Lesson
Properties of Real Numbers
7th - 9th grade
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Mathematics
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maclaraguia_legarte_04962
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  • Slide 1
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    Properties of Real Numbers

    Text
  • Slide 2
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    What is a real number?

    A real number is a value that represents a quantity along a continuous number line.

  • Question 3
    30 seconds
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    Q.

    Which is not true about real numbers?

    answer choices

    Real numbers can be ordered.

    The symbol for the set of real numbers is R, which is the letter R in the typeface "blackboard bold".

    They are not irrational numbers

  • Slide 4
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    Concepts about real numbers

    • Real numbers can be ordered. 
    • The symbol for the set of real numbers is , which is the letter R in the typeface "blackboard bold".
  • Slide 5
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    The numbers of Real numbers

    • counting (natural) numbers (){1, 2, 3, ... }
    • whole numbers {0, 1, 2, 3, ... }
    • integers (){... , -3, -2, -1, 0, 1, 2, 3, ...}
    • rational numbers () (such as -½, 6.25, )
    •  and irrational numbers



    FYI: The series of three dots ( ... ), seen within the sets above, is called an ellipsis.

    As used in mathematics, the ellipsis means "and so forth".

  • Question 6
    30 seconds
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    Q.

    The properties of the Real Number System will prove useful when working with equations, functions and formulas in Algebra.

    answer choices

    True

    False

  • Question 7
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    Q.

    The properties of real numbers, does not allow the creation of equivalent expressions which will often aid in solving problems.

    answer choices

    True

    False

  • Question 8
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    Q.

    In addition, they can be used to help explain or justify solutions.

    answer choices

    True

    False

  • Slide 9
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    Concepts about real numbers

    • will prove useful when working with equations, functions and formulas in Algebra,
    • as they allow for the creation of equivalent expressions which will often aid in solving problems.
    • In addition, they can be used to help explain or justify solutions.
  • Slide 10
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    Property (a, b and c are real numbers, variables or algebraic expressions)


  • Slide 11
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    1. Distributive Property

    a • (b + c) = a • b + a • c

    • "multiplication distributes across addition"

    • 3 • (4 + 5) = 3 • 4 + 3 • 5

  • Slide 12
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    2. Commutative Property of Addition

    a + b = b + a

    • "commute = to get up and move to a new location : switch places"

    • 3 + 4 = 4 + 3

  • Slide 13
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    3. Commutative Property of Multiplication

    a • b = b • a

    • "commute = to get up and move to a new location: switch places"

    • 3 • 4 = 4 • 3

  • Question 14
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    Q.

    8 + 4 = 12, so 4+8 =

    answer choices

    12

    3

    4

    14

  • Question 15
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    Q.

    Which of the following illustrates the Commutative Law of Multiplication?

    answer choices

    3 x 4 = 6 x 2

    3 x 4 = 12 x 1

    3 x 4 = 2 x 6

    3 x 4 = 4 x 3

  • Question 16
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    Q.

    Which one of the following illustrates the Commutative Law of Addition?

    answer choices

    5 + 7 = 7 + 5

    5 + 7 = 4 + 8

    5 + 7 = 3 + 9

    5 + 7 = 10 + 2

  • Question 17
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    Q.

    3 x ____ = 9 x 3

    answer choices

    7

    9

    27

    11

  • Question 18
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    Q.

    What is the missing number?


    6 + ____ = 7 + 6

    answer choices

    4

    13

    7

    9

  • Slide 19
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    4. Associative Property of Addition

    a + (b + c) = (a + b) + c

    • "regroup - elements do not physically move, they simply group with a new friend."

    • 3 + (4 + 5) = (3 + 4) + 5

  • Slide 20
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    5. Associative Property of Multiplication

    a • (b • c) = (a • b) • c

    • "regroup - elements do not physically move, they simply group with a new friend."

    • 3 • (4 • 5) = (3 • 4) • 5

  • Question 21
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    Q.

    Which of the following illustrates the Associative Law of multiplication?

    answer choices

    4 × (3 × 6) = (3 × 12) × 2

    4 × (3 × 6) = (6 × 6) × 2

    4 × (3 × 6) = (4 × 3) × 6

    4 × (3 × 6) = (3 × 8) × 3

  • Question 22
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    Q.

    Which one of the following illustrates the Associative Law of addition?

    answer choices

    3 + ( 2 + 4) = (4 + 4) + 1

    3 + (2 + 4) = (3 + 2) + 4

    3 + (2 + 4) = (5 + 2) + 2

    3 + (2 + 4) = (2 + 6) + 1

  • Question 23
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    Q.

    5 × (2 × 9) is also equal to:

    answer choices

    5 x (2 - 9)

    5 x (2 + 9)

    (5 x 2) x 9

    (5 x 2) + 9

  • Question 24
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    Q.

    What is the missing number?


    5 × (__× 9) = (5 × 8) × 9

    answer choices

    5

    360

    8

    9

  • Question 25
    30 seconds
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    Q.

    What is the missing number?


    4 + (____ + 5) = (4 + 7) + 5

    answer choices

    4

    5

    16

    7

  • Question 26
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    Q.

    7 + (4 + 2) = 13, so (7 + 4) + 2

    answer choices

    10

    12

    13

    14

  • Slide 27
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    6. Additive Identity Property

    a + 0 = a


    • "the value that returns the input unchanged"

    • 4 + 0 = 4

  • Slide 28
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    7. Multiplicative Identity Property

    a • 1 = a

    • "the value that returns the input unchanged"

    • 4 • 1 = 4

  • Question 29
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    Q.

    Which operation doesn't fully apply to the Identity Property ?

    answer choices

    Multiplication

    Addition

    Division

    Subtraction

    Mouctar

  • Question 30
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    Q.

    When using identity property the identity number always changes ?

    answer choices

    True

    False

    Split

    ...

  • Question 31
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    Q. Pick the answer that is an example of the identity property of addtion
    answer choices
    a + (-a) = 0
    1 + 1 = 2
    a + 0 = a
    a + b = b + a
  • Question 32
    20 seconds
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    Q.

    Identify the property

    a + 0 = a

    answer choices

    identity property of addition

    identity property of multiplication

    inverse property of addition

    multiplication property of zero

  • Question 33
    20 seconds
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    Q. Identify the property
    a + b = b + a
    answer choices
    Identity of addtion
    commutative of addition
    associative of addition
    symmetric
  • Slide 34
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    Closure Property of Addition

    a + b is a real number

    10 + 5 = 15 (a real number)


    "the sum of any two real numbers

    is another real number"



  • Slide 35
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    Closure Property of Multiplication

    a • b is a real number


    10 • 5 = 50 (a real number)


    "the product of any two real numbers is another real number"


  • Slide 36
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    Addition Property of Equality

    If a = b, then a + c = b + c.


    If x = 10,

    then x + 3 = 10 + 3


    "adding the same value to both sides of an equation will not change the truth value of the equation."

  • Slide 37
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    Subtraction Property of Equality


    If a = b, then a - c = b - c.


    If x = 10,

    then x - 3 = 10 - 3


    "subtracting the same value from both sides of an equation will not change the truth value of the equation."

  • Slide 38
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    Multiplication Property of Equality


    If a = b, then a • c = b • c.


    If x = 10,

    then x • 3 = 10 • 3


    "multiplying both sides of an equation by the same value will not change the truth value of the equation."

  • Slide 39
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    Division Property of Equality


    If a = b, then a / c = b / c, assuming c ≠ 0.


    If x = 10,

    then x / 3 = 10 / 3


    "dividing both sides of an equation by the same non-zero value will not change truth value of the equation."

  • Slide 40
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    Reflexive (or Identity) Property of Equality


    a = a


    12 = 12


    "a real number is always

    equal to itself"

  • Slide 41
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    Reflexive (or Identity) Property of Equality

    If a = b, then b = a.


    "quantities that are equal can be read forward or backward"

  • Slide 42
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    Transitive Property of Equality

    If a = b and b = c,then a = c.


    If 2a = 10 and 10 = 4b,

    then 2a = 4b.


    "if two numbers are equal to the same number, then the two numbers are equal to each other"

  • Slide 43
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    Law of Trichotomy

    Exactly ONE of the following holds:

     a < b, a = b, a > b


    If 8 > 6, then 8  6 and

    8 is not < 6.


    "for two real numbers a and b, a is either equal to b, greater than b, or less than b." (common sense)

  • Slide 44
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    Reflexive (or Identity) Property of Equality


    a = a


    12 = 12


    "a real number is always

    equal to itself"

  • Slide 45
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    Quiz

    Text
  • Question 46
    30 seconds
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    Q.

    It refers to "the value that brings you back to the identity element under addition"

    answer choices

    Associative Property

    Inverse Property

    Identity Property

    Distributive Property

  • Question 47
    30 seconds
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    Q.

    It refers to "multiplication distributes across addition".

    answer choices

    Distributive Property

    Commutative Property of Addition

    Commutative Property of Multiplication

    Associative Property of Addition

  • Question 48
    30 seconds
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    Q.

    It refers to "commute = to get up and move to a new location : switch places"

    answer choices

    Distributive Property

    Commutative Property

    Inverse Property

    Associative Property

  • Question 49
    30 seconds
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    Q.

    It refers to"regroup - elements do not physically move, they simply group with a new friend."

    answer choices

    Distributive Property

    Commutative Property of Addition

    Commutative Property of Multiplication

    Associative Property of Addition

  • Question 50
    30 seconds
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    Q.

    It refers to "the value that returns the input unchanged"

    answer choices

    Inverse Property

    Inverse Property

    Identity Property

    Commutative Property

  • Question 51
    30 seconds
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    Q.

    It refers to "for two real numbers a and b, a is either equal to b, greater than b, or less than b."

    answer choices

    Transitive Property

    Symmetric Property

    Law of Trichotomy

    Substitution Property

  • Question 52
    30 seconds
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    Q.

    It refers to "if two numbers are equal to the same number, then the two numbers are equal to each other"

    answer choices

    Transitive Property

    Symmetric Property

    Law of Trichotomy

    Substitution Property

  • Question 53
    30 seconds
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    Q.

    It refers to "quantities that are equal can be read forward or backward"

    answer choices

    Transitive Property

    Symmetric Property

    Law of Trichotomy

    Substitution Property

  • Question 54
    30 seconds
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    Q.

    It refers to "a value may be substituted for its equal."

    answer choices

    Transitive Property

    Symmetric Property

    Law of Trichotomy

    Substitution Property

  • Question 55
    30 seconds
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    Q.

    It refers to "the product of any two real numbers is another real number"

    answer choices

    Multiplicative Identity Property

    Multiplicative Inverse Property

    Closure Property of Multiplication

    Multiplication Property of Equality

  • Slide 56
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    Questions?

    Text
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