GRE Math : Simplifying Fractions

Study concepts, example questions & explanations for GRE Math

Create An Account

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Simplifying Fractions

For how many integers, , between 26 and 36 is it true that

$\frac{3}{x}_{,}\frac{4}{x}_{,}$ and $\frac{5}{x}$ are all in lowest terms?

Possible Answers:

Correct answer:

Explanation:

If is even, then $\frac{4}{x}$ is not in lowest terms, since both and 4 are divisible by 2. Therefore, the only possibilities are 27,29,31,33, and 35. But $\frac{3}{27}= \frac{1}{9}$ , $\frac{3}{33}= \frac{1}{11}$ , and $\frac{5}{35}= \frac{1}{7}$ , so only two integers satisfy the given condition: 29 and 31.

Report an Error

Example Question #2 : Simplifying Fractions

Mrs. Lawrence's class has students, of which are girls. If you were to choose a student at random, what's the probability that the student chosen would be a boy?

Possible Answers:

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{2}{7}$

Correct answer:

$\frac{3}{5}$

Explanation:

In order to find out the probability of choosing a boy, you must first find out how many boys there are. Since there are girls out of students, students should be boys.

Therefore, the probability of choosing a boy is,

$\frac{21}{35}$ .

However, this is not one of the answer choices; therefore, you must reduce the fraction.

In order to reduce a fraction, you have to find their GCM, or greatest common multiple. This is the biggest number that will go into both the numerator (21) and denominator (35) . The largest number is . Divide both the top and bottom by , and you will get the answer:

$\frac{3}{5}$

Report an Error

Example Question #3 : Simplifying Fractions

Simplify the fraction:

$\frac{0.0003(0.4)(0.0002)}{0.00000006(0.01)}$

Possible Answers:

0.4

0.04

Correct answer:

Explanation:

To simplify the fraction

$\frac{0.0003(0.4)(0.0002)}{0.00000006(0.01)}$

It may be helpful to write it in terms of scientific notation:

$\frac{3\cdot 10^{-4}(4\cdot 10^{-1})(2\cdot 10^{-4})}{6\cdot 10^{-8}(1\cdot 10^{-2})}$

$\frac{24\cdot 10^{-4-1-4}}{6\cdot 10^{-8-2}}$

$\frac{24\cdot 10^{-9}}{6\cdot 10^{-10}}$

$4\cdot10^{-9+10}$

$4\cdot10$

Report an Error

Example Question #2 : Simplifying Fractions

Simply the fraction:

$\frac{4a^3+12a^2b+12ab^2+4b^3}{3a^2+6ab+3b^2}$

Possible Answers:

$\frac{4}{3}(a+b)$

$\frac{3}{4(a+b)}$

$\frac{3}{4}(a+b)$

$\frac{4}{3(a+b)}$

Correct answer:

$\frac{4}{3}(a+b)$

Explanation:

To simplify the fraction

$\frac{4a^3+12a^2b+12ab^2+4b^3}{3a^2+6ab+3b^2}$

Begin by factoring out common terms in the numerator and denominator:

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

Now notice that the coefficients for the polynomials in the numerator and denominator match the form of Pascal's Triangle:

(a+b)^n

n=1: 1,1

n=2:1,2,1

n=3:1,3,3,1

n=4:1,4,6,4,1

The fraction can be rewritten as:

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

And finally reduced to

$\frac{4}{3}(a+b)$

Report an Error

All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Statistics Tutors in Boston, Reading Tutors in San Diego, Spanish Tutors in Philadelphia, Math Tutors in Chicago, SAT Tutors in Denver, ISEE Tutors in Houston, Math Tutors in Dallas Fort Worth, French Tutors in Boston, Spanish Tutors in San Francisco-Bay Area, Spanish Tutors in San Diego

Popular Courses & Classes

SAT Courses & Classes in Seattle, GRE Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Seattle, ACT Courses & Classes in Washington DC, LSAT Courses & Classes in Phoenix, GRE Courses & Classes in Seattle, SAT Courses & Classes in Boston, Spanish Courses & Classes in Los Angeles, ACT Courses & Classes in Los Angeles, Spanish Courses & Classes in New York City

Popular Test Prep

GMAT Test Prep in Miami, MCAT Test Prep in Washington DC, SAT Test Prep in New York City, GRE Test Prep in Denver, LSAT Test Prep in Boston, ACT Test Prep in Washington DC, GMAT Test Prep in Boston, GRE Test Prep in San Francisco-Bay Area, ACT Test Prep in Los Angeles, SSAT Test Prep in San Francisco-Bay Area

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)

Email address:
Your name:
Feedback:

GRE Math : Simplifying Fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : Simplifying Fractions

Example Question #2 : Simplifying Fractions

Example Question #3 : Simplifying Fractions

Example Question #2 : Simplifying Fractions

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details