# Properties of Addition

While math is full of rules that children need to remember, addition has three specific rules called properties. These properties detail how numbers can relate to each other within an addition equation. Children should understand these properties to make addition equations easier to answer.

## Commutative Property

The commutative property simply states that the order of the addends can change in an addition equation, and the answer will remain the same. In simpler language, you can change the order you add numbers without changing the answer. For example: 4 + 6 = 10 and 6 + 4 = 10. It doesn’t matter what order you add the numbers in. The answer will be the same.

## Associative Property

The associative property allows us to group numbers together to make adding simpler. This property tells us that you can change how numbers are grouped together without changing the answer. For example: (7 + 8) + 2 = 17 and 7 + (8 + 2) = 17. (Remember, operations inside parentheses are always completed first.) This is especially helpful when doing mental math problems. In the example above, it is probably easier for students to think of 8 + 2 = 10 first. Then they can just add on the 7 to make 17.

## Identity Property

The identity property tells us that when 0 is added to any number, the number remains the same. While this seems obvious to us, it is an important rule for children to learn. It should become automatic that when they see 7 + 0, they know the answer is still 7. This will be especially helpful as their math problems become larger and more difficult.

Take some time to go over these rules with your child. Make sure they understand the properties of addition and can use them in addition equations. Understanding these properties will be a big help to them as they continue to learn more about how numbers work. Do you teach your children about the properties of addition?

Photo by: Alan Cleaver