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Commutative and Associative Properties

Commutative and Associative Properties. Commutative and Associative Properties. Commutative Property – changing the order in which you add or multiply numbers does not change the sum or product.

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Commutative and Associative Properties

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  1. Commutative and Associative Properties

  2. Commutative and Associative Properties • Commutative Property – changing the order in which you add or multiply numbers does not change the sum or product. • Associative Property – changing the grouping of numbers when adding or multiplying does not change their sum or product. • Grouping symbols are typically parentheses (),but can include brackets [] or Braces {}.

  3. Commutative and Associative Properties Commutative Properties Commutative Property of addition - (Order) For any numbers a and b , a + b = b + a 45 + 5 = 5 + 45 50 = 50 Commutative Property of multiplication - (order) For any numbers a and b , a  b = b  a 6 8 = 8  6 48 = 48

  4. Commutative and Associative Properties Associative Properties Associative Property of addition - (grouping symbols) For any numbers a, b, and c, (a + b) + c = a + (b + c) (2 + 4) + 5 = 2 + (4 + 5) (6) + 5 = 2 + (9) 11 = 11 Associative Property of multiplication - (grouping symbols) For any numbers a, b, and c, (ab)c = a (bc) (2  3)  5 = 2  (3  5) (6)  5 = 2  (15) 30 = 30

  5. Commutative and Associative Properties Commutative and associative properties are very helpful to solve problems using mental math strategies Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property) Solve: 18 + 13 + 16 + 27 + 22 + 24 (18 + 22) + (16 + 24) + (13 + 27) (40) + (40) + (40) = 120

  6. Commutative and Associative Properties Commutative and associative properties are very helpful to solve problems using mental math strategies Solve: 4  7  25 Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) 4  25  7 Group numbers that can be formed easily. (Associative property) (4  25)  7 (100)  7 = 700

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