If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Properties of 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:
4+2=2+4
Notice how both sums are 6 even though the ordering is reversed.
Here's another example with more addends:
1+2+3+4=4+3+2+1
Which of these is an example of the commutative property of addition?
Choose 1 answer:

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:
(2+3)+4=2+(3+4)
Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:
=(2+3)+4
=5+4
=9
And here's how we evaluate the right-hand side:
=2+(3+4)
=2+7
=9
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.
Which of these is an example of the associative property of addition?
Choose 1 answer:

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:
0+4=4
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:
6+0=6
Which of these is an example of the identity property of addition?
Choose 1 answer:

Want to join the conversation?