Identity equality properties

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  • 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