Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : How to divide monomial quotients

Study concepts, example questions & explanations for Algebra 1

Create An Account

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Divide Monomial Quotients

Evaluate

$\frac{(12w^{2}-15w+21w^{3})}{3w}$

Possible Answers:

$2w^{2}+4w-5$

$7w^{2}+4w-5$

$2w^{2}-4w+5$

$-1+7w^{2}$

Correct answer:

$7w^{2}+4w-5$

Explanation:

$\frac{(12w^{2}-15w+21w^{3})}{3w}$

When dividing a polynomial by a monomial, we can use a divison called, term-by-term, dividing each of the top terms by the monomial.

$\frac{12w^{2}}{3w}-\frac{15w}{3w}+\frac{21w^{3}}{3w}$

Simplify.

$4w-5+7w^{2}$

Rewrite it with the leading coefficent first,

Final Answer: $7w^{2}+4w-5$

Report an Error

Example Question #2 : How To Divide Monomial Quotients

Simplify the fraction to its lowest terms:

$\frac{18x^4y^3z}{6xy^2z^3}$

Possible Answers:

3x^3yz^2

3x^5y^5z^4

$3x^3yz^{-2}$

3x^3yz^2

12x^3yz^2

Correct answer:

$3x^3yz^{-2}$

Explanation:

The first step is to divide the constants, 18 and 6, by the LCM, 6, to get 3. When dividing variables, if the variable is present in the numerator and denominator, subtract the exponent found in the numerator by the exponent in the denominator.

For , you have 4-1=3 .

For , you have 3-2=1 .

For , you have 1-3=-2 .

Then write the simplified answer as one term:

$3x^3yz^{-2}$

Report an Error

Example Question #3 : How To Divide Monomial Quotients

Divide:

$\frac{9x^4+6x^3-12x}{3x}$

Possible Answers:

3x^3+2x^2-4

6x^3+3x^2+9

3x^3+2x^2+4

6x^3+3x^2-9

Correct answer:

3x^3+2x^2-4

Explanation:

$\frac{9x^4+6x^3-12x}{3x}=\frac{9x^4}{3x}+\frac{6x^3}{3x}-\frac{12x}{3x}=3x^3+2x^2-4$

Report an Error

Example Question #1 : How To Divide Monomial Quotients

Siimplify:

$\frac{2x^{2}y^{3}z - 6xy^{2}z^{2}+10x^{3}yz^{3}}{2xyz} =\ ?$

Possible Answers:

$xy - yz+5xz^{2}$

$xy^{2}-3yz+5x^{2}z^{2}$

$xy^{2}-3xz+5xy$

$x^{2}y - 3xyz + 5x^{2}yz^{2}$

$xyz-3yz+5x^{2}yz^{2}$

Correct answer:

$xy^{2}-3yz+5x^{2}z^{2}$

Explanation:

For any polynomial division, divide each term in the numerator individually by the denominator:

$\frac{2x^{2}y^{3}z - 6xy^{2}z^{2}+10x^{3}yz^{3}}{2xyz} =$ $\frac{2x^{2}y^{3}z}{2xyz} - \frac{6xy^{2}z^{2}}{2xyz} + \frac{10x^{3}yz^{3}}{2xyz}=$

$xy^{2}-3yz+5x^{2}z^{2}$

Report an Error

Example Question #4 : How To Divide Monomial Quotients

Simplify:

$\frac{14x^2y}{7x}$

Possible Answers:

$\frac{1}{2xy}$

98x^3y

98xy

2xy

Correct answer:

2xy

Explanation:

When dividing monomials, consider the coefficients and variables separately. Rewrite the expression as $\left(\frac{14}{7}\right)\left(\frac{x^2}{x}\right)\left(y\right)$ , grouping common bases. For the coeffiecients, we can divide normally: $\left(\frac{14}{7} \right )=2$ . For the variables, we can keep the common base and subtract the exponents: $\left(\frac{x^2}{x} \right )=x^{2-1}=x$ . Then, multiply each portion all back together to obtain 2xy .

Report an Error

Example Question #1 : Simplifying Expressions

Simplify the expression.

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}$

Possible Answers:

$\small \frac{x^2y^5}{z^3}$

$\small \frac{xy^3}{z^3}$

$\small \frac{z^3}{x^2y^5}$

$\small \frac{z^3}{xy^3}$

Correct answer:

$\small \frac{xy^3}{z^3}$

Explanation:

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}$

Because we are only multiplying terms in the numerator, we can disregard the parentheses.

$\small \frac{(x^2y^2)(x^3y^4z)}{x^4y^3z^4}=\frac{x^2y^2x^3y^4z}{x^4y^3z^4}$

To combine like terms in the numerator, we add their exponents.

$\small \frac{x^5y^6z}{x^4y^3z^4}$

To combine like terms between the numerator and denominator, subtract the denominator exponent from the numerator exponent.

$x^{5-4}y^{6-3}z^{1-4}=xy^3z^{-3}$

Remember that any negative exponents stay in the denominator.

$\frac{xy^3}{z^3}$

Report an Error

Example Question #2 : How To Divide Monomial Quotients

Simplify: $\frac{5p^{7}}{25p^{^{4}}}$

Possible Answers:

$\frac{p^{7/4}}{5}$

$\frac{p^{-3}}{5}$

$\frac{p}{5}$

$\frac{p^{3}}{5}$

$5p^{3}$

Correct answer:

$\frac{p^{3}}{5}$

Explanation:

$p^{7}$ and $p^{4}$ cancel out, leaving $p^{3}$ in the numerator. 5 and 25 cancel out, leaving 5 in the denominator

Report an Error

Example Question #4 : How To Divide Monomial Quotients

Simplify the following:

$\frac{4x+6x^2}{2x}$

Possible Answers:

$\frac{1}{x}-1\frac{1}{2}$

2x(2-3x)

$\frac{2}{2x}-\frac{3}{2}$

$\frac{2-3x}{2x}$

2+3x

Correct answer:

2+3x

Explanation:

$\frac{4x+6x^2}{2x}$

First, let us factor the numerator:

4x+6x^2=x(4+6x)=2x(2+3x)

$\frac{2x(2+3x)}{2x}=2+3x$

Report an Error

Example Question #5 : How To Divide Monomial Quotients

Simplify the following:

$\frac{-2pl^2}{3yz}\div \frac{9lp^2}{5xy}$

Possible Answers:

$\frac{-18p^{3}l^{3}}{15xy^{2}z}$

$\frac{-10lx}{27zp}$

$\frac{-18}{15xyz}$

$\frac{5}{9}$

Correct answer:

$\frac{-10lx}{27zp}$

Explanation:

First, flip the numerator and the denominator of the second fraction to turn the division into multiplication.

$\frac{-2pl^2}{3yz}\div \frac{9lp^2}{5xy}=\frac{-2pl^2}{3yz} * \frac{5xy}{9lp^2}=\frac{-2pl^25xy}{3yz9lp^2}$

We can then cancel like terms.

From both the numerator and denominator, remove one , remove one , and remove one :

$\frac{-2l5x}{3z9p}$

Then we finish by multiplying the constants:

$\frac{-10lx}{27zp}$

Report an Error

Example Question #1 : How To Divide Monomial Quotients

Simplify this expression:

$\frac{x^{2}y^{-3}z^{4}}{x^{3}y^{-2}z^{2}}$

Possible Answers:

$xyz^{2}$

$\frac{yz^{2}}{x}$

$\frac{z^{2}}{xy}$

$\frac{1}{xyz^{2}}$

$\frac{xy}{z^{2}}$

Correct answer:

$\frac{z^{2}}{xy}$

Explanation:

When different powers of the same variable are multiplied, the exponents are added. When different powers of the same variable are divided, the exponents are subtracted. So, as an example:

$\frac{x^{3}}{x} = x^{\left ( 3-1\right )} = x^{2}$

For the above problem,

$\frac{x^{2}}{x^{3}} = \frac{1}{x} ; \frac{y^{-3}}{y^{-2}} = \frac{y^{2}}{y^{3}} = \frac{1}{y} ; \frac{z^{4}}{z^{2}} = z^{2}$

Therefore, the expression simplifies to:

$\left ( \frac{1}{x} \right ) \left ( \frac{1}{y} \right ) z^{2} = \frac{z^{2}}{xy}$

Report an Error

View Algebra Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Algebra Tutors

Arianna
Certified Tutor

Washington State University, Bachelor in Arts, Communication, General. City University of Seattle, Masters in Business Admini...

View Algebra Tutors

Ivory
Certified Tutor

Hopkinsville Community College, Associate, Associates in Science. Western Kentucky University, Bachelor in Arts, Psychology.

All Algebra 1 Resources

10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Miami, Calculus Tutors in Denver, SAT Tutors in Houston, Spanish Tutors in Atlanta, Algebra Tutors in Atlanta, Biology Tutors in New York City, LSAT Tutors in San Francisco-Bay Area, Physics Tutors in Los Angeles, Math Tutors in Boston, GRE Tutors in Miami

Popular Courses & Classes

Spanish Courses & Classes in Chicago, MCAT Courses & Classes in Phoenix, Spanish Courses & Classes in Seattle, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Miami, SAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Phoenix, GMAT Courses & Classes in San Diego, LSAT Courses & Classes in Philadelphia, GMAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

SSAT Test Prep in Houston, SSAT Test Prep in Washington DC, SAT Test Prep in Seattle, GMAT Test Prep in San Diego, SAT Test Prep in Boston, GMAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Chicago, MCAT Test Prep in Seattle, ISEE Test Prep in Atlanta, GMAT Test Prep in Denver

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Algebra 1 : How to divide monomial quotients

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #1 : How To Divide Monomial Quotients

Example Question #2 : How To Divide Monomial Quotients

Example Question #3 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

Example Question #4 : How To Divide Monomial Quotients

Example Question #1 : Simplifying Expressions

Example Question #2 : How To Divide Monomial Quotients

Example Question #4 : How To Divide Monomial Quotients

Example Question #5 : How To Divide Monomial Quotients

Example Question #1 : How To Divide Monomial Quotients

All Algebra 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: