Lesson
Properties of Real Numbers
Save
Edit
Instructor-led session
Live lessonStart a live lesson
Asynchronous learning
AssignAssign homework
56 slides PreviewShow answers
• Slide 1
Report an issue

Properties of Real Numbers

Text
• Slide 2
Report an issue

What is a real number?

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

• Question 3
30 seconds
Report an issue
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
Report an issue

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
Report an issue

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
Report an issue
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
30 seconds
Report an issue
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
30 seconds
Report an issue
Q.

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

answer choices

True

False

• Slide 9
Report an issue

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
Report an issue

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

• Slide 11
Report an issue
1. Distributive Property

a • (b + c) = a • b + a • c

• "multiplication distributes across addition"

• 3 • (4 + 5) = 3 • 4 + 3 • 5

• Slide 12
Report an issue

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
Report an issue

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
30 seconds
Report an issue
Q.

8 + 4 = 12, so 4+8 =

answer choices

12

3

4

14

• Question 15
30 seconds
Report an issue
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
30 seconds
Report an issue
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
30 seconds
Report an issue
Q.

3 x ____ = 9 x 3

answer choices

7

9

27

11

• Question 18
30 seconds
Report an issue
Q.

What is the missing number?

6 + ____ = 7 + 6

answer choices

4

13

7

9

• Slide 19
Report an issue

4. Associative Property of Addition

+ (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
Report an issue

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
30 seconds
Report an issue
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
30 seconds
Report an issue
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
30 seconds
Report an issue
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
30 seconds
Report an issue
Q.

What is the missing number?

5 × (__× 9) = (5 × 8) × 9

answer choices

5

360

8

9

• Question 25
30 seconds
Report an issue
Q.

What is the missing number?

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

answer choices

4

5

16

7

• Question 26
30 seconds
Report an issue
Q.

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

answer choices

10

12

13

14

• Slide 27
Report an issue

6. Additive Identity Property

a + 0 = a

• "the value that returns the input unchanged"

• 4 + 0 = 4

• Slide 28
Report an issue

7. Multiplicative Identity Property

a • 1 = a

• "the value that returns the input unchanged"

• 4 • 1 = 4

• Question 29
30 seconds
Report an issue
Q.

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

answer choices

Multiplication

Addition

Division

Subtraction

Mouctar

• Question 30
30 seconds
Report an issue
Q.

When using identity property the identity number always changes ?

answer choices

True

False

Split

...

• Question 31
30 seconds
Report an issue
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
Report an issue
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
Report an issue
Q. Identify the property
a + b = b + a
answer choices
Identity of addtion
commutative of addition
associative of addition
symmetric
• Slide 34
Report an issue

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
Report an issue

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
Report an issue

Addition Property of Equality

If a = b, then a + c = b + c.

If x = 10,

then + 3 = 10 + 3

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

• Slide 37
Report an issue

Subtraction Property of Equality

If a = b, then a - c = b - c.

If x = 10,

then - 3 = 10 - 3

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

• Slide 38
Report an issue

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
Report an issue

Division Property of Equality

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

If x = 10,

then / 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
Report an issue

Reflexive (or Identity) Property of Equality

a = a

12 = 12

"a real number is always

equal to itself"

• Slide 41
Report an issue

Reflexive (or Identity) Property of Equality

If a = b, then b = a.

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

• Slide 42
Report an issue

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
Report an issue

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 ba is either equal to b, greater than b, or less than b." (common sense)

• Slide 44
Report an issue

Reflexive (or Identity) Property of Equality

a = a

12 = 12

"a real number is always

equal to itself"

• Slide 45
Report an issue

Quiz

Text
• Question 46
30 seconds
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue
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
Report an issue

Questions?

Text
Report an issue
Why show ads?
Report Ad
Enter Code