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# Commutative property

The **commutative property** says that the order of the numbers when adding or multiplying can be changed without changing the answer. For example, both [math]2+8[/math] and [math]8+2[/math] are equal to 10, and both [math]5*7[/math] and [math]7*5[/math] are equal to 35. This can be done with any numbers, or with more than two numbers.

## Definition

The definition of commutative property of addition is [math]a+b=b+a[/math]. *a* and *b* are variables and can be any number.

Some operations like dividing are not commutative. For instance, [math]6\div3[/math] is 2, but [math]3\div6[/math] is [math]\frac{1}{2}[/math]. Subtraction is not commutative either: [math]6-2[/math] is 4, but [math]2-6[/math] is negative 4.

## Higher mathematics

In higher mathematics like calculus, there are other commutative operations besides adding and multiplying. Commutative property must hold for each two elements of an Abelian group.