1. are statements that are true for all numbers.
Properties:
are statements that are true for all numbers.
We will learn about the following properties:
Distributive Property
Commutative Property
Associative Property
Identity Properties
Properties Objective: Use Commutative, Associative, Identity, and Distributive Properties to solve problems.

2. Distributive Property:
Combines addition and multiplication.
You have to multiply each addend of the sum by the number outside the parenthesis.
Example: 3( )
3(4) + 3(6) 30

3. Examples:
6(1 + 4)
5(3 - 2)

4. Commutative Property:
The order in which two numbers are added or multiplied does not change their sum or product.
For example: = 3 + 4
7 = 7
5 × 3 = 3 × 5
15 = 15

5. Associative Property:
The way in which three numbers are grouped when they are added or multiplied does not change their sum or product (answers).
Example: ( 8+ 27) + 52 = 8 + ( )
= 87
5× ( 3 × 8) = (5 × 3) × 8
120 = 120

6. Identity Properties: The sum of an addend and 0 is the addend.
For example: = 8
The product of a factor and 1 is the factor.
For example: 7 × 1 = 7

7. Homework: Properties 6. 2 × (3 × 7) = ( 2 × 3) × 7 2. (2 + 7)5
Use the Distributive Property to evaluate each expression.
1. 3( 5 + 1)
2. (2 + 7)5
3. (10 + 2)7
4. 2( 9 – 8)
5. 4( 10 – 2)
Name the property shown by each statement.
× (3 × 7) = ( 2 × 3) × 7
= 3 + 6
8. 3( 9 + 7) = 3(9) + 3(7)
× 1 = 8
10. x + 0 = x