Properties
Lee Ann SnyderTED 628
Summer 2010
What is a property?
• In algebra, properties are statements that are true for any number.
• You can use properties to help solve problems that you will encounter from this point forward in math class.
There are 4 properties you need to know:
• The Commutative Property
• The Associative Property
• The Distributive Property
• The Identity Property
Properties Main Menu
The Commutative
Property
The Associative
Property
The Distributive
Property
The Identity
Property
Review each of the properties in any order you would like!
Properties Review
The Commutative Property
• The Commutative Property of Addition tells us that the order in which two numbers are added does not change the sum
Symbols
A + B = B + A
Example
2 + 5 = 5 +2
7 = 7
The Commutative Property of Addition
3 + 2 = 2 + 3
5 = 5
2 + 1 = 1 + 2
3 = 3
The Commutative Property
• The Commutative Property of Multiplication tells us that the order in which two numbers are multiplied does not change the product
Symbols
A B = B A
Example
2 5 = 5 2
10 = 10
The Commutative Property of Multiplication
Properties
Main Menu
The Associative Property
• The Associative Property of Addition tells us that the way in which numbers are grouped when they are added does not change the sum
Symbols
(a + b) + c = a + (b + c)
Example
(4 + 5) + 3 = 4 + (5 + 3)
9 + 3 = 4 + 8
12 = 12
The Associative Property of Addition
=
The Associative Property
• The Associative Property of Multiplication tells us that the way in which numbers are grouped when they are multiplied does not change the product
Symbols
(a b) c = a (b c)
Example
(4 5) 3 = 4 (5 3)
20 3 = 4 15
60 = 60
The Associative Property of Multiplication
5 (3 7) = (5 3) 7
5 21 = 15 7
105 = 105
Properties
Main Menu
The Distributive Property
• The Distributive Property combines addition and multiplication. It tells us that to multiply any number by a sum, multiply each number on the inside of the parentheses by the number outside the parentheses
Symbols
a (b + c) = ab + ac
Example
4 (5 + 3) = 4 5 + 4 3
4 8 = 20 + 12
32 = 32
The Distributive Property
Properties
Main Menu
The Identity Property
• The Additive Identity property tells is that when zero is added to any number, the sum is that number
Symbols
a + 0 = a Example
7 + 0 = 7
The Additive Identity Property
The Identity Property
• The Multiplicative Identity property tells is that when any number is multiplied by one, the product is that number
Symbols
a 1 = a Example
5 1 = 5
The Multiplicative Identity Property
Properties
Main Menu
How well do you know the properties?
• On the following slides, you will have to identify the property that is shown.
• If you would like to look over any of the properties before you begin, return to the Properties Main Menu
Begin Properties Review!
What property is shown?
Commutative Property Associative Property
Distributive Property Identity Property
Correct!
• This is an example of the Commutative Property
Next Question
Incorrect
• This is an example of the Commutative Property
Next Question
What property is shown?
Commutative Property Associative Property
Distributive Property Identity Property
Correct!
• This is an example of the Distributive Property
Next Question
Incorrect
• This is an example of the Distributive Property
Next Question
What property is shown?
Commutative Property Associative Property
Distributive Property Identity Property
Correct!
• This is an example of the Associative Property
Next Question
Incorrect
• This is an example of the Associative Property
Next Question
What property is shown?
Commutative Property Associative Property
Distributive Property Identity Property
Correct!
• This is an example of the Associative Property
Next Question
Incorrect
• This is an example of the Associative Property
Next Question
What property is shown?
Commutative Property Associative Property
Distributive Property Identity Property
Correct!
• This is an example of the Distributive Property
Next Question
Incorrect
• This is an example of the Distributive Property
Next Question
What property is shown?
Commutative Property Associative Property
Distributive Property Identity Property
Correct!
• This is an example of the Identity Property
More Practice
Incorrect
• This is an example of the Identity Property
More Practice
Need more practice?
• Click here to see how well you know the addition properties!
• Click here to see how well you know the multiplication properties!
• Use this website to fill in the blanks to make true statements using addition properties
• Use this website to fill in the blanks to make true statements using multiplication properties
Images• http://schools-wikipedia.org/images/232/23287.png• http://www.sunclipse.org/downloads/pandas/pandas-commute.jpg • http://www.allmathwords.org/images/2m3dot.gif • http://www.i-know.ro/upload/editor/Commutative-Property.jpg • http://www.loisterms.com/assoc2.gif • http://image.tutorvista.com/Qimages/QD/51649.gif• http://www.education.vic.gov.au/images/content/studentlearning/mathsconti
nuum/st275bag.JPG
• http://www.loisterms.com/assoc4.gif• http://www.studyzone.org/testprep/math4/a/positi3.gif• http://www.solving-math-problems.com/associative-property.html • http://www.coolmath.com/reference/math-dictionary-D.html• http://www.kitchentablemath.net/twiki/bin/view/Kitchen/FavoriteBooks?skin
=plain • http://www.coolmath.com/prealgebra/06-properties/06-properties-additive-id
entity-01.htm
• http://regentsprep.org/Regents/math/ALGEBRA/AN1/propT2.htm• http://www.coolmath.com/prealgebra/06-properties/08-properties-multiplicat
ive-identity-01.htm
• http://www.solving-math-problems.com/associative-property.html • http://www.gradeamathhelp.com/math-properties.html