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