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Algebra 1 Notes: Lesson 1-4: Identity and Equality Properties

Learn about properties like Additive Identity, Multiplicative Identity, and more. Understand the properties using examples and step-by-step explanations.

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Algebra 1 Notes: Lesson 1-4: Identity and Equality Properties

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  1. Algebra 1 Notes:Lesson 1-4:Identity and Equality Properties

  2. Vocabulary • Additive Identity

  3. Vocabulary • Additive Identity a + 0 = a • 0 is the additive identity • Multiplicative Identity

  4. Vocabulary • Additive Identity a + 0 = a • Multiplicative Identity b · 1 = b • 1 is the multiplicative identity • - Multiplicative Property of Zero

  5. Vocabulary • Additive Identity a + 0 = a • Multiplicative Identity b · 1 = b • Multiplicative Property of Zero c· 0 = 0 • Multiplicative Inverses

  6. Vocabulary • Additive Identity a + 0 = a • Multiplicative Identity b · 1 = b • Multiplicative Property of Zero c· 0 = 0 • Multiplicative Inverses ¼ · 4 = 1 • “Reciprocal”

  7. Vocabulary • Reflexive Property of Equality

  8. Vocabulary • Reflexive Property of Equality a = a

  9. Vocabulary • Reflexive Property of Equality a = a 2 + 3 = 2 + 3 • Symmetric Property of Equality

  10. Vocabulary • Reflexive Property of Equality a = a 2 + 3 = 2 + 3 • Symmetric Property of Equality If a = b, then b = a.

  11. Vocabulary • Reflexive Property of Equality a = a 2 + 3 = 2 + 3 • Symmetric Property of Equality If a = b, then b = a. If 3 + 6 = 9, then 9 = 3 + 6.

  12. Vocabulary • Transitive Property of Equality

  13. Vocabulary • Transitive Property of Equality If a = b and b = c, then a = c.

  14. Vocabulary • Transitive Property of Equality If a = b and b = c, then a = c. If 5 + 7 = 12 and 12 = 8 + 4, then 5 + 7 = 8 + 4. • Substitution Property of Equality

  15. Vocabulary • Transitive Property of Equality If a = b and b = c, then a = c. If 5 + 7 = 12 and 12 = 8 + 4, then 5 + 7 = 8 + 4. • Substitution Property of Equality If a = b, then a may be replaced by b.

  16. Vocabulary • Transitive Property of Equality If a = b and b = c, then a = c. If 5 + 7 = 12 and 12 = 8 + 4, then 5 + 7 = 8 + 4. • Substitution Property of Equality If a = b, then a may be replaced by b.If n = 15, then 3n = 3 · 15.

  17. Example 1 Name the property used in each equation. Then find the value of n. a) n 12 = 0

  18. Example 1 Name the property used in each equation. Then find the value of n. a) n 12 = 0 n = 0

  19. Example 1 Name the property used in each equation. Then find the value of n. a) n 12 = 0 n = 0Multiplicative Property of Zero b)

  20. Example 1 Name the property used in each equation. Then find the value of n. a) n 12 = 0 n = 0Multiplicative Property of Zero b) n = 5

  21. Example 1 Name the property used in each equation. Then find the value of n. a) n 12 = 0 n = 0Multiplicative Property of Zero b) n = 5 Multiplicative Inverse Property

  22. Example 2 Evaluate: ¼(12 - 8) + 3(15  5 - 2) Name the property used in each step.

  23. Example 2 ¼(12 - 8) + 3(15  5 – 2)

  24. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) Substitution

  25. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) Substitution

  26. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) Substitution Substitution

  27. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) Substitution Substitution

  28. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) Substitution Substitution Substitution

  29. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) Substitution Substitution Substitution

  30. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) 1 + 3(1) Substitution Substitution Substitution Multiplicative Inverse

  31. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) 1 + 3(1) Substitution Substitution Substitution Multiplicative Inverse

  32. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) 1 + 3(1) 1 + 3 Substitution Substitution Substitution Multiplicative Inverse Multiplicative Identity

  33. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) 1 + 3(1) 1 + 3 Substitution Substitution Substitution Multiplicative Inverse Multiplicative Identity

  34. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) 1 + 3(1) 1 + 3 4 Substitution Substitution Substitution Multiplicative Inverse Multiplicative Identity Substitution

  35. Example 2 ¼(12 - 8) + 3(15  5 – 2) ¼(4) + 3(15 ÷ 5 – 2) ¼(4) + 3(3 – 2) ¼(4) + 3(1) 1 + 3(1) 1 + 3 4 Substitution Substitution Substitution Multiplicative Inverse Multiplicative Identity Substitution

  36. Try on your own! Include the property with each step 2 ( 3  2 – 5 ) + 3  ⅓

  37. Assignment Pgs. 23-25 12-28 (evens) 39 – 43 (all)

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