This presentation is set up that math properties are linked with music. There is a front slide for each property so you do not have to show the entire presentation at once. It can be shown in segments.

1. Properties of Mathematics Everything you need to know and more……

2. Properties of Mathematics Operations and Properties

3. Properties of Mathematics No, not these operations!!!

4. Properties of Mathematics These operations….of NUMBERS!!!! Addition Subtraction Multiplication Division

5. Properties of Mathematics No, not these properties!!!

6. Properties of Mathematics These properties…….of NUMBERS!!!! Associative Property of Multiplication Commutative Property of Multiplication Identity Property of Multiplication Inverse Property of Multiplication Multiplicative Property of Zero Multiplicative Property of -1 Associative Property of Addition Commutative Property of Addition Identity Property of Addition Inverse Property of Addition Substitution Property Distributive Property Reflexive Property Symmetric Property Transitive Property Addition Property Subtraction Property Multiplication Property Division Property

7. Properties of Mathematics Hmmmmm….…What’s the difference between…… operations of NUMBERS and properties of NUMBERS ???? and OPERATION of numbers…. is the WAY we calculate numbers…… (add, subtract, multiply, & divide) PROPERTIES of numbers…. are the METHODS we use to calculatenumbers…… WAY METHODS

8. Properties of Mathematics So Let’s get started.… PROPERTIES OF NUMBERS

9. Properties of Mathematics Addition, Subtraction, Multiplication & Division Properties

10. Properties of Mathematics When you have each side of an expression equal to the other side, you can add, subtract, multiply or divide the SAME number on each side and not change the equalities. Addition Property a = b a + c = b + c Subtraction Property a = b a - c = b - c Multiplication Property a = b a ∙ c = b ∙ c Division Property a = b, (c ≠ 0) =

11. Properties of Mathematics Addition Property Subtraction Property 1 = 1 1 +5= 1 +5 6 = 6 1 = 1 1 - 5= 1 - 5 -4 = -4 Multiplication Property Division Property 2 = 2 2 ∙ 5= 2 ∙ 5 10 = 10 10 = 10 10 ÷ 5= 10 ÷ 5 6 = 6

12. Properties of Mathematics IDENTITY PROPERTIES

13. Properties of Mathematics The Identity Property Addition a + 0 = a Multiplication a ∙ 1 = a

14. Addition 5 + 0 = 5 Multiplication 5 ∙ 1 = 5 Properties of Mathematics The Identity Property

15. Properties of Mathematics REFLEXIVE PROPERTY

16. Properties of Mathematics a = a Reflexive Property 1=1 9x=9x x + y=x + y 3(x-2)= 3(x-2)

17. Properties of Mathematics SYMMETRIC PROPERTY

18. The Symmetric property is an equality relationship that switches one expression on one side of an equation to the other side. (note: keep expressions exactly “as is” .) a + b = c c = a + b Properties of Mathematics Symmetric Property 9 - 5=4 5=9 - 4 5=9 - 4 9-4=5

19. Properties of Mathematics COMMUTATIVE PROPERTY

20. The Commutative property of addition or multiplication changes the “position of a term” on one side of an expression. AdditionMultiplication Properties of Mathematics Commutative Property a ∙ = ∙ b b a b + = + b a a a b b a

21. ADDITION3 + 8=11 8 + 3=11 11=11 MULTIPLICATION2∙5∙ 4 =40 5 ∙ 2∙ 4 =40 40=40 Properties of Mathematics Commutative Property

22. Properties of Mathematics ASSOCIATIVE PROPERTIES

23. Properties of Mathematics The Associative property ASSOCIATES (groups) terms of numbers or variables with other terms using parentheses. (notice: original term positions never change) ADDITIONa+(b+ c)=(a+b)+ c MULTIPLICATION(a∙b) c =a (b∙ c) Associative Property

24. Properties of Mathematics ADDITION MULTIPLICATION Associative Property 1+(7+ 5)=( 1+5)+ 7 1+(12)=(6)+ 7 13=13 (1∙7) 5 =1 (7∙ 5) (7) 5 =1 (35) 35=35

25. Properties of Mathematics INVERSE PROPERTY OF ADDITION

26. Properties of Mathematics The Inverse property of multiplication cancels out a number or variable by the using the “inverse” or “opposite” operation of the number or variable. a + -a = 0 Inverse Property of Addition = 0 1 + -1 -7 + 7

27. Properties of Mathematics INVERSE PROPERTY OF MULTIPLICATION

28. Properties of Mathematics The Inverse property of multiplication “cancels out” a number or variable by the using the “inverse” or “opposite” operation of the number or variable and gives a new value of “1”. Inverse Property of Multiplication a ∙ = 1

29. Properties of Mathematics Inverse Property of Multiplication = = 1 3x∙ 5∙ = = 1 ∙.52 = = 1 ∙ = = 1 a ∙ = 1

30. Properties of Mathematics Multiplicative Property of Zero Multiplicative Property of -1

31. Any number or variable multiplied by zero will become zero. Any number or variable multiplied by -1 will become the “opposite sign” of that number or variable. Properties of Mathematics Multiplicative Property of Zero a ∙ 0 = 0 7 ∙ 0 = 0 0 x = 0 0 = 0 ∙ 5y Multiplicative Property of -1 a ∙ -1 = -a 7 ∙ -1 = -7 -5y ∙ -1 = 5y -1 ∙ 3= -3

32. Properties of Mathematics DISTRIBUTIVE PROPERTY

33. The distributive property “distributes”(multiplies) a number or variable “among” the other terms in the parentheses. (multiply) a(b + c) = ab + ac Or reverse….. ab + ac = a(b + c) Properties of Mathematics Distributive Property

34. 5(x + 2) = 5(x) + 5(2) 5(x + 2) = 5x + 10 Or reverse….. 3x + 3y = 3(x+ y) Properties of Mathematics Distributive Property

35. Properties of Mathematics SUBSTITUTION PROPERTY

36. Properties of Mathematics The Substitution property “takes the place of” some number, variable or term for something else in your mathematical expression. Substitution Property =b a b + c = d a

37. Properties of Mathematics Substitution Property x = 4 4 2x + 5 = ? 2 ( ) 4 + 5 = ? 8 + 5 = ? 13 = 13

38. Properties of Mathematics TRANSITIVE PROPERTY

39. The Commutative property of addition or multiplication changes the “position of a term” on one side of an expression. Properties of Mathematics Transitive Property c a c b a = = = b

40. Properties of Mathematics Transitive Property = 17 8 + y = Z - 5 17 8 + y Z - 5 =

41. http://streaming.discoveryeducation.com/images/assetDetail/button_download.gif http://streaming.discoveryeducation.com/images/assetDetail/button_download.gif Properties of Mathematics Acknowledgements