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

Algebra 1 Notes: Lesson 1-6: Commutative and Associative Properties. Vocabulary Commutative Property. Vocabulary Commutative Property - The order in which you add or multiply numbers does not change their sum or product. . Vocabulary

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

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  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 + aa 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 56 560

  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 7 100 14

  14. Evaluate 2 25 7 4 25 4 2 7 100 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 + 32 + 7b

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

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

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

  26. Example 1 Simplify 8(2b + 4) + 7b. 8(2b + 4) + 7b = 8(2b) + 8(4) + 7b = 16b + 32 + 7b = 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+ 20yDistributive Property = 14x

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