Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Monomials

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

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 14 15 16 Next →

Example Question #81 : Monomials

Divide the following monomial quotients:

$\frac{32y^{3}}{4x}$

Possible Answers:

$\frac{4y}{x^{2}}$

$\frac{8y^{3}}{x}$

12xy

$\frac{8y}{x}$

Correct answer:

$\frac{8y^{3}}{x}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{32}{4}=8$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{1}{x} =x^{-1}=\frac{1}{x}$

$\frac{y^{3}}{1}=y^{3}$

Combine these to get the final answer:

$\frac{8y^{3}}{x}$

Report an Error

Example Question #81 : Monomials

Divide the following monomial quotients:

$\frac{28y^{2}}{7y}$

Possible Answers:

$3y^{2}$

$\frac{4}{y}$

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{28}{7}=4$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{y^{2}}{y}=y$

Combine these to get the final answer:

Report an Error

Example Question #81 : Monomials

Divide the following monomial quotients:

$\frac{16xy^{2}}{2xy}$

Possible Answers:

$\frac{y}{4}$

$8y^{2}$

$\frac{y}{x}$

Correct answer:

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{16}{2}=8$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x}{x} =x^{1-1}=1$

$\frac{y^{2}}{y}=y^{2-1}=y$

Combine these to get the final answer:

Report an Error

Example Question #84 : Monomials

Divide the following monomial quotients:

$\frac{x^{15}y}{x^{3}y^{2}}$

Possible Answers:

$\frac{x^{3}}{y}$

$\frac{x^{12}}{y}$

$\frac{x^{18}}{y}$

$\frac{x^{5}}{y^{2}}$

Correct answer:

$\frac{x^{12}}{y}$

Explanation:

To solve this problem, divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

$\frac{x^{15}}{x^{3}} =x^{15-3}=x^{12}$

$\frac{y}{y^{2}}=y^{1-2}=\frac{1}{y}$

Combine these to get the final answer:

$\frac{x^{12}}{y}$

Report an Error

Example Question #41 : How To Divide Monomial Quotients

Divide the following monomial quotients:

$\frac{15xy}{3x^{2}}$

Possible Answers:

$\frac{5x}{y}$

5xy

$\frac{5y}{x}$

Correct answer:

$\frac{5y}{x}$

Explanation:

To solve this problem, split it into two steps:

1. Divide the coefficients

$\frac{15}{3}=5$

2. Divide the variables. We also need to remember the following laws of exponents rule: When dividing variables, subtract the exponents.

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

$\frac{y}{1}=y$

Combine these to get the final answer:

$\frac{5y}{x}$

Report an Error

Example Question #42 : How To Divide Monomial Quotients

Divide: $\frac{9x}{33x^2}$

Possible Answers:

$\frac{3}{11x}$

$\frac{1}{24x}$

$-\frac{1}{24x}$

$\frac{3x}{11}$

24x

Correct answer:

$\frac{3}{11x}$

Explanation:

In order to simplify this fraction, write the factors out for the numerator and denominator.

$\frac{9x}{33x^2} = \frac{3\cdot 3\cdot x}{3\cdot 11 \cdot x \cdot x}$

Cancel out the common terms in the numerator and denominator.

$\frac{3\cdot 3\cdot x}{3\cdot 11 \cdot x \cdot x} = \frac{3}{11x}$

The answer is: $\frac{3}{11x}$

Report an Error

Example Question #82 : Monomials

Evaluate:

$\frac{21x+14x^2+28x^3}{7x}$

Possible Answers:

x^2+2x+7

$\frac{4x^2}{2x+3}$

4x^2+2x+3

21x^2+7x+14

$\frac{4x+2}{7x}$

Correct answer:

4x^2+2x+3

Explanation:

We can simplify this monomial by cancelling out like terms in the numerator and denominator:

$\frac{21x+14x^2+28x^3}{7x}=\frac{7x(3+2x+4x^2)}{7x}=4x^2+2x+3$

Report an Error

Example Question #83 : Monomials

Evaluate:

$\frac{64x^{6}y^{-3}z^7}{12x^{4}y^{-2}z^9}$

Possible Answers:

$\frac{3z^3}{16x^{2}y}$

$\frac{3x^{2}y}{16z^2}$

$\frac{16x^{2}}{3yz^2}$

$\frac{16x^{2}}{3y^{-1}z^2}$

$\frac{4x^{2}}{yz^2}$

Correct answer:

$\frac{16x^{2}}{3yz^2}$

Explanation:

To evaluate, we must cancel out like values on the numerator and denominator:

$\frac{64x^{6}y^{-3}z^7}{12x^{4}y^{-2}z^9}=\frac{64x^{6}y^{2}z^7}{12x^{4}y^{3}z^9}=\frac{16x^{2}}{3yz^2}$

Report an Error

Example Question #45 : How To Divide Monomial Quotients

Divide the following

$\frac{24a^4bc^5}{2abc^2}$

Possible Answers:

24a^3c^3

12abc

12a^3c^3

12a^5b^2c^7

12a^3bc^3

Correct answer:

12a^3c^3

Explanation:

To solve, we will divide the monomials using the quotient of powers.

SOLUTION A

We have

$\frac{24a^4bc^5}{2abc^2}$

We know

$a^4 = a \cdot a \cdot a \cdot a$

and

$c^5 = c \cdot c \cdot c \cdot c \cdot c$

and so on.

Let's expand the original problem. We get

$\frac{24 \cdot a \cdot a \cdot a \cdot a \cdot b \cdot c \cdot c \cdot c \cdot c \cdot c}{2 \cdot a \cdot b \cdot c \cdot c}$

Now, we know we can look at the numerator and cancel anything in the denominator. So,

$\frac{24 \cdot {\color{Red} a} \cdot a \cdot a \cdot a \cdot {\color{Blue} b} \cdot {\color{Green} c} \cdot {\color{Green} c} \cdot c \cdot c \cdot c}{2 \cdot {\color{Red} a} \cdot {\color{Blue} b} \cdot {\color{Green} c} \cdot {\color{Green} c}}$

We can cancel the variables that have been highlighted. So, we get

$\frac{24 \cdot a \cdot a \cdot a \cdot c \cdot c \cdot c}{2}$

We can divide the integers, leaving us with

$12 \cdot a \cdot a \cdot a \cdot c \cdot c \cdot c}$

Which equals

12a^3c^3

SOLUTION B

We can solve this a different way by using a shortcut. When dividing monomials, simply subtract the quotients with the same base.

$\frac{24{\color{Red} a^4}{\color{Blue} b}{\color{Green} c^5}}{2{\color{Red} a}{\color{Blue} b}{\color{Green} c^2}}$

The different variables have been highlighted. Now, we subtract.

$\frac{24a^{4-1}b^{1-1}c^{5-2}}{2}$

$\frac{24a^3c^3}{2}$

12a^3c^3

Report an Error

Example Question #46 : How To Divide Monomial Quotients

Find the quotient of the following

$\frac{36x^3y^2}{9xy^2}$ .

Possible Answers:

4xy

6x^4y^4

6x^2y

4x^4y^4

4x^2

Correct answer:

4x^2

Explanation:

When dividing polynomials, you subtract the powers with the same base.

$\frac{36x^3y^2}{9xy^2}$

$\frac{36}{9}x^{3-1}y^{2-2}$

$\frac{36}{9}x^2y^0$

We know that anything raised to the zero power equals 1.

So we get

$\frac{36}{9}x^2$

We simplify the integers.

We get

4x^2

Report an Error

← Previous 1 2 … 5 6 7 8 9 10 11 12 13 14 15 16 Next →

View Algebra Tutors

Li
Certified Tutor

McMurry University, Bachelor of Science, Computer Science. Texas Tech University, Master of Science, Computer Science.

View Algebra Tutors

Bose
Certified Tutor

California University of Pennsylvania, Master of Science, Applied Mathematics. California University of Pennsylvania, Bachelo...

View Algebra Tutors

Ayan
Certified Tutor

Vellore Institute of Technology, Bachelor, Chemical Engineering. University of Calgary, Master's/Graduate, Chemical and Petro...

All Algebra 1 Resources

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

Popular Subjects

MCAT Tutors in Phoenix, SSAT Tutors in San Diego, MCAT Tutors in San Francisco-Bay Area, Computer Science Tutors in Phoenix, Calculus Tutors in Atlanta, Spanish Tutors in Phoenix, LSAT Tutors in Philadelphia, Computer Science Tutors in New York City, MCAT Tutors in Dallas Fort Worth, Spanish Tutors in Denver

Popular Courses & Classes

ACT Courses & Classes in Washington DC, LSAT Courses & Classes in Miami, Spanish Courses & Classes in New York City, GRE Courses & Classes in Los Angeles, MCAT Courses & Classes in Miami, LSAT Courses & Classes in San Diego, GRE Courses & Classes in Philadelphia, GRE Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Miami, GRE Courses & Classes in Atlanta

Popular Test Prep

ISEE Test Prep in Atlanta, GMAT Test Prep in Dallas Fort Worth, LSAT Test Prep in Houston, GMAT Test Prep in Seattle, SSAT Test Prep in New York City, ACT Test Prep in Washington DC, LSAT Test Prep in Chicago, GRE Test Prep in Atlanta, LSAT Test Prep in Washington DC, LSAT Test Prep in Dallas Fort Worth

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 : Monomials

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #81 : Monomials

Example Question #81 : Monomials

Example Question #81 : Monomials

Example Question #84 : Monomials

Example Question #41 : How To Divide Monomial Quotients

Example Question #42 : How To Divide Monomial Quotients

Example Question #82 : Monomials

Example Question #83 : Monomials

Example Question #45 : How To Divide Monomial Quotients

SOLUTION A

SOLUTION B

Example Question #46 : 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: