Algebraic Properties

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Algebraic Properties!
Grade Level 8th Grade Course Algebra 1 Subject
Algebraic Properties of Identity and
Equality Created by Miss Au
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Goals

• At the end of the lesson you will be able to
• Recognize and use the properties of identity and
  equality, nine times out of ten.
• Use the Distributive Property to evaluate and
  simplify expressions ninety percent of the time.
• Recognize and use the Commutative and Associative
  Properties nine times out of ten.

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They will help you navigate through the lesson!
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Main Menu
Lesson One Identity Properties Lesson Two
Equality Properties Lesson Three The
Distributive Property Lesson Four Commutative
and Associative Properties Fun Quiz Take this
fun quiz to test your skills in using Algebraic
Properties!
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Identity Properties
First we will talk about the additive identity.
You already know that the sum of any number and
0 is equal to the number. What you may not have
known is that this means that 0 is called the
additive identity.
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Additive Identity Key Concept
This table summarizes the key idea of the
additive identity.
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Multiplicative Identity
Lets move on to multiplication. You already
know that 4 1 4. And you know that the
product of any number and 1 is equal to the
number. Did you know that there is a name for
that? 1 is called the multiplicative identity.
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Multiplicative Property of Zero
Take a look at this equation. 6 m 0 The
value of m is 0. You know that the product of
any number and 0 is equal to 0. The name for
this is the Multiplicative Property of Zero.
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Multiplicative Inverses
? 8 1 Two numbers whose product is 1 are
called multiplicative inverses or reciprocals.
Zero has no reciprocal because 0 times any
number is 0.
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Multiplication Properties Key Concepts
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Lesson 2. 2. Stick around and continue to glean
knowledge from Lesson 1. Choose wisely!
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Reflexive Property
Lets talk about the reflexive property. The
reflexive property states that any quantity is
equal to itself. In symbols that is For any
number a, a a. Here is an example 5 5 and
3 4 3 4
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Symmetric Property
If one quantity equals a second quantity, then
the second quantity equals the first. For any
numbers a and b, if a b, then b a. If 8 5
3, then 5 3 8.
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Transitive Property
If one quantity equals a second quantity and the
second quantity equals a third quantity, then the
first quantity equals the third quantity. For
any numbers a, b, and c, if a b and b c, then
a c. If 5 7 8 4 and 8 4 12, then 5
7 12.
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Substitution Property
A quantity may be substituted for its equal in
any expression. If a b, then a may be replaced
by b in any expression. If n 16, then 4 n
4 16.
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Lesson 3. 2. Stick around and continue to glean
knowledge from Lesson 2. Choose wisely!
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The Distributive Property
In Symbols For any numbers a, b, and c, a(b
c) ab ac and (b c)a ba ca and a(b -
c) ab ac and (b - c)a ba ca.
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The Distributive Property Continued
Lets look at some examples of the distributive
property. 3(2 5) 3 2 3 5 4(9 7) 4
9 4 7 3(7) 6 15 4(2) 36
- 28 21 21 8 8
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Lesson 4. 2. Stick around and continue to glean
knowledge from Lesson 3. Choose wisely!
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The Commutative Property
Words The order in which you add or multiply
numbers does not change their sum or
product. Symbols For any numbers a and b, a
b b a and a b b a. Examples 5 6 6
5, 3 2 2 3
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The Associative Property
Words The way you group three or more numbers
when adding or multiplying does not change
their sum or product. Symbols For any numbers
a, b, and c, (a b) c a (b c) and (ab)c
a(bc). Examples (2 4) 6 2 (4 6),
(3 5) 4 3 (5 4)
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You have two options! 1. Click the House
button to return to the main menu and move on to
the Fun Quiz. 2. Stick around and continue to
glean knowledge from Lesson 4. Choose wisely!
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Fun Quiz
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Which property is illustrated below? If 3 5
8, then 8 3 5.
A. The Reflexive Property B. The Symmetric
Property C. The Transitive Property D. The
Substitution Property
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Sorry!
The statement, if 3 5 8, then 8 3 5, does
not represent the Reflexive Property. An
example of the Reflexive Property would be 3 5
3 5 Try again!
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Sorry!
The statement, if 3 5 8, then 8 3 5, does
not represent the Transitive Property. An
example of the Transitive Property would be If 3
6 4 5 and 3 6 9, then 4 5 9. Try
again!
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Sorry!
The statement, if 3 5 8, then 8 3 5, does
not represent the Substitution Property. An
example of the Substitution Property would be If
n 12, then 2n 2 12. Try again!
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Correct!!
The Symmetric Property is represented by the
statement If 3 5 8, then 8 3 5. Good
job!
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Use the Distributive Property to simplify 10(m
3).
A. 10m - 3 B. 10m 30 C. 30 10m D. 10m - 30
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Sorry!
10(m 3) does not simplify to 10m 3. Why are
the parentheses there? Try again!
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Sorry!
10(m 3) does not simplify to 10m 30. Check
your signs. Try again!
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Sorry!
10(m 3) does not simplify to 30 10m. Check
your signs. Did you get your terms mixed? Try
again!
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Correct!!
10(m 3) simplifies to 10m 30. Good job!
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Which illustrates the Commutative Property of
Addition?
A. (2 3) 7 5 7 B. (2 3) 7 14  C.
(2 3) 7 (3 2) 7 D. (2 3) 7 2 (3
7)
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Sorry!
(2 3) 7 5 7 does not illustrate the
Commutative Property of Addition. Try again!
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Sorry!
(2 3) 7 14 does not illustrate the
Commutative Property of Addition. Try again!
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Sorry!
(2 3) 7 2 (3 7) does not illustrate the
Commutative Property of Addition. It does,
however, illustrate the Associative Property of
Addition. Try again!
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Correct!!
(2 3) 7 (3 2) 7 illustrates the
Commutative Property of Addition. Good job!
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Congratulations!!
You have completed this unit on algebraic
properties of identity and equality. Please
click on the button in the bottom right corner to
return to the Title slide.