We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : How to divide variables

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Divide Variables

$\dpi{100} \frac{1}{3}\div \frac{1}{9}$

Possible Answers:

$\dpi{100} 2$

$\dpi{100} \frac{1}{3}$

$\dpi{100} \frac{1}{27}$

$\dpi{100} 3$

Correct answer:

$\dpi{100} 3$

Explanation:

Never divide fractions! Simply flip the fraction that follows the division symbol, and then multiply it by the first fraction. So this expression becomes:

$\dpi{100} \frac{1}{3}\times \frac{9}{1}=\frac{9}{3}=3$

Report an Error

Example Question #2 : How To Divide Variables

Divide:

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

Possible Answers:

2x^2-x+3

2x^3-x^2+3

2x^2+x+3

2x^3+x^2+3

Correct answer:

2x^2-x+3

Explanation:

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

Report an Error

Example Question #3 : How To Divide Variables

Simplify:

$\frac{4x^{4}- 8 x^{2} - 16} {2x}$

Possible Answers:

$2x^{3} - 12x$

$2x^{3} - 4 x^{2} -8$

$2x^{3} - 4 x -8$

$2x^{3} - 4 x^{2} - \frac{8} {x}$

$2x^{3} - 4 x - \frac{8} {x}$

Correct answer:

$2x^{3} - 4 x - \frac{8} {x}$

Explanation:

$\frac{4x^{4}- 8 x^{2} - 16} {2x}$

$= \frac{4x^{4}} {2x} - \frac{ 8 x^{2}} {2x} - \frac{16} {2x}$

$= \frac{2x^{4-1}} {1} - \frac{ 4 x^{2-1}} {1} - \frac{8} {x}$

$= \frac{2x^{3}} {1} - \frac{ 4 x^{1}} {1} - \frac{8} {x}$

$= 2x^{3} - 4 x - \frac{8} {x}$

Report an Error

Example Question #2 : How To Divide Variables

If $x\neq 0$ , divide:

$\frac{8x^4+4x^3-16x}{4x}$

Possible Answers:

2x^3+x^2-4

2x^3-x^2-4

2x^3+x^2+4

2x^3-x^2+4

x^3+x^2-4

Correct answer:

2x^3+x^2-4

Explanation:

$\frac{8x^4+4x^3-16x}{4x}$

$=\frac{8x^4}{4x}+\frac{4x^3}{4x}-\frac{16x}{4x}$

=2x^3+x^2-4

Report an Error

Example Question #5 : How To Divide Variables

Divide:

$\frac{16y^3 - 4y^2 + 8y}{4y}$

Possible Answers:

4y^2 - y + 2

12y^2 - y + 4

y^2 - 2y + 8

4y^2 + 2

4y^3 - y^2 + 2y

Correct answer:

4y^2 - y + 2

Explanation:

In this division problem, you can simplify first the coefficients, then the variables.

Each of the coefficients in the numerator is divisible by the coefficient in the denominator, allowing you to divide out and cancel the 4 in the denominator:

$\frac{16y^3 - 4y^2 + 8y}{4y} = \frac{4y^3 - y^2 + 2y}{y}$

Finally, you can simplify the varaibles. Remember that when simplifying variables in a fraction (division problem), you subtract the numerator variable's exponent by the denominator variable's exponent. You can do this with each term in this problem, because each term in the numerator has at least a :

$\frac{4y^3 - y^2 + 2y}{y} = 4y^2 - y +2$

Report an Error

Example Question #215 : Algebraic Concepts

Divide:

$\frac{7x^4 + 21x^2 - 14}{7x^2}$

Possible Answers:

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

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

3x^2 + 3

x^2 + 1

Correct answer:

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

Explanation:

In this division problem, you can simplify first the coefficients, then the variables.

Each of the coefficients in the numerator is divisible by the coefficient in the denominator, allowing you to divide out and cancel the 7 in the denominator:

$\frac{7x^4 + 21x^2 - 14}{7x^2} = \frac{x^4 + 3x^2 - 2}{x^2}$

You can only do this with the first two terms in the numerator, since the final term does not have a variable. Instead, the final term will keep x^2 in the denominator:

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

Report an Error

Example Question #3 : How To Divide Variables

Divide:

$\frac{x^2+2xy+xy^2}{x}$

Possible Answers:

x+2y+y^2

2x^2+2y+y^2

x^2+2y+y^2

2x+2y+y^2

Correct answer:

x+2y+y^2

Explanation:

$\frac{x^2+2xy+xy^2}{x}=\frac{x^2}{x}+\frac{2xy}{x}+\frac{xy^2}{x}=x+2y+y^2$

Report an Error

Example Question #1 : How To Divide Variables

Which of the following is a factor of $(8-2)^{2}$ ?

