2. Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties 5.Inverse Properties 6.Distributive Property

3. On Tab 2: Commutative Properties  Changing the order of the numbers in addition or multiplication 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 a b = b a.

4. On Tab 3: Associative Properties  Changing the grouping of the numbers in addition or multiplication 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 (a b) c = a (b c)

5. On Tab 4: Identity Properties  Adding zero to a number does not change its value. 2 + 0 = 2 & 0 + 2 = 2 a + 0 = a & 0 + a = a  Multiplying a number by 1 does not change the value of the number. 5 ∙ 1 = 5 & 1 ∙ 5 = 5 a ∙ 1 = a & 1 ∙ a = a Addition Multiplication

6. On Tab 5: Inverse Properties  Opposites add to zero. 3 + -3 = 0 a + (-a) = 0  A number multiplied by its reciprocal is always 1. Addition Multiplication

7. On Tab 6: Distributive Property  Multiplication distributes over addition & subtraction.

8. Let’s play “Name that property!”

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

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

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

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

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

14. (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

15. 3 + 7 = 7 + 3 Commutative Property of Addition 2.

16. 8 + 0 = 8 Identity Property of Addition 3.

17. 6 4 = 4 6 Commutative Property of Multiplication 5.

18. 17 + (-17) = 0 Inverse Property of Addition 6.

19. 2(5) = 5(2) Commutative Property of Multiplication 7.

20. even + even = even Closure Property 8.

21. 3(2 + 5) = 32 + 35 Distributive Property 9.

22. 6(78) = (67)8 Associative Property of Multiplication 10.

23. 5 1 = 5 Identity Property of Multiplication 11.

25. 6(3 – 2n) = 18 – 12n Distributive Property 12.

26. 2x + 3 = 3 + 2x Commutative Property of Addition 13.

27. ab = ba Commutative Property of Multiplication 14.

28. a + 0 = a Identity Property of Addition 15.

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

30. a1 = a Identity Property of Multiplication 17.

31. a +b = b + a Commutative Property of Addition 18.

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

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

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

35. Properties of Real Numbers 1.Objective: To apply the properties of operations. 2.Commutative Properties 3.Associative Properties 4.Identity Properties 5.Inverse Properties 6.Distributive Property