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Commutative And Associative Properties

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Commutative And Associative Properties

  1. 1. Commutative and Associative Properties of Real Numbers<br />
  2. 2. Commutative Property of Addition<br />3 + 2 = 2 + 3<br />5 = 5<br />In general,<br />a + b = b + a<br />The order in which you add does not matter.<br />
  3. 3. Commutative Property of Multiplication<br />5∙ 10 = 10 ∙ 5<br />50 = 50<br />In general,<br />a ∙ b = b ∙ a<br />The order in which you multiply does not matter.<br />
  4. 4. The Commutative Property does not hold for subtraction and division.<br />Look at the following examples:<br /> 1) Does 8 – 3 = 3 – 8 ? <br /> 5 ≠ -5 No! <br /> 2) Does 8 ÷ 4 = 4 ÷ 8 ?<br /> 2 ≠ ½ No!<br />If you change the order in a subtraction or division problem, you get a different answer.<br />
  5. 5. Summaryof the Commutative Property<br />The Commutative Property has to do with the order of the numbers.<br />Holds true for Addition and Multiplication<br />Does NOT hold true for Subtraction and Division<br />
  6. 6. Associative Property <br />of Addition <br />(a + b) + c = a + (b+ c)<br />(2 + 3) + 4 = 2 + (3 + 4)<br />5 + 4 = 2 + 7<br />9 = 9<br />It does not matter how the addends are grouped. It changes the order in which you add them, but the answer is the same.<br />of Multiplication<br />(a ∙ b) ∙ c = a ∙ (b ∙ c)<br />(2 ∙ 3) ∙ 4 = 2 ∙ (3 ∙ 4)<br />6 ∙ 4 = 2 ∙12<br />24 = 24<br />It does not matter how the factors are grouped. It changes the order in which you multiply them, but the answer is the same.<br />
  7. 7. The Associative Property does not hold for subtraction and division.<br />Look at the following examples:<br /> 1) Does (9 – 5) – 3 = 9 – (5 – 3) ?<br /> 4 – 3 = 9 – 2<br /> 1 ≠ 7 No!<br /> 2) Does (8 ÷ 4 ) ÷ 2 = 8 ÷ (4 ÷ 2) ? <br /> 2 ÷ 2 = 8 ÷2<br /> 1 ≠ 4 No!<br />
  8. 8. Summary of the Associative Property<br />The Associative Property has to do with how the numbers are grouped together and therefore which pair you operate on first.<br />Holds true for Addition and Multiplication<br />Does not hold true for Subtraction and Division<br />
  9. 9. Identify the Property Shown<br /> 17 + 43 = 43 + 17<br /> (4 ∙ 5) ∙ 2 = 4 ∙ (5 ∙ 2)<br /> (8 + 3) + 5 = (3 + 8) + 5<br /> (7 + 2) + 3 = 2 + (7 + 3)<br />

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