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Lesson 1: Properties of numbers

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, plus, 2, equals, 2, plus, 4.
Associative property of addition: Changing the grouping of addends does not change the sum. For example, left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.
Identity property of addition: The sum of 0 and any number is that number. For example, 0, plus, 4, equals, 4.

The commutative property of addition says that changing the order of addends does not change the sum. Here's an example:
4, plus, 2, equals, 2, plus, 4
Notice how both sums are 6 even though the ordering is reversed.
Here's another example with more addends:
1, plus, 2, plus, 3, plus, 4, equals, 4, plus, 3, plus, 2, plus, 1
Which of these is an example of the commutative 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:
start color #11accd, left parenthesis, 2, plus, 3, right parenthesis, plus, 4, end color #11accd, equals, start color #e07d10, 2, plus, left parenthesis, 3, plus, 4, right parenthesis, end color #e07d10
Remember that parentheses tell us to do something first. So here's how we evaluate the left-hand side:
empty space, start color #11accd, left parenthesis, 2, plus, 3, right parenthesis, plus, 4, end color #11accd
equals, 5, plus, 4
equals, 9
And here's how we evaluate the right-hand side:
empty space, start color #e07d10, 2, plus, left parenthesis, 3, plus, 4, right parenthesis, end color #e07d10
equals, 2, plus, 7
equals, 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?

The identity property of addition says that the sum of 0 and any number is that number. Here's an example:
0, plus, 4, equals, 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, plus, 0, equals, 6
Which of these is an example of the identity property of addition?

## Want to join the conversation?

• 2+2+2 = 3+3 Above said this was incorrect selection. Both sides equal 6. The one below has two different answers. Why wouldn't it be this one?
• In the document, It says that how the numbers are grouped does not change the the final answer. This means that while the number stay the same on both sides, the way they are grouped no longer matters.
• This is very simple...
Example:
2+3=3+2
This is the use of the commutative property of addition; for any of you guys who were having trouble.

Now if you want to know how to do the identity property of addition, look at this:
2+0=2
Very easy. :)
• I am in 7th grade and this was somewhat easy. but what is the point of properties of addition?
• Properties of addition help make it easier to solve problems. Think of them as a special trick that lets you "break the rules" and simplify the problem.
• whay does the earth move and we dont
• we do you just don't notice.
• which property should I use if I need a balance that's not negative?
• what is 8x + 7 = 21
• 8x+7=21. Firstly, subtract 7 from both sides. This way you can isolate the variable.
8x=14. Then, divide both sides by 8. This ensures you get just x on one side, so you can have a strict x=?
This comes out to x=7/4, or 1.75