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Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
Identity equality properties
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Identity equality properties

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  1. Identity & Equality Properties 1-4
  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. 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. 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 <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. 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. 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. Glencoe/McGraw-Hill 2003

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