Multiply integers.
       Multiply integers.
         2     3   =     6
                               Ways to Show Multiplication
                               Ways to Show Multiplication
      Factors     Product              2 ∙ 3
                                       2(3)
                                       (2)(3)
                                          
                                       2     3
                                       2x
         Properties of Multiplication
         Properties of Multiplication
           Property               Example                  Word Form                Symbolic Form
         Multiplicative          0(4) = 0             The product of a 
         Property of 0           5(0) = 0             number and 0 is 0.                0 ∙ a = 0
         Multiplicative                               The product of a 
         Identity                4(1) = 4             number and 1 is that              1 ∙a = a
                                                      number.
         Commutative                                  Changing the order 
         Property of           3(5) = 5(3)            of factors does not               ab = ba
         Multiplication                               affect the product.
         Associative                                  Changing the 
         Property of          (2 ∙ 3) ∙ 4 = 24        grouping of three or 
                              2 ∙ (3 ∙ 4) = 24                                     a(bc) = (ab)c
         Multiplication                               more factors does not 
                                                      affect the product.
         Distributive                                 A sum multiplied by 
         Property of       2(3 + 4) = 2(3) + 2(4) a factor is equal to 
         Multiplication                               the sum of that factor        a(b + c) = ab + ac
         over Addition     3(x + 2) = 3x + 3(2)       multiplied by each 
                                                      addend.
       Multiplying Numbers with Different Signs
        Multiplying Numbers with Different Signs
            3(4)   =   12
            3(3)   =   9        When multiplying two numbers 
            3(2)   =   6        that have different signs, the 
            3(1)   =   3        product is negative.
            3(0)   =   0
            3(–1) = –3
            3(–2) = –6
            3(–3) = –9
       Multiplying Numbers with the Same Sign
       Multiplying Numbers with the Same Sign
          –3(4)  =  –12
          –3(3)  =  –9        When multiplying two numbers 
          –3(2)  =  –6        that have the same sign, the 
          –3(1)  =  –3        product is positive.
          –3(0)  =   0
          –3(–1) =  3
          –3(–2) =  6
          –3(–3) =  9
        Multiplying Integers
        Multiplying Integers
           –2(7)                   Different = answer negative           = –14 
           3(–5)                   Different = answer negative          = –15
           –6(–2)                  Same = answer positive               = 12 
            5(–2)                  Different = answer negative          = –10
            3(6)                   Same = answer positive               = 18 
           – 3(– 8)                Same = answer positive               = 24