Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×

Commutative Properties Changing the order of the numbers in + or x will not change the result. Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a. Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

Associative Properties Changing the grouping of the numbers in + or x will not change the result. Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

Distributive Property Multiplication distributes over addition. x x

Additive Identity Property There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

Multiplicative Identity Property There exists a unique number 1 such that the number 1 preserves identities under multiplication. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

Additive Inverse Property For each real number a there exists a unique real number –a such that their sum is zero. a + (-a) = 0 In other words opposites add to zero.

Multiplicative Inverse Property For each real number a there exists a unique real number such that their product is 1.

Let’s play “Name that property!”

State the property or properties that justify the following. 3 + 2 = 2 + 3 Commutative Property

State the property or properties that justify the following. 10(1/10) = 1 Multiplicative Inverse Property

State the property or properties that justify the following. 3(11 – 10) = 33 – 30 Distributive Property

State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

Commutative Property of Addition 1. Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

Identity Property of Addition 2. Which Property? 8 + 0 = 8 Identity Property of Addition

Commutative Property of Multiplication 3. Which Property? 6 • 4 = 4 • 6 Commutative Property of Multiplication

Inverse Property of Addition 4. Which Property? 17 + (-17) = 0 Inverse Property of Addition

Commutative Property of Multiplication 5. Which Property? 2(5) = 5(2) Commutative Property of Multiplication

Associative Property of Addition 6. Which Property? (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition

7. Which Property? even + even = even Closure Property

Distributive Property 8. Which Property? 3(2 + 5) = 3•2 + 3•5 Distributive Property

Associative Property of Multiplication 9. Which Property? 6(7•8) = (6•7)8 Associative Property of Multiplication

Identity Property of Multiplication 10. Which Property? 5 • 1 = 5 Identity Property of Multiplication

Identity Property of Addition 11. Which Property? 51/7 + 0 = 51/7 Identity Property of Addition

Distributive Property 12. Which Property? 6(3 – 2) = 18 – 12 Distributive Property

Commutative Property of Addition 13. Which Property? 2 + 3 = 3 + 2 Commutative Property of Addition

Commutative Property of Multiplication 14. Which Property? ab = ba Commutative Property of Multiplication

Identity Property of Addition 15. Which Property? a + 0 = a Identity Property of Addition

Associative Property of Multiplication 16. Which Property? a(bc) = (ab)c Associative Property of Multiplication

Identity Property of Multiplication 17. Which Property? a•1 = a Identity Property of Multiplication

Commutative Property of Addition 18. Which Property? a +b = b + a Commutative Property of Addition

Distributive Property 19. Which Property? a(b + c) = ab + ac Distributive Property

Associative Property of Addition 20. Which Property? a + (b + c) = (a +b) + c Associative Property of Addition

Inverse Property of Addition 21. Which Property? a + (-a) = 0 Inverse Property of Addition

Assignment: Identifying Properties HOMEWORK TIME! Week: 5 Assignment: Identifying Properties Due Date: A day: 08/25/17 - Friday B day: 08/24/17 - Thursday