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The commutative property

The commutative property is a property we find in both ordinary addition and multiplication. Let's look at it from the perspective of each operation:

Addition: x + y = y + x. For example 1 + 3 = 3 + 1. In both cases, you get a sum of 4.

Multiplication: xy = yx. For example, 3 x 4 = 4 x 3. In both cases, you get a product of 12.

In other words, for both properties, the order in which the terms appear in the equation are irrelevant. Regardless of the order, you will always obtain the same result.

Remembering how to understand the commutative property is simple. We can simply think of a "commuter." Just as the purpose of a "commuter" is to move people and objects around, so also, the commutative property in mathematics has to do with "moving" terms around in different orders. Indeed, the word "commute" comes from the Latin word "commutare," meaning "to exchange" or "to change."

The first definition of its Latin etymology is particularly instructive, since application of the commutative property involves an 'exchange' of the places of the terms. Note that a component of the Latin word 'commutare' is 'mutare,' from which we get the English word "mutate," meaning "to change."