# Algebra: Properties Objective: Use communicative, Associative, Identity, and Distributives properties to solve problems. Properties: are statements that.

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Algebra: Properties Objective: Use communicative, Associative, Identity, and Distributives properties to solve problems. Properties: are statements that are true for all numbers. We will learn about the following properties: 1.Distributive Property 2.Commutative Property 3.Associative Property 4.Identity Properties

Distributive Property: Combines addition and multiplication. You have to multiply each addend of the sum by the number outside the parenthesis. Example: 3( 4 + 6 ) 3(4) + 3(6) 12 + 18 30

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

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

Associative Properties: 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 + (27 + 52) 87 = 87 5× ( 3 × 8) = (5 × 3) × 8 120 = 120

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

Homework: Properties 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. 6. 2 × (3 × 7) = ( 2 × 3) × 7 7. 6 + 3 = 3 + 6 8. 3( 9 + 7) = 3(9) + 3(7) 9. 8 × 1 = 8 10. X + 0 = X

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