also equal to 24. Thus 4 × 6 = 6 × 4. Therefore, the commutative property holds true for the multiplication of numbers.

Note: The commutative property does not hold for subtraction and division operations. Let us take the example of numbers 6 and 2.

6 – 2 = 4, but 2 – 6 = -4. Thus, 6 – 2 ≠ 2 – 6.
6 ÷ 2 = 3, but 2 ÷ 6 = 1/3. Thus, 6 ÷ 2 ≠ 2 ÷ 6

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Commutative Property of Subtraction

The commutative property is not applicable to subtraction. The commutative law only applies to addition and multiplication. Let us see why it does not apply on subtraction. For example, 8 – 5 = 3, but 5 – 8 = -3. Thus, 8 – 5 ≠ 5 – 8.

Let us learn the difference between the associative and commutative property. Both associative property and commutative property state that the order of numbers does not affect the result of addition and multiplication. So, what is the difference between the two? Let us find out.

Observe the table given below to see the comparison of commutative property vs associative property.

Commutative Property Associative Property The word ‘commutative’ is derived from ‘commute’ which means move around, switch, or swap the numbers. The word ‘associative’ is derived from ‘associate’ which deals with the grouping of numbers. The order of numbers can be changed in the case of addition and multiplication of two numbers without changing the final result. The grouping of numbers can be changed in the case of addition and multiplication of three numbers without changing the final result.

Formula:

A + B = B + A

A × B = B × A

Formula:

A + (B + C) = (A + B) + C = (A + C) + B

A × (B × C) = (A × B) × C = (A × C) × B

Important Notes:

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.

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☛ Related Topics

Check out some interesting articles related to the commutative property in math.

Properties of Natural Numbers
Properties of Whole Numbers
Properties of Rational Numbers
Properties of Integers

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