Division of Monomials || How to divide monomials

In this post we will learn methods for dividing monomial with another monomial.

To understand the concept, you should have basic knowledge of algebraic expression along with the concept of constants and variables.

How to divide Monomials?

Before moving on to understand the process of monomial division, let us understand the basics of monomials.

What are monomials?

Monomials are algebraic expression with only one entity.
The entity can be made of constants, variables or both.

Examples of monomials:
\mathtt{\Longrightarrow \ 2x}\\\ \\ \mathtt{\Longrightarrow \ 6}\\\ \\ \mathtt{\Longrightarrow \ 9x^{2} y}

Steps for Dividing Monomials

Suppose we have to divide the given two monomials.
\mathtt{6x^{3} y\ \ \div \ 3x^{2} \ } [/latex[</p> <p style="font-size:18px">In order to divide the monomials, follow the below steps:</p> <p style="font-size:18px">(i) First <strong>write the expression in the form of fraction</strong>.</p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" src="https://wtskills.com/wp-content/uploads/2021/07/image-104.png" alt="How to divide monomials" class="wp-image-15396" width="284" height="96" srcset="https://wtskills.com/wp-content/uploads/2021/07/image-104.png 474w, https://wtskills.com/wp-content/uploads/2021/07/image-104-300x101.png 300w" sizes="(max-width: 284px) 100vw, 284px" /></figure> <p></p> <p style="font-size:18px">(ii) <strong>Write all the factors</strong> of both the monomials</p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" src="https://wtskills.com/wp-content/uploads/2021/07/image-105.png" alt="Dividing Monomials" class="wp-image-15397" width="273" height="81" srcset="https://wtskills.com/wp-content/uploads/2021/07/image-105.png 485w, https://wtskills.com/wp-content/uploads/2021/07/image-105-300x89.png 300w" sizes="(max-width: 273px) 100vw, 273px" /></figure> <p></p> <p style="font-size:18px">(iii) <strong>Cancel out the common terms</strong> in numerator and denominator</p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" src="https://wtskills.com/wp-content/uploads/2021/07/image-106.png" alt="Steps to divide monomials " class="wp-image-15398" width="235" height="75" srcset="https://wtskills.com/wp-content/uploads/2021/07/image-106.png 390w, https://wtskills.com/wp-content/uploads/2021/07/image-106-300x95.png 300w" sizes="(max-width: 235px) 100vw, 235px" /></figure> <p></p> <p style="font-size:18px">(iv)<strong> Write the remaining terms</strong>.</p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" src="https://wtskills.com/wp-content/uploads/2021/07/image-107.png" alt="Dividing Monomial examples with solution" class="wp-image-15399" width="123" height="42"/></figure> <p style="font-size:18px">Hence, 2xy is the solution of the given division.</p> <div style="height:100px" aria-hidden="true" class="wp-block-spacer"></div> <h3><strong>Shortcut method of dividing monomials</strong></h3> <p style="font-size:18px">We can <strong>use the exponent law</strong> in order to divide the same variables.</p> <p style="font-size:18px">According to exponent law of division, <strong>the division of exponent with the same base can be done by subtracting the powers</strong>. </p> <figure class="wp-block-image size-large is-resized"><img loading="lazy" src="https://wtskills.com/wp-content/uploads/2021/07/image-108.png" alt="Exponent division formula" class="wp-image-15400" width="199" height="111"/></figure> <p style="font-size:18px">Let us solve the above example again. Suppose we have to divide the below monomials. [latex] \mathtt{6x^{3} y\ \ \div \ 3x^{2} \ }

Follow the below steps:

(a) Write the monomial in form of fraction

dividing monomial in algebra

(b) Divide the constant with constant.
Apply the law of exponent with the same variable

Questions on monomial division

Hence, 2xy is the solution.

I hope both the method of monomial division is clear to you.
Let us see some solved examples for further understanding.

Examples of Monomial Division

(01) Divide the below monomials.
\mathtt{9a^{7} b^{3} \ \div \ 3a^{4} b^{2}}


(a) Write the division in fractional form

\mathtt{\Longrightarrow \ \frac{\mathtt{9a^{7} b^{3} \ }}{\mathtt{3a^{4} b^{2} \ }} \ }

(b) Write all the factors of constant and variables.

examples of monomial division

(c) Eliminate the common factors

questions on dividing monomials

Hence, \mathtt{\ 3a^{3} b} is the solution.

Shortcut Method

First representing the division into fractional form.

Shortcut method to divide monomial

Now use the exponent law of division for same variables.

Algebra lessons for grade 6 math

Hence, \mathtt{\ 3a^{3} b} is the solution.

(02) Divide the below monomials.
\mathtt{40m^{2} n\ \div \ 4\ mn^{2} \ \ }

(a) Write the binomials in fractional form.

monomial division solve examples

(b) Write all the factors of numerator and denominator.

how to divide monomials

(c) Eliminate the common factors from numerator and denominator.

Steps to divide monomial

Hence, \mathtt{10\ m\ n^{-1}} is the solution.

Shortcut Method

Represent the division in the form of fraction.

Learn steps to divide monomials

Use the exponent law of division to divide the common variables.

Shortcut to divide monomials

Hence, \mathtt{10\ m\ n^{-1}} is the solution

(03) Divide the given monomials.
\mathtt{13\ a^{3} bc^{2} \ \div \ 5\ a^{4} b^{3} \ }

(a) Write the binomial in fraction form.

Monomial question with solution

(b) Write all the factors in numerator and denominator

Free algebra math lessons for grade 6

(c) Eliminate the common factors in numerator and denominator.

Free online math lessons

Hence, \mathtt{\frac{13}{5} \ a^{-1} b^{-2} c^{2}} is the solution.

Shortcut Method
First write the binomials in fraction form.

Prepare for SAT exams

Now use the exponent law of division for further simplification.

Dividing monomials with examples

The above expression is the solution.

(04) Divide the below monomials
\mathtt{27\ p^{-1} q^{-3} \ \div \ 9\ p^{-2} q\ \ }

(a) Write the monomial in form of fraction.

Prepare for SAT exams

Converting the negative power into positive one by taking reciprocal.

Learn math as per common core state standard for mathematics

(b) Write all the factors of numerator and denominator

learn how to solve math problems

(c) Eliminate the common factors from numerator and denominator

dividing monomial by monomial

Hence, \mathtt{3\ p q^{-4} \ \ } is the solution.

Shortcut Method
First represent the number in fraction form.

shortcut method of dividing monomials

Now use the exponent division formula to divide the same variables.

How to divide monomials

Hence, we get the same solution.

(05) Divide the below monomials
\mathtt{\ 100\ a^{2} b^{3} \ \div \ 13\ a^{3} \ b^{-5} \ \ }

(a) Represent the division in form of fraction

dividing monomials

Converting -ve power to +ve one by taking the reciprocal.

how to divide monomials

(b) Use the exponent division formula to subtract the same variables.

Monomial shortcut division method

Hence, \mathtt{\frac{100}{13} \ a^{-1} b} is the solution.

Leave a Comment

Your email address will not be published. Required fields are marked *

You cannot copy content of this page