Commutative Properties
    Commutative Properties
  Changing the order of the numbers in 
  Changing the order of the numbers in 
  addition or multiplication will not 
  addition or multiplication will not 
  change the result.
  change the result.
   Commutative Property of Addition 
   Commutative Property of Addition 
  states: 2 + 3 = 3 + 2 or a + b = b + a.
  states: 2 + 3 = 3 + 2 or a + b = b + a.
   Commutative Property of 
   Commutative Property of 
  Multiplication states: 4 • 5 = 5 • 4 or 
  Multiplication states: 4 • 5 = 5 • 4 or 
  ab = ba.
  ab = ba.
    Associative Properties
    Associative Properties
  Changing the grouping of the 
  Changing the grouping of the 
  numbers in addition or multiplication 
  numbers in addition or multiplication 
  will not change the result.
  will not change the result.
  Associative Property of Addition 
  Associative Property of Addition 
  states: 3 + (4 + 5)= (3 + 4)+ 5 or        
  states: 3 + (4 + 5)= (3 + 4)+ 5 or        
  a + (b + c)= (a + b)+ c 
  a + (b + c)= (a + b)+ c 
  Associative Property of Multiplication 
  Associative Property of Multiplication 
  states: (2 • 3) • 4 = 2 • (3 • 4) or   
  states: (2 • 3) • 4 = 2 • (3 • 4) or   
  (ab)c = a(bc) 
  (ab)c = a(bc) 
      Distributive Property 
      Distributive Property 
   Multiplication distributes over addition.
                         .
   Multiplication distributes over addition
            
       abc abac
           
       325 3235
    Additive Identity Property
    Additive Identity Property
  There exists a unique number 0 such 
  There exists a unique number 0 such 
  that zero preserves identities under 
  that zero preserves identities under 
  addition.
  addition.
  a + 0 = a and 0 + a = a
  a + 0 = a and 0 + a = a
  In other words adding zero to a 
  In other words adding zero to a 
  number does not change its value.
  number does not change its value.
  Multiplicative Identity Property
   Multiplicative Identity Property
   There exists a unique number 1 such 
   There exists a unique number 1 such 
   that the number 1 preserves identities 
   that the number 1 preserves identities 
   under multiplication.
   under multiplication.
   a ∙ 1 = a and 1 ∙ a = a
   a ∙ 1 = a and 1 ∙ a = a
   In other words multiplying a number by 
   In other words multiplying a number by 
   1 does not change the value of the 
   1 does not change the value of the 
   number.
   number.