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Math Help - Properties of Real Numbers

  1. #1
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    Properties of Real Numbers

    This is a reference chart for anyone who needs to review algebra 1 real number properties or use in class.

    Property (a, b and c are real numbers, variables or algebraic expressions)

    Distributive Property
    a • (b + c) = a • b + a • c
    Sample
    3 • (4 + 5) = 3 • 4 + 3 • 5

    Commutative Property of Addition
    a + b = b + a
    Sample
    3 + 4 = 4 + 3

    Commutative Property of Multiplication
    a • b = b • a
    Sample
    3 • 4 = 4 • 3

    Associative Property of Addition
    a + (b + c) = (a + b) + c
    Sample
    3 + (4 + 5) = (3 + 4) + 5

    Associative Property of Multiplication
    a • (b • c) = (a • b) • c
    Sample
    3 • (4 • 5) = (3 • 4) • 5

    Additive Identity Property
    a + 0 = a
    Sample
    4 + 0 = 4

    Multiplicative Identity Property
    a • 1 = a
    Sample
    4 • 1 = 4

    Additive Inverse Property
    a + (-a) = 0
    Sample
    4 + (-4) = 0

    Multiplicative Inverse Property
    a(1/a), where a cannot be zero.
    Sample
    2(1/2) = 1

    Zero Property of Multiplication
    a • 0 = 0
    Sample
    4 • 0 = 0

    Closure Property of Addition
    a + b is a real number
    Sample
    10 + 5 = 15 (a real number)

    Closure Property of Multiplication
    a • b is a real number
    Sample
    10 • 5 = 50 (a real number)

    Addition Property of Equality
    If a = b, then a + c = b + c.
    Sample
    If x = 10,
    then x + 3 = 10 + 3

    Subtraction Property of Equality
    If a = b, then a - c = b - c.
    Sample
    If x = 10,
    then x - 3 = 10 - 3

    Multiplication Property of Equality
    If a = b, then a • c = b • c.
    Sample
    If x = 10,
    then x • 3 = 10 • 3

    Division Property of Equality
    If a = b, then a / c = b / c,
    assuming c ≠ 0.
    Sample
    If x = 10,
    then x / 3 = 10 / 3

    Substitution Property
    If a = b, then a may be substituted for b, or conversely.
    Sample
    If x = 5, and x + y = z,
    then 5 + y = z.

    Reflexive (or Identity) Property of Equality
    a = a
    Sample
    12 = 12

    Symmetric Property of Equality
    If a = b, then b = a.
    Sample
    If 3 = 3*1, then 3*1 = 3

    Transitive Property of Equality
    If a = b and b = c,
    then a = c.
    Sample
    If 2a = 10 and 10 = 4b,
    then 2a = 4b.

    Law of Trichotomy
    Exactly ONE of the following holds:
    a < b, a = b, a > b
    Sample
    If 8 > 6, then 8 6 and
    8 is not < 6.
    Last edited by nycmath; March 14th 2014 at 03:53 PM. Reason: Extend Title
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  2. #2
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    Re: Properties of Real Numbers

    Is there a question in all of that?
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    Re: Properties of Real Numbers

    Plato,

    This is a reference chart for anyone who needs to review algebra 1 real number properties or use in class.
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    Re: Properties of Real Numbers

    Those "properties" are all true of the rational numbers as well as the real numbers. To specifically talk about the real numbers you have to add a "completeness property": if a set of real numbers has an upper bound then it has a least upper bound.
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    Re: Properties of Real Numbers

    Quote Originally Posted by HallsofIvy View Post
    Those "properties" are all true of the rational numbers as well as the real numbers. To specifically talk about the real numbers you have to add a "completeness property": if a set of real numbers has an upper bound then it has a least upper bound.
    This is a reference chart for anyone who wants or needs to quickly review algebra 1 properties. It is not my intention to tutor or teach properties of real numbers.
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