Possible Answers:

Correct answer:

Explanation:

The first step to solving this question is to reduce $(8-2)^{2}$ .

$(8-2)^{2}$

$6^{2}$

The only number listed that is a factor of 36 is 18, given that 2 times 18 is 36. Therefore, 18 is the correct answer.

Report an Error

Example Question #218 : Algebraic Concepts

Divide:

$\frac{4x^{3}+8x^{2}-12x}{4x}$

Possible Answers:

$x^{4}+2x^{3}-3x^{2}$

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

The expression cannot be simplified further.

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

$4x^{2}+8x-12$

Correct answer:

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

Explanation:

To divide this problem we simplify it first. In this problem we can separate the big fraction into three smaller fractions.

$\frac{4x^{3}+8x^{2}-12x}{4x}=\frac{4x^{3}}{4x}+\frac{8x^{2}}{4x}-\frac{12x}{4x}$

Then from here, we can pull out a from both the numerator and denominator of each smaller fraction.

$\frac{4x(x^2)}{4x}+\frac{4x(2x)}{4x} - \frac{4x(3)}{4x}$

Now we cancel terms and get the following result:

x^2+2x-3

Report an Error

Example Question #219 : Algebraic Concepts

Simplify:

$\frac{2x^{4}+6x^{3}+8}{2x}$

Possible Answers:

$4x^{3}+12x^{2}+16x$

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

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

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

$4x^{3}+6x^{2}+16x$

Correct answer:

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

Explanation:

To simplify this problem we first separate the large fraction into three smaller fractions.

$\frac{2x^{4}+6x^{3}+8}{2x}$

$=\frac{2x^{4}}{2x}+\frac{6x^{3}}{2x}+\frac{8}{2x}$

From here we can factor out from the numerator and denominator of the first two fractions.

$= \frac{2x(x^3)}{2x}+\frac{2x(3x^2)}{2x}+\frac{8}{2x}$

The can be canceled out in the first two fractions. From here we can factor out a from the numerator and denominator of the third fraction.

$=x^3+3x^2+\frac{2(4)}{2(x)}$

Thus becoming:

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

Report an Error

View Tutors

Evgenii
Certified Tutor

View Tutors

Pavan
Certified Tutor

University of Tennessee, Knoxville, Master's/Graduate, Mechanical Engineering. Pennsylvania State University, Master's/Gradua...

View Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in Philadelphia, Spanish Tutors in Los Angeles, SSAT Tutors in Phoenix, Math Tutors in Chicago, GRE Tutors in Washington DC, GRE Tutors in Atlanta, Calculus Tutors in San Diego, MCAT Tutors in Atlanta, Spanish Tutors in Houston, Chemistry Tutors in Chicago

Popular Courses & Classes

GRE Courses & Classes in Philadelphia, SAT Courses & Classes in Chicago, GMAT Courses & Classes in Seattle, MCAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Miami, ISEE Courses & Classes in Seattle, SAT Courses & Classes in New York City, LSAT Courses & Classes in New York City, GRE Courses & Classes in Phoenix, ISEE Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in Denver, SSAT Test Prep in San Diego, SAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Boston, SAT Test Prep in Chicago, GMAT Test Prep in New York City, SAT Test Prep in Miami, SSAT Test Prep in New York City, SAT Test Prep in Phoenix, ISEE 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

ISEE Upper Level Math : How to divide variables

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Divide Variables

Example Question #2 : How To Divide Variables

Example Question #3 : How To Divide Variables

Example Question #2 : How To Divide Variables

Example Question #5 : How To Divide Variables

Example Question #215 : Algebraic Concepts

Example Question #3 : How To Divide Variables

Example Question #1 : How To Divide Variables

Example Question #218 : Algebraic Concepts

Example Question #219 : Algebraic Concepts

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: