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Identity equality properties

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Identity equality properties

  1. 1. Identity & Equality Properties 1-4
  2. 2. Warm-Ups <ul><li>1.  10 - x > 6;  {3, 5, 6, 8} </li></ul><ul><li>2.  4x + 2< 58;  {11, 12, 13, 14, 15} </li></ul><ul><li>  Evaluate: </li></ul><ul><li>3.  (3 + 6) / 3^2  </li></ul><ul><li>4.  20/4*8/10 </li></ul><ul><li>  </li></ul><ul><li>5.  9(3) - 4^2 + 6^2 /2 </li></ul>
  3. 3. Vocabulary: <ul><li>additive identity </li></ul><ul><li>multiplicative identity </li></ul><ul><li>multiplicative inverses </li></ul><ul><li>reciprocal </li></ul>
  4. 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. 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. 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. 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. 8. Identify Properties <ul><li>Name the property used in each equation.  Then find the value of n. </li></ul><ul><li>a.  n * 12 = 0 </li></ul><ul><li>b.  n * 1/5 = 1 </li></ul><ul><li>c.  0 + n = 8 </li></ul>
  9. 9. Properties of Equality <ul><li>Reflexive:  any quantity is equal to itself </li></ul><ul><li>            ex.  7 = 7 or 2 + 3 = 2 + 3 </li></ul><ul><li>Symmetric:  If one quantity equals a second quantity, then the second quantity equals the first quantity. </li></ul><ul><li>            ex.  9 = 6 + 3 </li></ul><ul><li>Transitive:  If one quantity equals a second quantity and the second quantity equals a third quantity , then the first quantity equals the third quantity. </li></ul><ul><li>            ex.  5 + 7 = 8 + 4 = 12 </li></ul><ul><li>Substitution:A quantity may be substituted for its equal in any expression  </li></ul><ul><li>            ex.  n = 15, 3n = 3*15 </li></ul>
  10. 10. Evaluate Using Properties <ul><li>Evaluate and name the property used in each step: </li></ul><ul><li>1/4(12 - 8) + 3(15/5 - 2) </li></ul>
  11. 11. Glencoe/McGraw-Hill 2003

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