The document discusses several key properties related to identity and equality in mathematics. It defines: - The additive identity as 0, since the sum of any number and 0 is equal to the number. - The multiplicative identity as 1, since the product of any number and 1 is equal to the number. - The multiplicative property of zero, where the product of any number and 0 is equal to 0. - Multiplicative inverses or reciprocals as two numbers whose product is 1. Zero has no reciprocal. It also discusses properties of equality like reflexive, symmetric, and transitive properties and using substitution.

1. Identity & Equality Properties 1-4

2. Warm-Ups 1. 10 - x > 6; {3, 5, 6, 8} 2. 4x + 2< 58; {11, 12, 13, 14, 15} Evaluate: 3. (3 + 6) / 3^2 4. 20/4*8/10 5. 9(3) - 4^2 + 6^2 /2

3. Vocabulary: additive identity multiplicative identity multiplicative inverses reciprocal

4. The sum of any number and 0 is equal to the number. Thus, 0 is called the additive identity . Additive Identity: Words: For any number a , the sum of a and 0 is a . Symbols: a + 0 = 0 + a = a Examples: 5 + 0 = 0 + 5 = 5

5. Multiplicative Identity - the product of any number and 1 is equal to the number, 1 is called the multiplicative identity. ex. 7 * n = 7 Words: For any number a , the product of a and 1 is a . Symbols: a * 1 = 1 * a = a Example: 12 * 1 = 12, 1 * 12 = 12

6. Multiplicative Property of Zero - the product of any number and 0 is equal to 0. ex. 9 * m = 0 Words: For any number a , the product of a and 0 is 0. Symbols: a * 0 = 0 * a = 0 Example: 8 * 0 = 0 * 8 = 0

7. Two numbers whose product is 1 are called multiplicative inverses or reciprocals . Zero has no reciprocal because any number times 0 is 0. ex. 1/3 * 3 = 1 Symbols: a/b * b/a = b/a * a/b = 1 Example: 2/3 * 3/2 = 6/6 = 1

8. Identify Properties Name the property used in each equation. Then find the value of n. a. n * 12 = 0 b. n * 1/5 = 1 c. 0 + n = 8

9. Properties of Equality Reflexive: any quantity is equal to itself ex. 7 = 7 or 2 + 3 = 2 + 3 Symmetric: If one quantity equals a second quantity, then the second quantity equals the first quantity. ex. 9 = 6 + 3 Transitive: If one quantity equals a second quantity and the second quantity equals a third quantity , then the first quantity equals the third quantity. ex. 5 + 7 = 8 + 4 = 12 Substitution:A quantity may be substituted for its equal in any expression ex. n = 15, 3n = 3*15

10. Evaluate Using Properties Evaluate and name the property used in each step: 1/4(12 - 8) + 3(15/5 - 2)

11. Glencoe/McGraw-Hill 2003