1. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Same Signs Different Signs 1) + 3 + 4 =+7 Objective- To solve problems involving operations with integers. Combining Integers +3 +4

2. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 Objective- To solve problems involving operations with integers. Combining Integers -4 -2

3. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 Objective- To solve problems involving operations with integers. Combining Integers +1 +5

4. Objective- To solve problems involving operations with integers. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers -3 -5

5. Objective- To solve problems involving operations with integers. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers 5) + 5 + 9 = 6) - 3 - 13 = 7) 4 + 6 = 8) -6 + -7 = +14 -16 +10 -13

6. Objective- To solve problems involving operations with integers. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers 5) + 5 + 9 = 6) - 3 - 13 = 7) 4 + 6 = 8) -6 + -7 = +14 -16 +10 -13 1) - 3 + 4 = -3 +4 +1

7. Objective- To solve problems involving operations with integers. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers 5) + 5 + 9 = 6) - 3 - 13 = 7) 4 + 6 = 8) -6 + -7 = +14 -16 +10 -13 1) - 3 + 4 = +2 -4 +1 2) + 2 - 4 =-2

8. Objective- To solve problems involving operations with integers. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers 5) + 5 + 9 = 6) - 3 - 13 = 7) 4 + 6 = 8) -6 + -7 = +14 -16 +10 -13 1) - 3 + 4 = -5 +1 2) + 2 - 4 =-2 3) -5 + 1 =-4

9. Objective- To add integers using properties of real numbers. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers 5) + 5 + 9 = 6) - 3 - 13 = 7) 4 + 6 = 8) -6 + -7 = +14 -16 +10 -13 1) - 3 + 4 = +5 -12 +1 2) + 2 - 4 =-2 3) -5 + 1 =-4 4) +5 - 12 =-7 Difference of the numbers

10. 7 6 5 4 3 2 1 0 -2 -3 -4 -5 -6 -7 -8 Combining Integers Same Signs Different Signs 1) + 3 + 4 =+7 2) - 2 - 4 =-6 3) 1 + 5 =+6 4) -5 - 3 =-8 Sum of the numbers 5) + 5 + 9 = 6) - 3 - 13 = 7) 4 + 6 = 8) -6 + -7 = +14 -16 +10 -13 1) - 3 + 4 =+1 2) + 2 - 4 =-2 3) -5 + 1 =-4 4) +5 - 12 =-7 Difference of the numbers 5) - 8 + 3 = 6) +6 - 13 = 7) -9 + 15 = 8) +11 - 4 = -5 -7 +6 +7 Objective- To add integers using properties of real numbers.

11. Combine the following integers. 1) -6 + 10 = 2) +4 - 9 = 3) -2 + -7 = 4) +6 + 8 = 5) -3 + 12 = 6) -4 - 13 = 7) +5 - 18 = 8) -2 + -6 = 9) +7 - 5 = 10) -9 + -8 = 11) -6 + 4 = 12) -2 + 19 = 13) -8 + -32 = 14) +15 - 4 = +4+4 -5 -9 +14 +9+9 -17 -13 -8-8 +2+2 -17 -2 +17 -40 +11

12. Commutative Properties Commutative Property of Addition a + b = b + a Commutative Property of Multiplication Example: 3 + 5 = 5 + 3 Example: Properties of Real Numbers

13. Are the following operations commutative? 1) Subtraction 2) Division a - b = b - a Counterexamples 8 - 5 = 5 - 8 3 = -3 Therefore, subtraction is not commutative. Counterexample - a single example that proves a statement false. Therefore, division is not commutative.

14. Associative Properties Associative Property of Addition ( a + b ) + c = a + ( b + c ) Associative Property of Multiplication Example: ( 4 + 11 ) + 6 = 4 + ( 11 + 6 )

15. 3 = 7 Are the following operations associative? 1) Subtraction 2) Division (a - b) - c = a - (b - c) (10 - 5) - 2 = 10 - (5 - 2) 5 - 2 = 10 - 3 Therefore, subtraction is not associative. Therefore, division is not associative.

16. 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

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

18. Identify the property shown below. 1) (2 + 10) + 3 = (10 + 2) + 3 2) 3) (6 + 8) + 9 = 6 + (8 + 9) 4) 5) 6) 5 + 0 = 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.

19. Use a property to simplify each expression below. Identify the property used. 1) 2) 7 + ( 43 + 29 ) Comm. Prop. of Mult. ( 7 + 43 ) + 29 ( 50 ) + 29 79 Assoc. Prop. of Add.