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

2. Commutative Properties Numbers can be added or multiplied in any order. a + b = b + a 1 + 3 = 3 + 1 a × b = b × a 2 x 6 = 6 x 2 Why is this important? 15 + 7 + 5 $4. 30 + $10.50 + $0.70 + $0.50 6 x 12 x 5

3. Does Commutative Property work with Subtraction? 10 - 5 = 5 - 10 Does Commutative Property work with Division? 50 ÷ 10 = 10 ÷ 50

4. 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!!!! 5 + 0 = 5A + 0 = A

5. 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

6. 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: (29 + 13) + 7 = 29 + (13 + 7) Notice how adding the 13 + 7 first makes completing the problem easier mentally

7. 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

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

9. 4 ( 45)= 4 (40) + 4(5) 20(13)=