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Simplifying Algebra with Commutative and Associative Properties

Learn how to simplify algebraic expressions using Commutative and Associative Properties in mathematics. Understand the rules that govern changing the order of numbers in addition and multiplication without altering the result. Explore examples of the Commutative and Associative Properties, as well as the Identity Property, through clear explanations and illustrations.

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Simplifying Algebra with 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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