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 Identityb · 1 = b 1 is the multiplicative identity - Multiplicative Property of Zero

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

6. Vocabulary -Additive Identity a + 0 = a -Multiplicative Identityb · 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 = 0 Multiplicative 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 = 0 Multiplicative 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 = 0 Multiplicative 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

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

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

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 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 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 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 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 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 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)