2. PROPERTIES OF REAL NUMBERS

4. Commutative Property Associative Property Distributive Property Identity Property + x Inverse Property + X

6. Changing the order of the numbers in addition or multiplication will not change the result.

7. Commutative Property of Addition states Commutative Property of Multiplication states

8. 1 + 2= __ + 1 4. _ = 5. 4 _ + 9 = 9 + 1 2. 7 = 7. _

10. Changing the grouping of the numbers in addition or multiplication will not change the result.

11. Associative Property of Addition states 3 + (4 + 5)= (3 + 4)+ 5 Associative Property of Multiplication states 3 x(4 x 5)= (3 x 4)x 5

12. 3 + (7 + 5) 5 X (11 X 2) 1 + (2 + 7)

13. Multiplication distributes over addition.

15. There exists a unique number 0 such that zero preserves identities under addition.

16. a + 0 = a and 0 + a = a In other words adding zero to a number does not change its value.

17. There exists a unique number 1 such that the number 1 preserves identities under multiplication.

18. a ∙ 1 = a and 1 ∙ a = a In other words multiplying a number by 1 does not change the value of the number.

19. ADDITITIVE IDENTITY PROPERTY MULTIPLICATIVE IDENTITY PROPERTY a + 0 = a 0 + a = a a ∙ 1 = a 1 ∙ a = a

20. 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.

21. For each real number a there exists a unique real number such that their product is 1.

23. Let’s play “Name that property!”

24. PROPERTIES OF REAL NUMBERS Commutative Property Associative Property Distributive Property Identity Property + x Inverse Property + X Closure Property

25. STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 3 + 2 = 2 + 3 Commutative Property

26. STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 10(1/10) = 1 Multiplicative Inverse Property

27. STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 3(x – 10) = 3x – 30 Distributive Property

28. STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

29. STATE THE PROPERTY OR PROPERTIES THAT JUSTIFY THE FOLLOWING. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

30. 3 + 7 = 7 + 3 Commutative Property of Addition 2.

31. 8 + 0 = 8 Identity Property of Addition 3.

32. 6 4 = 4 6 Commutative Property of Multiplication 5.

33. 17 + (-17) = 0 Inverse Property of Addition 6.

34. 2(5) = 5(2) Commutative Property of Multiplication 7.

35. (2 + 1) + 4 = 2 + (1 + 4) Associative Property of Addition 1.

36. even + even = even Closure Property 8.

37. 3(2 + 5) = 32 + 35 Distributive Property 9.

38. 6(78) = (67)8 Associative Property of Multiplication 10.

39. 5 1 = 5 Identity Property of Multiplication 11.

40. PROPERTIES OF REAL NUMBERS Commutative Property Associative Property Distributive Property Identity Property + x Inverse Property + X Closure Property