4_Real_Number_Properties_Notes

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1. Real Number PropertiesStudents will identify real numberproperties. 2. Definitionsã Commutative Property over Addition says that we can add numbers in any order…
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  • 1. Real Number PropertiesStudents will identify real numberproperties.
  • 2. Definitions• Commutative Property over Addition says that we can add numbers in any order a+b=b+a
  • 3. Definitions• Commutative Property over Multiplication says that we can multiply in any order (a)(b) = (b)(a)
  • 4. Definitions• Associative Property over Addition tells us that we can group numbers in a sum any way we want and get the same answer. (a + b) + c = a + (b + c)
  • 5. Definitions• Associative Property over Multiplication tells us that we can group numbers in a product any way we want and get the same answer. (ab)(c)= (a)(bc)
  • 6. Definitions• Distributive Property states that the product of a number and a sum is equal to the sum of the individual products of addends and the number. a(b + c) = ab + ac
  • 7. Definitions• Identity Property for Addition states that zero can be added to any real number and the result is that number. a+0=a
  • 8. Definitions• Identity Property for Multiplication states that one can be multiplied by any real number and the result is that number. a .1 = a
  • 9. Definitions• Opposites or Additive Inverses have a sum of 0. a + (-a) = 0
  • 10. Definitions• Reciprocals or Multiplicative Inverses have a product of 1. a . 1/a= 1
  • 11. Definitions• Absolute Value the distance a number is from zero on the number line. I –a I = a - I -a I = -a
  • 12. In your composition notebook, choose one of the following:• How do you distinguish the differences between the commutative property over addition and the associative property over multiplication? Give one example of each using variables and constants.
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