Commutative property

property of binary operations, for which changing the order of the operands does not change the result

The commutative property of addition and multiplication tells us that it does not matter which number we add first, or multiply first. We will still get the same answer if we add them backwards. The same thing goes for multiplying backwards. An example is 8+2=10 and 2+8=10

The definition of commutative property of addition is, when we substitute any number for a and b for example, .

For example, , because and are both . It doesn't matter whether the or the comes first. 2+3=3+2 is the same as , when and .

We can substitute fractions too. . Either way, it adds to .

And for good mathematicians, we can substitute irrational numbers as well: .

Some operations like dividing are not commutative. For instance, 6 divided by 3 is 2, but 3 divided by 6 is 1/2. Do not divide backwards. Dividing is not commutative. Subtracting is not commutative either: 6−2 is 4, but 2−6 is minus 4. Exponentiation is not commutative, either: For example, 2³ is 8, but 3² is 9.

In higher mathematics, there are other commutative operations besides adding and multiplying.