CLASS-6
DIVISION OF ALGEBRAIC EXPRESSION OF MONOMIAL BY MONOMIAL

DIVISION OF ALGEBRAIC EXPRESSION OF MONOMIAL BY MONOMIAL -

Dividing one monomial by another monomial is a relatively straightforward operation in algebra. When you divide a monomial (a single-term expression) by another monomial, you can simply divide their coefficients (numeric values) and subtract the exponents of the variables. Here's how it works:

Let's say you have two monomials:

  1. Monomial M₁:-  a₁ xⁿ
  2. Monomial M₂:-  a₂ xᵐ

To divide M₁​ by M₂, follow these steps:

  1. Divide the coefficients (​a₁ and a₂):-

              a₁

         --------- 

              a₂

    2. Subtract the exponents of the variables (n and m):-

              xⁿˉᵐ

     Now, you have the result of dividing the monomial M₁ by the monomial M₂​:

             a₁ xⁿ           a₁

         ---------- = -------- xⁿˉᵐ

             a₂ xᵐ           a₂

Here's an example to illustrate this:

Divide the monomial 4x⁵ by the monomial 2x².

               M₁ ​=  4x⁵

               M₂ =  2x²

                                   4

  1. Divide the coefficients: ------- = 2

                                   2

   2.  Subtract the exponents of the variables: 5 − 2 = 3

          So, the result is:

           4x⁵           2

       --------- = ------- x⁵ˉ² =  2x³  

           2x²           1

Therefore, when you divide the monomial 4x⁵ by the monomial 2x², the result is 2x³.      (Ans.)


When you divide a monomial by another monomial, you are essentially performing a simple division of coefficients and subtracting the exponents of the variables. Here's how to do it:

Let's say you want to divide one monomial, M₁​, by another monomial, M₂ ​:           

  1. Monomial M₁:-  a₁ xⁿ
  2. Monomial M₂:-  a₂ xᵐ

Where:

  • ​a₁ and a₂​ are coefficients.
  • x is the variable.
  • n and m are non-negative integers representing the exponents.

To divide M₁ by M₂​, follow these steps:

  1. Divide the coefficients a₁ and a₁ :  

                a₁

           ---------- 

                a₂

    2. Subtract the exponents of x :

              n - m

    3. Put it all together: 

                    a₁

               --------- xⁿˉᵐ

                    a₂

  So, when you divide M₁ by M₂​, you get the result as:            

                    a₁

               --------- xⁿˉᵐ

                    a₂

    Here are some examples to illustrate this:

  1.  Divide 3x⁵ by 2x² 

        M₁ = 3x⁵

        M₂ = 2x²

       M₁          3x⁵           3                3

    ------- = -------- = ------- x⁵ˉ² = ------ x³       (Ans.)

       M₂          2x²           2                2


    2.  Divide 4x⁴ by 7x²

         M₁ = 4x⁴

         M₂ = 7x²

        M₁          4x⁴           4                 4

    -------- = -------- = ------- x⁴ˉ² = ------- x²            (Ans.)

        M₂          7x²           7                 7


    3. Divide 2x⁷ by 2x³        

         M₁ = 2x⁷

         M₂ = 7x²

        M₁           2x⁷           1                        

    -------- = --------- = ------- x⁷ˉ³ =  x⁴                 (Ans.)

        M₂           2x³           1                       

So, when you divide one monomial by another, you simply divide the coefficients and subtract the exponents of the variables to obtain the simplified result.


Divide Monomial by Monomial via Finding the Coefficient -


Example.1) Divide 32a³b⁷c² by 4ac⁴b⁵

Ans.)

Algebra


Example.2) Divide 16a⁵b²by 24a²b².

Ans.)

Algebra