Properties of Numbers as Variable

Commutativity

 

We studied that

   Commutativity (link) over addition is

       2 + 3 = 3 + 2

 

We can also write this as variables

  a + b = b + a

 

Similarly,

  Commutativity (link) over multiplication is

    4 × 5 = 5 × 4

 

We can also write this as variables

     a × b = b × a

 

Associativity

Similarly,

       Associativity (link) over addition is

(2 + 5) + 4 = 2 + (5 + 4)

              7 + 4 = 2 + 9

        11 = 11

 

We can also write this as variables,

    (a + b) + c = a + (b + c)

 

And,

  Associativity (link) over multiplication is

  (3 × 4) × 5 = 3 × (4 × 5)     

      12 × 5 = 3 × 20

      60 = 60  

 

We can also write this as variables

   (a × b) × c = a × (b × c)

 

Distributivity

 

Also,

       Distributivity is

    7 × (30 + 8) = 7 × 30 + 7 × 8

 

Writing in variables

    a × (b + c) = a × b + a × c