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**

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

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}}

**Solution**

(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.

(c) **Eliminate the common factors**

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

**Shortcut Method**

First **representing the division into fractional form**.

Now **use the exponent law **of division for same variables.

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

**(02) Divide the below monomials**.

\mathtt{40m^{2} n\ \div \ 4\ mn^{2} \ \ }

**Solution**

(a) Write the **binomials in fractional form.**

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

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

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

**Shortcut Method**

Represent the division in the form of fraction.

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

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} \ } **Solution**

(a) Write the binomial in **fraction form**.

(b)** Write all the factors** in numerator and denominator

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

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

**Shortcut Method**

First write the binomials in **fraction form.**

Now use the **exponent law of division** for further simplification.

The above expression is the solution.

**(04) Divide the below monomials**

\mathtt{27\ p^{-1} q^{-3} \ \div \ 9\ p^{-2} q\ \ }

**Solution**

(a) Write the monomial in form of fraction.

**Converting the negative power into positive** one by taking reciprocal.

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

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

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

**Shortcut Method**

First represent the number in fraction form.

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

Hence, we get the same solution.

**(05) Divide the below monomials**

\mathtt{\ 100\ a^{2} b^{3} \ \div \ 13\ a^{3} \ b^{-5} \ \ }

**Solution**

(a) Represent the division in form of fraction

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

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

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