# Properties ofÂ addition

Explore the commutative, associative, and identity properties of addition.

In this article, we'll learn the three main properties of addition. Here's a quick summary of these properties:

**Commutative property of addition:**Changing the order of addends does not change the sum. For example, $4 + 2 = 2 + 4$.

**Associative property of addition:**Changing the grouping of addends does not change the sum. For example, $(2 + 3) + 4 = 2 + (3 + 4)$.

**Identity property of addition:**The sum of $0$ and any number is that number. For example, $0 + 4 = 4$.

## Commutative property of addition

The commutative property of addition says that changing the order of addends does not change the sum. Here's an example:

Notice how both sums are $6$ even though the the ordering is reversed.

Here's another example with more addends:

## Associative property of addition

The associative property of addition says that changing the grouping of the addends does not change the sum. Here's an example:

Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:

And here's how we evaluate the right-hand side:

Notice that both sides sum to $9$ even though we added the $2$ and the $3$ first on the left-hand side, and we added the $3$ and the $4$ first on the right-hand side.

## Identity property of addition

The identity property of addition says that the sum of $0$ and any number is that number. Here's an example:

This is true because the definition of $0$ is "no quantity", so when we add $0$ to $4$, the quantity of $4$ doesn't change!

The commutative property of addition tells us that it doesn't matter if the $0$ comes before or after the number. Here's an example of the identity property of addition with the $0$ after the number: