Division of Monomials is the method of dividing monomials by simplifying the expressions in the expanded form. By finding the product of the quotient of numerical coefficients and the quotient of the literal coefficients, we can find the Division of monomials. The resultant of the division of monomial by monomial is also a monomial. The complete information of monomials and terms are given in 6th Grade Math articles.

Read More:

- Multiplication of Two Monomials
- Multiplication of Polynomial by Monomial
- Multiplication of Two Binomials

## Division of Monomial by a Monomial | How to Divide Two Monomials Together?

In Division of Two Monomials, we solve the quotient of numerical coefficients and then solve the quotient of their literal coefficients. Check out the process of solving the division of monomial by monomial below.

**Method I:**

(i) Take the monomials and note down coefficients and variables separately.

(ii) Write each variable and constant in an expanded form.

(iii) Cancel the common terms in the numerator and denominator.

(iv) Write down the remaining part to get the result.

**Example:** Divide 15m^{3} by 3m^{2}

**Solution:**

Given monomials are 15m^{3} and 3m^{2}.

Expand the given terms.

15m^{3} = 15 Ã— m Ã— m Ã— m

3m^{2} = 3 Ã— m Ã— m

Now, divide 15m^{3} by 3m^{2} with the expanded terms.

\(\frac { 15 Ã— m Ã— m Ã— m }{ 3 Ã— m Ã— m } \)

Now, cancel the like terms from the numerator and denominator.

\(\frac { 15 Ã— m Ã— m Ã— m }{ 3 Ã— m Ã— m } \) = 5m

Therefore, the answer is 5m.

**Method II:**

(i) Identify the coefficients and variables.

(ii) We can write each numerical part in the expanded form and then cancel the common terms to both numerator and denominator.

(iii) For the variables, keep the common base and subtract the exponents from both, the numerator as well as the denominator.

(iv) Finally, simplify the expression and write down the answer.

**Example:** 9p^{3} by 3p^{2}

**Solution:
**Given monomials are 9p

^{3}and 3p

^{2}.

Expand the constants.

9 = 3 Ã— 3.

Keep the common base and subtract the exponents from both, the numerator as well as the denominator.

p is the common base in the given monomials. Therefore, subtract the exponents of the base p.

\(\frac { 3 Ã— 3 Ã— p

^{3}}{ 3 Ã— p

^{2}} \)

3 Ã— p

^{3 – 2}= 3p.

Therefore, the answer is 3p.

Do Refer:

### Division of Monomials Examples with Solutions

Check how to divide a Monomial by a Monomial and solve all the problems. The below problems are on the Division of Two Monomials with a detailed explanation. Use our Worksheet on Dividing Monomials to find various problems with a similar concept.

**Question 1.** Divide 36xyz by 9xy

**Solution:**

Given monomials are 36xyz and 9xy.

Expand the given terms.

36xyz = 9 Ã— 4 Ã— x Ã— y Ã— z.

9xy = 9 Ã— x Ã— y.

Now, divide 36xyz by 9xy with the expanded terms.

\(\frac { 9 Ã— 4 Ã— x Ã— y Ã— z }{ 9 Ã— x Ã— y } \)

Now, cancel the like terms from the numerator and denominator.

\(\frac { 9 Ã— 4 Ã— x Ã— y Ã— z }{ 9 Ã— x Ã— y } \) = 4z.

Therefore, the answer is 4z.

**Question 2.** Divide 45a^{3}b^{3} by 15a^{2}b

**Solution:
**Given monomials are 45a

^{3}b

^{3}and 15a

^{2}b.

Expand the constants.

45 = 15 Ã— 3.

Keep the common base and subtract the exponents from both, the numerator as well as the denominator.

a, b are the common base in the given monomials. Therefore, subtract the exponents of the base a and base b.

\(\frac { 15 Ã— 3 Ã— a

^{3}Ã— b

^{3 }}{ 15 Ã— a

^{2}Ã— b } \)

3 Ã— a

^{3 – 2}Â Ã— b

^{3 – 1}= 3ab

^{2}.

Therefore, the answer is 3ab^{2}.

**Question 3.** Divide 18m^{2} by 9m^{2}

**Solution:**

Given monomials are 18m^{2} and 9m^{2}.

Expand the given terms.

18m^{2} = 9 Ã— 2 Ã— m Ã— m.

9m^{2} = 9 Ã— m Ã— m.

Now, divide 18m^{2} by 9m^{2} with the expanded terms.

\(\frac { 9 Ã— 2 Ã— m Ã— m }{ 9 Ã— m Ã— m } \)

Now, cancel the like terms from the numerator and denominator.

\(\frac { 9 Ã— 2 Ã— m Ã— m }{ 9 Ã— m Ã— m } \) = 2.

Therefore, the answer is 2.

**Question 4.** Divide 42a^{7} by 6a^{5}

**Solution:
**Given monomials are 42a

^{7}and 6a

^{5}.

Expand the constants.

42 = 7 Ã— 6.

Keep the common base and subtract the exponents from both, the numerator as well as the denominator.

a is the common base in the given monomials. Therefore, subtract the exponents of the base a and base b.

\(\frac { 7 Ã— 6 Ã— a

^{7}}{ 6 Ã— a

^{5}Â } \)

7 Ã— a

^{7 – 5}= 7a

^{2}.

Therefore, the answer is 7a^{2}.

### FAQs on Dividing Two Monomials and then Simplifying the Product

**1. What Is Dividing Monomials?**

Dividing monomials is the method of dividing every term of the monomial by another monomial.

**2. What are the methods to divide a monomial by a monomial?**

We can go through the two methods to divide a monomial by a monomial. We can expand the terms and divide two monomials and also we can subtract the exponents of the variables having the same base.

**3. Is it possible to Divide Negative Monomials?**

Yes, we can divide Negative Monomials where the monomials have negative coefficients. If both the monomials have negative coefficients, then the negative signs cancel out and we get the positive coefficient as output.

**4. What Is the Property we use When Dividing Two Monomials?**

We use the Quotient Property to divide monomials.

### Conclusion

Check out the article which consists of Division of Monomials, Examples, and Faqs. The complete concept is explained clearly with examples. Solve all the given problems and also read out all the faqs and steps to solve the division of monomial by monomial to know the concept.