2. 5 - -2 = -(9) + -(-10) = 77 11

3. (-1/2)(1 3/5)(10/-9) write answer as a fraction Rewrite mixed numbers as improper fractions (-1/2)(8/5)(10/-9) Cross cancel (-1/2)(8/5)(10/-9) (-1/1)(4/1)(2/-9) Count the number of negative signs (-1/2)(8/5)(10/-9) 2 neg odd positive 14 1 2

4. (-1/2)(1 3/5)(10/-9) write answer as a fraction Answer 8/9 Count the number of negative signs (-1/1)(4/1)(2/-9) Mult tops then bottoms

5. Go over homework  Worksheet +-/* integers

6. 1-5 Properties of Numbers C3

7. Properties of Numbers 1. Commutative of Addition & Multiplication 2. Associative of Addition & Multiplication 3. Identity of Addition & Multiplication 4. Zero of Multiplication 5. Distributive

8. The Commutative Property  Background  The word commutative comes from the verb “to commute.”  Definition on dictionary.comdictionary.com  Commuting means changing, replacing, or exchanging  People who travel back and forth to work are called commuters.  Traffic Reports given during rush hours are also called commuter reports.

9. Here are two families of commuters. Commuter A Commuter B Commuter A Commuter B Commuter A & Commuter B changed lanes. Remember… commute means to change. A + B = B + A A x B = B x A

10. The Commutative Property A + B = B + A A x B = B x A A + B = B + A A x B = B x A

11. Commutative Property of Addition Changing the order of the addends does not change the sum A + B = B + A1 + 2 + 3 = 3 + 1 + 2 4 + 5 + 6 = 5 + 6 + 4

12. Commutative Property of Multiplication Changing the order of the factors does not change the product A x B = B x A 1 x 2 x 3 = 3 x 1 x 2 4 x 5 x 6 = 5 x 6 x 4

13. Properties of Multiplication and Addition 1. Commutative of Addition & Multiplication 2. Associative of Addition & Multiplication 3. Identity of Addition & Multiplication 4. Zero of Multiplication 5. Distributive

14. The Associative Property  Background  The word associative comes from the verb “to associate.”  Definition on dictionary.comdictionary.com  Associate means connected, joined, or related  People who work together are called associates.  They are joined together by business, and they do talk to one another.

15. Let’s look at another hypothetical situation Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who he calls first?

16. ACB Here are three associates. B calls A firstHe calls C last If he called C first, then called A, would it have made a difference? NO!

17. (The Role of Parentheses)  In math, we use parentheses to show groups.  In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS) So….

18. The Associative Property (A x B) x C = A x (B x C) AC B AC B THEN The parentheses identify which two associates talked first. (A + B) + C = A + (B + C)

19. Associative Property of Addition Changing the grouping of the addends does not change the sum (1 + 2) + 3 = 1 +( 2 + 3) (4 + 5) + 6 = 4 + ( 5 + 6 ) (A + B) + C = A +( B + C)

20. Associative Property of Multiplication Changing the grouping of the factors does not change the product (1 x 2) x 3 = 1 x( 2 x 3) (4 x 5) x 6 = 4 x ( 5 x 6 ) (A x B) x C = A x ( B x C)

21. Properties of Multiplication and Addition 1. Commutative of Addition & Multiplication 2. Associative of Addition & Multiplication 3. Identity of Addition & Multiplication 4. Zero of Multiplication 5. Distributive

22. The Identity Property of Addition I am me! You cannot change My identity!

23. Identity Property of Addition A + 0 = A + 0 =

24. Identity Property of Addition The sum of zero and anything is anything 0+ 3 = 3 18 + 0 = 18 0 + C = C

25. Identity Property of Multiplication A x 1 = A x 1 =

26. Identity Property of Multiplication The product of one and anything is anything 1 x 3 = 3 18 x 1 = 18 1 x C = C

27. Properties of Multiplication and Addition 1. Commutative of Addition & Multiplication 2. Associative of Addition & Multiplication 3. Identity of Addition & Multiplication 4. Zero of Multiplication 5. Distributive

28. Zero Property of Multiplication A x 0 = 0 x 0 = 0

29. Zero Property of Multiplication The product of zero and anything is zero 3 x 0 = 0 18 x 0 =0 0 x C = 0

30. Properties of Multiplication and Addition 1. Commutative of Addition & Multiplication 2. Associative of Addition & Multiplication 3. Identity of Addition & Multiplication 4. Zero of Multiplication 5. Distributive

31. Distributive Property Think of a teacher distributing something to every student in the class. and

32. The Distributive Property Four is multiplying the quantity “x + 3” That means four will multiply both the x and the 3!  Multiply 4 times x PROBLEM: 4(x + 3)  Copy the operation sign  Multiply 4 times 3 4(x + 3) 4 times x4 times 3 4x4x+12 Answer:

33. Distributive Property You take the number on the outside of the parentheses and give it to everything on the inside of parentheses by way of multiplication. 3(a +b) = 3a + 3b 14 + 10 = 2(7 + 5) ac + bc = (a + b)c

34. Let’s practice ! Look at the problem. Identify which property it represents.

35. 12 x 0 = 0 Zero Property of Multiplication (9 + 8) + 7 = 9 + (8 + 7) The Associative Property of Addition

36. 3 x1 = 3 The Identity Property of Multiplication a + b = b + a The Commutative Property of Addition

37. 9 x 7 = 7 x 9 The Commutative Property of Multiplication (a + b) + c = a + (b + c) The Associative Property of Addition

38. 4 x1 = 4 Identity Property of Multiplication a + 0 = a The Identity Property of Addition

39. (4 x 3) x 2 = 4 x (3 x 2) The Associative Property of Multiplication 4(x + 3) = 4x + 12 The Distributive Property of Multiplication

40. a x b = b x a The Commutative Property of Multiplication Moving numbers! 6(5a)=(6 ∙ 5)a The Associative Property of Multiplication

41. a x 0 = 0 Zero Property of Multiplication ac + bc = (a + b)c Distributive Property

42. (a x b) x c = a x (b x c) The Associative Property of Multiplication A Parentheses! C B 16 + ½ = ½ + 16 The Communtative Property of Addition

43. Find the product: 1.) 5(a+6) = 2.) (v-2)9= 3.) -4(t+3)=4.) (-11+w)(-2)= 5.) -2(34)(50)=6.) –(4)*6*-25= 5a + 309v -18 -4t -1222 -2w -3400 600 -2w+22

44. Homework Distributive and property worksheet