# CLASS-6DIVISION 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.) Example.2) Divide 16a⁵b²by 24a²b².

Ans.) 