Question

Taking a=-5, b=4 and c=-3, verify the following properties for multiplication of integers: (a) Commutative property (b) Associative property (c) Distributive property of multiplication over addition (d) Distributive property of multiplication over subtraction​

Answer 1

a = -5                 b = 4               c = -3

a) Commutative property

      This property states that $a+b = b+a$

        To verify we take,

        LHS = $a+b$

                = $-5+4$

                = $-1$

        RHS = $b+a$

                = $4-5$

                = $-1$

  Hence, LHS = RHS    , Verified.

b) Associative property

  This property states that $a+(b+c) = (a+b) +c$

    To verify we take,

     LHS = $a+(b+c)$

             = $-5+(4-3)$

             = $-5+1$

             = $-4$

             

 RHS = $(a+b) +c$

         = $(-5+4)+(-3)$

         = $-1 -3$

         = $-4$

Hence, LHS=RHS            , Verified

c) Distributive propert of multiplication over addition

   This property states that $a(b+c) = ab+ac$

      To verify we take,

  LHS = $a(b+c)$

          = $-5(4-3)$

          = $-5(1)$

          = $-5$

RHS = $ab+ac$

        = $-5(4) + (-5)(-3)$

        = $-20+15$

        = $-5$

Hence, LHS=RHS            , Verified

d) Distributive propert of multiplication over subtraction

     This property states that $a(b-c) = ab-ac$

      To verify we take,

          LHS = $a(b-c)$

                  = $-5(4+3)$

                  = $-5(7)$

                  = $-35$

     RHS = $ab-ac$

        = $-5(4) - (-5)(-3)$

        = $-20-15$

        = $-35$

Hence, LHS=RHS            , Verified