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\times 7}
and 👁 {\displaystyle 7\times 5}
are equal to 35. This can be done with any numbers, or with more than two numbers.

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 👁 {\textstyle {\frac {1}{2}}}
. Subtraction is not commutative either: 👁 {\displaystyle 6-2}
is 4, but 👁 {\displaystyle 2-6}
is negative 4. This is because 👁 {\textstyle 6\div 3=6\times {\frac {1}{3}}}
and 👁 {\displaystyle 6-2=6+-2}
. Division and multiplication are shorthand for special types of multiplication and addition that says "change the second number, then continue."

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.