Call Now to Set Up Tutoring:

(888) 888-0446

Algebra 1 : Algebra 1

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 #512 : Variables

Divide: $\frac{x^3 yz^2}{x^5yz^3}$

Possible Answers:

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

$\frac{1}{x^2z}$

$\textup{The denominator cannot be zero.}$

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

$\frac{1}{x^2yz}$

Correct answer:

$\frac{1}{x^2z}$

Explanation:

Each variable in this expression can be solved separately. When we are dividing the powers of the same base, we can simply subtract the powers.

$\frac{x^3}{x^5} = x^{3-5} = x^{-2}$

The negative exponent can be converted to: $\frac{1}{x^2}$

Dividing the terms on the numerator and denominator will give us .

$\frac{y}{y} = \frac{y^1}{y^1} = y^{1-1}= y^0 = 1$

Divide $\frac{z^2}{z^3}$ and simplify to a fraction.

$\frac{z^2}{z^3} = z^{2-3} = z^{-1} = \frac{1}{z}$

Multiply all the terms.

$(\frac{1}{x^2})(1)(\frac{1}{z}) = \frac{1}{x^2z}$

The answer is: $\frac{1}{x^2z}$

Report an Error

Example Question #513 : Variables

Divide: $\frac{3xy^2}{9x^2y^4}$

Possible Answers:

$\frac{1}{3x^2y^2}$

$\frac{3}{xy}$

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

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

$\frac{1}{3xy^2}$

Correct answer:

$\frac{1}{3xy^2}$

Explanation:

Write out the factors for the numerator and denominator.

$\frac{3xy^2}{9x^2y^4}= \frac{3 \cdot x \cdot y^2}{3\cdot3\cdot x \cdot x \cdot y^2 \cdot y^2}$

Cancel the common factors on the top and bottom.

The answer is: $\frac{1}{3xy^2}$

Report an Error

Example Question #521 : Variables

Simplify the following:

$\frac{8a^2b^3}{-2ab}$

Possible Answers:

-6a^2b^2

-4a^3b^4

-4a^2b^2

-4ab^2

-6ab^2

Correct answer:

-4ab^2

Explanation:

Given the problem

$\frac{8a^2b^3}{-2ab}$

we will write it like

$(\frac{8}{-2})(\frac{a^2b^3}{ab})$

We can easily simplify the first part

$(-4)(\frac{a^2b^3}{ab})$

Now, when dividing, to simplify monomials containing the same base, you substract their exponents. We get

$(-4)(a^{2-1}b^{3-1})$

(-4)(a^1b^2)

(-4)(ab^2)

-4ab^2

Report an Error

Example Question #522 : Variables

Solve: $\frac{5x^2y}{15xy^6}$

Possible Answers:

$\frac{y^5}{3x}$

$\frac{x}{3y^5}$

$\frac{3x}{y^5}$

$\frac{1}{3xy^5}$

$\frac{xy^4}{3}$

Correct answer:

$\frac{x}{3y^5}$

Explanation:

In order to solve this expression, we need to write out the factors of the numerator and denominator.

$\frac{5x^2y}{15xy^6} = \frac{5\cdot x \cdot x \cdot y}{5 \cdot 3 \cdot x \cdot y \cdot y^5}$

We can then cancel out the common terms.

The answer is: $\frac{x}{3y^5}$

Report an Error

Example Question #523 : Variables

Divide: $\frac{6ab^2}{6b^3}$

Possible Answers:

$\frac{1}{ab}$

$\frac{12a}{b^3}$

$\frac{1}{6ab}$

$\frac{6}{ab}$

$\frac{a}{b}$

Correct answer:

$\frac{a}{b}$

Explanation:

In order to divide, we should split the top and bottom into their factors.

$\frac{6ab^2}{6b^3} = \frac{6 \times a \times b^2}{6 \times b \times b^2}$

The six and b^2 terms can be cancelled in the numerator and denominator.

The answer is: $\frac{a}{b}$

Report an Error

Example Question #524 : Variables

Divide: $\frac{18x^2y^3}{36x^5y^{-3}}$

Possible Answers:

$\frac{y^6}{2x^3}$

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

$\frac{1}{2x^3}$

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

$\frac{1}{2x^3y^6}$

Correct answer:

$\frac{y^6}{2x^3}$

Explanation:

When similar bases of a certain power are divided, their powers can be subtracted.

Evaluate each term.

$\frac{18}{36} = \frac{1}{2}$

When dealing with negative exponents, they can be rewritten as the reciprocal of the positive exponent.

$\frac{x^2}{x^5} = x^{2-5} = x^{-3} = \frac{1}{x^3}$

$\frac{y^3}{y^{-3}} = y^{3-(-3)} = y^6$

Multiply all the terms together.

