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

Vocabulary -Additive Identity

Vocabulary -Additive Identity a + 0 = a 0 is the additive identity -Multiplicative Identity

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

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

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

Vocabulary -Reflexive Property of Equality

Vocabulary -Reflexive Property of Equality a = a

Vocabulary -Reflexive Property of Equality a = a = Symmetric Property of Equality

Vocabulary -Reflexive Property of Equality a = a = Symmetric Property of Equality If a = b, then b = a.

Vocabulary -Reflexive Property of Equality a = a = Symmetric Property of Equality If a = b, then b = a. If = 9, then 9 =

Vocabulary -Transitive Property of Equality

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

Vocabulary -Transitive Property of Equality If a = b and b = c, then a = c. If = 12 and 12 = 8 + 4, then = Substitution Property of Equality

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

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

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

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

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)

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

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

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

Example 2 ¼(12 - 8) + 3(15  5 – 2)

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

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

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

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

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

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

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

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

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 Multiplicative Identity

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 Multiplicative Identity

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 Multiplicative Identity Substitution

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 Multiplicative Identity Substitution

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

Assignment Pgs (evens) 39 – 43 (all)