Same Signs Different Signs 1) =+7 Objective- To solve problems involving operations with integers. Combining Integers +3 +4

Same Signs Different Signs 1) =+7 2) =-6 Objective- To solve problems involving operations with integers. Combining Integers -4 -2

Same Signs Different Signs 1) =+7 2) =-6 3) =+6 Objective- To solve problems involving operations with integers. Combining Integers +1 +5

Objective- To solve problems involving operations with integers Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers -3 -5

Objective- To solve problems involving operations with integers Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers 5) = 6) = 7) = 8) =

Objective- To solve problems involving operations with integers Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers 5) = 6) = 7) = 8) = ) =

Objective- To solve problems involving operations with integers Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers 5) = 6) = 7) = 8) = ) = ) =-2

Objective- To solve problems involving operations with integers Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers 5) = 6) = 7) = 8) = ) = ) =-2 3) =-4

Objective- To add integers using properties of real numbers Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers 5) = 6) = 7) = 8) = ) = ) =-2 3) =-4 4) =-7 Difference of the numbers

Combining Integers Same Signs Different Signs 1) =+7 2) =-6 3) =+6 4) =-8 Sum of the numbers 5) = 6) = 7) = 8) = ) =+1 2) =-2 3) =-4 4) =-7 Difference of the numbers 5) = 6) = 7) = 8) = Objective- To add integers using properties of real numbers.

Combine the following integers. 1) = 2) = 3) = 4) = 5) = 6) = 7) = 8) = 9) = 10) = 11) = 12) = 13) = 14) =

Commutative Properties Commutative Property of Addition a + b = b + a Commutative Property of Multiplication Example: = Example: Properties of Real Numbers

Are the following operations commutative? 1) Subtraction 2) Division a - b = b - a Counterexamples = = -3 Therefore, subtraction is not commutative. Counterexample - a single example that proves a statement false. Therefore, division is not commutative.

Associative Properties Associative Property of Addition ( a + b ) + c = a + ( b + c ) Associative Property of Multiplication Example: ( ) + 6 = 4 + ( )

3 = 7 Are the following operations associative? 1) Subtraction 2) Division (a - b) - c = a - (b - c) (10 - 5) - 2 = 10 - (5 - 2) = Therefore, subtraction is not associative. Therefore, division is not associative.

Commutative vs. Associative Commutative( Flip-flop )Associative ( Re-group ) Commutative Situations 1) Drinking orange juice and then eating cereal. 2) Doing math homework and then science homework. Flip-flop Re-grouping

Identities Identity Property of Addition x + 0 = x Identity Property of Multiplication Properties of Zero Multiplication Property of Zero Division Property of Zero

Identify the property shown below. 1) (2 + 10) + 3 = (10 + 2) + 3 2) 3) (6 + 8) + 9 = 6 + (8 + 9) 4) 5) 6) = 5 7) Comm. Prop. of Add. Mult. Prop. of Zero Assoc. Prop. of Add. Comm. Prop. of Mult. Identity Prop. of Add. Identity Prop. of Mult. Assoc. Prop. of Mult.

Use a property to simplify each expression below. Identify the property used. 1) 2) 7 + ( ) Comm. Prop. of Mult. ( ) + 29 ( 50 ) Assoc. Prop. of Add.