Commutativity, Associativity, Distributivity as variable

Expression with variables →
Chapter 11 Class 6 Algebra
Concept wise

Properties of Numbers as Variable

Last updated at April 16, 2024 by

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

 

 

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.