The properties of real numbers help us simplify math expressions and help us better understand the concepts of algebra.

Commutative Properties Numbers can be added or multiplied in any order. a + b = b + a = a × b = b × a 2 x 6 = 6 x 2 Why is this important? $ $ $ $ x 12 x 5

Does Commutative Property work with Subtraction? = Does Commutative Property work with Division? 50 ÷ 10 = 10 ÷ 50

Identity Properties Identity property of addition - the sum of zero and any number or variable is the number or variable itself. When you add 0 to any number, it will always keep its identity!!!! = 5A + 0 = A

Identity property of multiplication - the product of 1 and any number or variable is the number or variable itself. 5 X 1= 5B x 1 = B Identity Properties

Associative Properties The associative property of addition - when adding more than two numbers the grouping of the numbers does not change the sum. (a + b) + c = a + (b + c) Example: ( ) + 7 = 29 + (13 + 7) Notice how adding the first makes completing the problem easier mentally

The associative property of multiplication - when multiplying more than two numbers the grouping of the factors does not change the product. (a x b) x c = a x (b x c) Example: (6 x 4) x 5 = 6 x (4 x 5) Notice how multiplying the 4 and 5 first makes completing the problem easier. Associative Properties

Distributive Properties The distributive property lets you multiply a sum by multiplying each number separately and then add the products.

4 ( 45)= 4 (40) + 4(5) 20(13)=