Properties Of  Mathematics 2007
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Properties Of Mathematics 2007

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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......

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.

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  • 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