Commutative and Associative Properties

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

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 {}.

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

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

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