## Properties of Addition

### Properties of Addition: Learn

There are four mathematical properties which involve addition. The properties are the commutative, associative, identity and distributive properties.

**Commutative Property**: When two numbers are added, the sum is the same regardless of the order of the addends.

For example 4 + 2 = 2 + 4

To remember the commutative property, it might be helpful to think about the
word *commute* which means to switch places between home and work
(or home and school). In the example above, you can see the 4 and the 2
*commuting* or switching places.

**Associative Property**: When three or more numbers are added, the sum is the same regardless of the grouping of the addends.

For example (2 + 3) + 4 = 2 + (3 + 4)

To remember the associative property, it might be helpful to think about the
word *associate*, which as a verb means to interact with a group (maybe
you associate with a certain group of friends!). The parentheses are
*grouping* operators, that is, they form groups of numbers and
operations. You can see in the example above, the 3 can associate with
either the 2 or the 4, but the value of each side is still a total of 9.

**Identity Property**: The sum of any number and zero is the original number.

For example 5 + 0 = 5.

To remember the identity property, it might be helpful to think of it as a question and answer: What number can I add so that the value is not changed? Zero. In the example above, the 5 gets to keep its identity because adding zero does not change its value.

**Distributive Property**: The sum of two numbers times a third number is equal to the sum of each addend times the third number.

For example 4 * (6 + 3) = 4*6 + 4*3

The distributive property is the only property that combines multiplication and addition.
That makes it *very* important!

### Properties of Addition: Practice

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