Example 1: Jacky's mother asked him whether the addition of two natural numbers is an example of the commutative property. Can you help Jacky find out whether it is commutative or not?
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Commutative Property
The commutative property deals with 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.
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 Formula
If two numbers A and B are given, then the formula of commutative property of numbers is given as,
A + B = B + A
A × B = B × A
A - B ≠ B - A
A ÷ B ≠ B ÷ A
Step-by-step explanation:
A+B
A×B
A-B≠B-A
A÷B≠B÷A
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