1. PROPERTIES USED IN ALGEBRA

2. What are they? ■Commutative Property ■Associative Property ■Identity Property ■Distributive Property ■Inverse Property

3. Why learn about these properties? By knowing each of these properties, it will give you more strategies for solving numeric and algebraic expressions using mental math!

4. Commutative Property ■Property of addition ■a + b = b +a Examples: 1) 3+2 = 2+3 5 = 5 2) 4+5 = 5+4 9 = 9 ■Property of multiplication ■ab = ba Examples: 1) (2)(3) = (3)(2) 6 = 6 2) 4(5) = (5)(4) 20 = 20 Comes from the word “commute” or to move around! Think of the numbers rearranging themselves from one side of the equation to the other!

5. Associative Property ■Property of Addition ■a + (b + c) = (a + b) + c Example: 3 + (2 + 5) = (3 + 2) + 5 3 + 7 = 5 + 5 10 = 10 Comes from the word “associate” or to group together! Think of different ways you could regroup the numbers in order to solve the problem in your head easier! Property of Multiplication a(bc) = (ab)c Example: (3 x 2)4 = 3(2 x 4) (6)4 = 3(8) 24 = 24

6. Distributive Property ■Property of addition ■a (b + c) = ab +ac Example: 6( 3 + 2) = 6(3) + 6(2) 6(5) = 18 + 12 30 = 30 ■Property of multiplication ■a (b – c) = ab - ac Example: 5 (4 – 2) = 5(4) – 5(2) 5(2) = 20 - 10 10 = 10 Comes from the word “distribute” or to give out! The multiplication distributes among the addition or subtraction! Think about distributing the outside integer to the integers within the parathesis!

7. Identity Property ■Property of Multiplication ■a x 1 = a –Simply just multiply by 1 to keep a the same Example: 5 x 1 = 5 ■Property of Addition –a + 0 = a –Simply just add zero to keep a the same Example: 6 + 0 = 6 Your identity is who you are. The same is true with this property. It is to add or multiply the integer that will keep the original number the same (or keep its identity).

8. Inverse Property ■Property of Multiplication ■a x 1/a = 1 Example: 3 x 1/3 = 3/3 = 1 ■Property of Addition ■a + -a = 0 Example: 4 + -4 = 0 Inverse means opposite! When you multiply an integer by its opposite, you will ALWAYS get 1. When you add an integer by its opposite, you will ALWAYS get 0.