# Math Properties

/These are a few of the key Math Properties that are the foundation of middle school math.

**Math Properties**

**Commutative Property of Addition** - When numbers are added the order of the numbers does not change the sum

Ex. 2 + 3 = 3 + 2

**Commutative Property of Multiplication** - When numbers are being multiplied, the order of the numbers does not change the product.

Ex. 5 x 4 = 4 x 5

**Identity Property of Addition** - What can you add to "5" so that the sum is "5"? Zero of course.

Ex. 5 + 0 = 5

**Identity Property of Multiplication**- What can you multiply to "10" so that the product is "10"? One!

Ex. 10 x 1 = 10

**Associative Property of Addition** - If you have a series of numbers you are adding, you can group them any way you like and the sum will be the same.

Ex. 2 + (4 + 5) = (2 + 4) + 5

**Associative Property of Multiplication** - If you have a series of numbers you are multiplying, you can group them any way you like and the product will be the same.

Ex. 2 (3 x 7) = (2 x 3) x 7

**Inverse Property of Addition** - The inverse is the opposite of a number. When you add the inverse of a number you will always get Zero.

Example: 4 + -4 = 0

**Inverse Property of Multiplication** - When you multiply a number by its inverse you will always get a one.

Example: 5 x 1/5 = 1

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

Example. 5 (4 + 6) = (5 x 4) + (5 x 6)

**Multiplication Property of zero** - The product of any number and 0 (zero) will always be 0 (zero)