Commutative Definition

Author: nayaknandan85

Introduction to Commutative Definition:
There are three basic number properties that apply to arithmetic operations. Associative Property, Commutative Property, and Distributive Property are the three basic number properties applied to arithmetic operations. "Commutative" is a property an operation between two numbers (or other mathematical elements) may or may not have. The operation is commutative if it doesn't matter which element is named first.

Definition of Commutative:
Commutative property is one of the basic properties of numbers. The word "commute" denotes "exchange" or "swap over". Commutative property definition states that numbers may be added or multiplied in any order.
Commutative property definition of Addition explains that changing the order of addends doesn't change the sum. Commutative definition can be explained more formally. If + places for an operation and A, B are factors from a given set, then + is commutative if, for all such elements A + B = B + A.
Commutative property definition of Multiplication describes that changing the order of factors doesn't change the product. Commutative can be explained more formally. If * places for an operation and A, B are factors from a given set, then * is commutative if, for all such elements A * B = B * A.

Commutative in Real Life:
An operation is commutative if you may change the order of the numbers involved without changing the result. Addition and multiplication both are commutative definition. Subtraction is not commutative because 2 - 1 is not equal to 1 - 2.
Counting a combination of different coins gives you of commutative property. For example, suppose you have 20 quarters and 10 dimes. It does not matter whether you sum-up the quarters first and then the dimes OR sum-up the dimes first and then the quarters OR add a quarter and a dime alternately, finally the total is going to be $6.
Commutative property is applicable for both addition and multiplication.

Example for Commutative Definition:
Addition is commutative, 5 + 7 has the same value as 7 + 5. But subtraction is not a commutative definition because the variation 5 - 7 does not have the same value as 7-5.
Similarly, multiplication is also a commutative function, 6 * 3 has the same value as 3 * 6. Division, on the other hand, is not commutative definition, and the ratio of `6 / 3` does not have the same value as `3 / 6` .
Addition and multiplications are two basic arithmetic processes in mathematics. Addition produce a sum of given numbers where as multiplication produce a produce of given numbers. Identity property of addition and multiplication is the process of producing a result as a same number itself. The element used for this identity property is called identity element. This element is different for addition and multiplication.

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