Commutative property

property of binary operations, for which changing the order of the operands does not change the result
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The commutative property says that the order of the numbers when adding or multiplying can be changed without changing the answer. For example, both ${\displaystyle 2+8}$ and ${\displaystyle 8+2}$ are equal to 10, and both ${\displaystyle 5*7}$ and ${\displaystyle 7*5}$ 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 ${\displaystyle a+b=b+a}$ . a and b are variables and can be any number.

Some operations like dividing are not commutative. For instance, ${\displaystyle 6\div 3}$  is 2, but ${\displaystyle 3\div 6}$  is ${\displaystyle {\frac {1}{2}}}$ . Subtraction is not commutative either: ${\displaystyle 6-2}$  is 4, but ${\displaystyle 2-6}$  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.