$\frac{1}{2}\cdot\frac{1}{x^3}\cdot y^6 = \frac{y^6}{2x^3}$

The answer is: $\frac{y^6}{2x^3}$

Report an Error

Example Question #525 : Variables

Divide the monomials: $\frac{3x^3y}{6xy^2z}$

Possible Answers:

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

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

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

$\frac{1}{2x^2yz}$

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

Correct answer:

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

Explanation:

Rewrite both the numerator and denominator by factors.

$\frac{3x^3y}{6xy^2z} = \frac{3 \times x \times x \times x \times y}{3 \times 2 \times y \times y \times z}$

Cancel all the common terms on the top and bottom.

The answer is: $\frac{x^2}{2yz}$

Report an Error

Example Question #526 : Variables

Divide the monomials: $\frac{3x^2y^5z}{3x^2y^{-5}z^3}$

Possible Answers:

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

$\frac{y^{10}}{z^2}$

$\frac{1}{y^{10}z^2}$

$y^{10}z^2$

$\frac{z^2}{y^{10}}$

Correct answer:

$\frac{y^{10}}{z^2}$

Explanation:

Some of the terms of the given expression can already be simplified.

Cancel out the 3x^2 terms.

$\frac{y^5z}{y^{-5}z^3}$

When we are dividing powers of a similar base, it is the same as subtracting the exponents.

$\frac{y^5}{y^{-5}} = y^{5-(-5)}= y^{10}$

$\frac{z}{z^3} = z^{1-3} = z^{-2} = \frac{1}{z^2}$

A negative exponent can be written as one over the base's positive exponent.

Multiply both terms together.

$y^{10} \cdot \frac{1}{z^2}= \frac{y^{10}}{z^2}$

The answer is: $\frac{y^{10}}{z^2}$

Report an Error

Example Question #4751 : Algebra 1

Simplify: $\frac{8xz^3}{2z}$

Possible Answers:

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

4xz^2

4z^2

4x^2z^2

4x-z^2

Correct answer:

4xz^2

Explanation:

In order to simplify this fraction, we will need to rewrite the numerator using factors.

$\frac{8xz^3}{2z}=\frac{2\cdot 4 \cdot x \cdot z^3}{2z}$

Cancel the common terms in the numerator and denominator.

The answer is: 4xz^2

Report an Error

Example Question #61 : How To Divide Monomial Quotients

Divide the monomials: $\frac{3x^6yz^3}{3x^{-6}y^6z^5}$

Possible Answers:

y^5z^2

$\frac{1}{y^5z^2}$

$\frac{x^{12}}{y^5z^2}$

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

Correct answer:

$\frac{x^{12}}{y^5z^2}$

Explanation:

When powers of a similar base are divided, the powers can be subtracted.

The coefficients will cancel.

Subtract each power for each variable.

$x^{6-(-6)}=x^{12}$

$y^{1-6}= y^{-5} = \frac{1}{y^5}$

$z^{3-5}= z^{-2} = \frac{1}{z^2}$

Multiply and combine each of these terms together.

$x^{12} \times \frac{1}{y^5} \times \frac{1}{z^2}$

The answer is: $\frac{x^{12}}{y^5z^2}$

Report an Error

View Algebra Tutors

Blossom
Certified Tutor

University of Maryland-Baltimore County, Bachelor of Science, Computer Science.

View Algebra Tutors

Wesley
Certified Tutor

San Diego State University, Bachelor of Science, Psychology.

View Algebra Tutors

Louis
Certified Tutor

University of California-Los Angeles, Bachelor in Arts, Film Production.

All Algebra 1 Resources

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

Popular Subjects

Reading Tutors in Seattle, Algebra Tutors in Denver, French Tutors in Atlanta, MCAT Tutors in San Francisco-Bay Area, Math Tutors in Miami, GMAT Tutors in San Diego, ISEE Tutors in Dallas Fort Worth, GMAT Tutors in Atlanta, GRE Tutors in New York City, MCAT Tutors in Philadelphia

Popular Courses & Classes

ISEE Courses & Classes in New York City, GRE Courses & Classes in Denver, LSAT Courses & Classes in Washington DC, SAT Courses & Classes in Denver, Spanish Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Chicago, LSAT Courses & Classes in San Diego, GMAT Courses & Classes in Chicago, ISEE Courses & Classes in Boston, SSAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in San Francisco-Bay Area, SAT Test Prep in Chicago, GMAT Test Prep in Los Angeles, SAT Test Prep in Los Angeles, GRE Test Prep in Philadelphia, SSAT Test Prep in Denver, LSAT Test Prep in Chicago, GMAT Test Prep in Chicago, GRE Test Prep in Boston, GRE Test Prep in Los Angeles

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 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #512 : Variables

Example Question #513 : Variables

Example Question #521 : Variables

Example Question #522 : Variables

Example Question #523 : Variables

Example Question #524 : Variables

Example Question #525 : Variables

Example Question #526 : Variables

Example Question #4751 : Algebra 1

Example Question #61 : 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: