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Commutative And Associative Properties
- 1. Commutative and AssociativeProperties of Real Numbers
- 2. Commutative Property ofAddition3 + 2 = 2 + 35 = 5In general,a + b = b + aThe order in which you add does not matter.
- 3. Commutative Property ofMultiplication5∙ 10 = 10 ∙ 550 = 50In general,a ∙ b = b ∙ aThe order in which you multiply does not matter.
- 4. The Commutative Propertydoes not hold for subtraction and division.Look at the following examples: 1) Does 8 – 3 = 3 – 8 ? 5 ≠ -5 No! 2) Does 8 ÷ 4 = 4 ÷ 8 ? 2 ≠ ½ No!If you change the order in a subtraction or division problem, you get a different answer.
- 5. Summaryof the CommutativePropertyThe Commutative Property has to do with the order of the numbers.Holds true for Addition and MultiplicationDoes NOT hold true for Subtraction and Division
- 6. Associative Property ofAddition (a + b) + c = a + (b+ c)(2 + 3) + 4 = 2 + (3 + 4)5 + 4 = 2 + 79 = 9It does not matter how the addends are grouped. It changes the order in which you add them, but the answer is the same.of Multiplication(a ∙ b) ∙ c = a ∙ (b ∙ c)(2 ∙ 3) ∙ 4 = 2 ∙ (3 ∙ 4)6 ∙ 4 = 2 ∙1224 = 24It does not matter how the factors are grouped. It changes the order in which you multiply them, but the answer is the same.
- 7. The Associative Propertydoes not hold for subtraction and division.Look at the following examples: 1) Does (9 – 5) – 3 = 9 – (5 – 3) ? 4 – 3 = 9 – 2 1 ≠ 7 No! 2) Does (8 ÷ 4 ) ÷ 2 = 8 ÷ (4 ÷ 2) ? 2 ÷ 2 = 8 ÷2 1 ≠ 4 No!
- 8. Summary of theAssociative PropertyThe Associative Property has to do with how the numbers are grouped together and therefore which pair you operate on first.Holds true for Addition and MultiplicationDoes not hold true for Subtraction and Division
- 9. Identify the PropertyShown 17 + 43 = 43 + 17 (4 ∙ 5) ∙ 2 = 4 ∙ (5 ∙ 2) (8 + 3) + 5 = (3 + 8) + 5 (7 + 2) + 3 = 2 + (7 + 3)