1. Algebra 1 Notes: Lesson 1-6: Commutative and Associative Properties

2. Vocabulary
Commutative Property

3. Vocabulary
Commutative Property - The order in which you add or multiply numbers does not change their sum or product.

4. Vocabulary
Commutative Property - The order in which you add or multiply numbers does not change their sum or product. a + b = b + a a  b = b  a

5. Vocabulary
Commutative Property - The order in which you add or multiply numbers does not change their sum or product. a + b = b + a a  b = b  a
Associative Property

6. Vocabulary
Commutative Property - The order in which you add or multiply numbers does not change their sum or product. a + b = b + a a  b = b  a
Associative Property - The way you group three or more numbers when adding or multiplying does not change their sum or product.
(a + b) + c = a + (b + c) (a  b)  c = a  (b  c)

7. Evaluate
2  8  5  7

8. Evaluate
2  8  5  7 2  5  8  7

9. Evaluate
2  8  5  7 2  5  8  7 10  56

10. Evaluate
2  8  5  7 2  5  8  7 10 

11. Evaluate
2  25  7  4

12. Evaluate
2  25  7  4 25  4  2  7

13. Evaluate
2  25  7  4 25  4  2   14

14. Evaluate
2  25  7  4 25  4  2   14 1,400

15. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b

16. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b

17. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b

18. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b

19. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b

20. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b +

21. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b + 32

22. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b b

23. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b b

24. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b b
= 23b

25. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b b
= 23b + 32

26. Example 1
Simplify 8(2b + 4) + 7b.
8(2b + 4) + 7b = 8(2b) + 8(4) + 7b
= 16b b
= 23b + 32

27. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.

28. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3( )

29. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3( )

30. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y)

31. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y)

32. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y) +

33. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y) +

34. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y) + 5( )

35. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y) + 5( )

36. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y) + 5(x + 4y)

37. Example 2
Use the expression three times the sum of 3x and 2y increased by five times the sum of x and 4y.
Write an algebraic expression for the verbal expression.
3(3x + 2y) + 5(x + 4y)

38. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)

39. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 3(3x)

40. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 3(3x) + 3(2y)

41. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 3(3x) + 3(2y) + 5(x)

42. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 3(3x) + 3(2y) + 5(x) + 5(4y)

43. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 3(3x) + 3(2y) + 5(x) + 5(4y) Distributive Property

44. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 3(3x) + 3(2y) + 5(x) + 5(4y) Distributive Property

45. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive

46. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive

47. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive

48. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive Property
= 14x

49. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive Property
= 14x

50. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive Property
= 14x

51. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive Property
= 14x + 26y

52. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive Property
= 14x + 26y Substitution

53. Example 2 b) Simplify the expression and indicate the properties used.
3(3x + 2y) + 5(x + 4y)
= 9x + 6y + 5x + 20y Distributive Property
= 14x + 26y Substitution

54. Assignment
Pg. 35
16 – 26 (even)
28 – 31 (all)
32 – 48 (even)