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Commutative and Associative Properties

Commutative and Associative Properties. Commutative and Associative Properties. Properties are rules in mathematics. You can use math properties to simplify algebraic expressions!. Commutative and Associative Properties.

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Commutative and Associative Properties

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  1. Commutative and Associative Properties

  2. Commutative and Associative Properties • Properties are rules in mathematics. • You can use math properties to simplify algebraic expressions!

  3. Commutative and Associative Properties • Commutative Property means changing the order in which you add or multiply numbers does not change the sum or product. • Associative Property means 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 {}.

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

  5. Associative Properties Example of 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 Example of 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

  6. Identity Properties • Identity Property means when you add 0 to something or multiply a number by 1, the result is IDENTICAL to the original number. • Example: 4+0=4 AND a+0=a • Example: 7x1=7 AND a(1)=a

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