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9/19/11 Properties: Associative and Commutative

9/19/11 Properties: Associative and Commutative. Property : an attribute or quality (sun is hot , elephants are large …) Can you think of properties other things have?. 9/19/11 Properties: Associative and Commutative.

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9/19/11 Properties: Associative and Commutative

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  1. 9/19/11 Properties:Associative and Commutative Property: an attribute or quality (sun is hot, elephants are large…) Can you think of properties other things have?

  2. 9/19/11 Properties:Associative and Commutative Commutative Property: re-ordering the numbers doesn’t change the result Numbers: 3 + 4 = 4 + 3 2 x 6 = 6 x 2 Algebra*: a + b = b + a ab = ba Associative Property: re-grouping the numbers doesn’t change the result Numbers: (3 + 4) + 5 = 3 + (4 + 5) (2 x 4) x 5 = 2 x (4 x 5) Algebra*: (a + b) + c = a + (b + c) (ab)c = a(bc)

  3. 9/19/11 Properties:Associative and Commutative These are properties of addition and multiplication, NOT subtraction or division. Why? For example: 10 + 5 = 5 + 10 10 x 5 = 5 x 10 10 – 5 = 5 – 10? 10 ÷ 5 = 5 ÷ 10?

  4. 9/19/11 Properties:Associative and Commutative COMMUTATIVE --- ORDER (numbers move)

  5. 9/19/11 Properties:Associative and Commutative ASSOCIATIVE --- LAZY (numbers don’t have to move)

  6. SAMPLES Rewrite using commutative. 1) 6 + 7 + 8 2) 7 x 2 Rewrite using associative. 3) (10 x 6) x 5 4) 1 + 2 + (3 + 4) + 5 Which property? 5) 4 + 6 + 7 = 7 + 4 + 6

  7. 9/19/11 HW - Properties Rewrite using commutative. Rewrite using associative. 1) 3 x 6 x 7 5) (8 + 9) + 5 2) 10 + 12 6) 1 x (2 x 3) 3) 1 + 2 + 3 7) 2 + 4 + 6 + 8 • (5 + 4) + 3 8) 3 x (4 x 5) x 2 Which property? 9) 9 + 10 = 10 + 9 10) (3 x 10) x 2 = 3 x (10 x 2) 11) (1 + 2) + 3 = (3 + 1) + 2

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