GRE Math : How to find the reciprocal of a fraction

Study concepts, example questions & explanations for GRE Math

Create An Account Create Tests & Flashcards

All GRE Math Resources

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

Example Questions

Example Question #1 :How To Find The Reciprocal Of A Fraction

Carpenter A takes 45 hours to build a table. Carpenter B takes 30 hours. When they work together, how long will it take them to build a table?

Possible Answers:

$25\ hrs$

$18\ hrs$

$20\ hrs$

$15\ hrs$

$10\ hrs$

Correct answer:

$18\ hrs$

Explanation:

Write their respective rates as fractions:

Carpenter A: $\dpi{100} \small \frac{1\ table}{45\ hours}$

Carpenter B: $\dpi{100} \small \frac{1\ table}{30\ hours}$

把它们加到一起寻找他们的结合率。冷杉st find a common denominator. The smallest multiple of both 45 and 30 is 90:

$\dpi{100} \small \frac{2}{90}+\frac{3}{90}=\frac{5}{90}=\frac{1\ table}{18\ hours}$

Therefore, they take 18 hours to build a table together.

Report an Error

Example Question #1 :How To Find The Reciprocal Of A Fraction

What is the sum of the reciprocal of, the reciprocal of, the reciprocal of, and xyz ?

Possible Answers:

None of the other answers

$\frac{x^2+y^2+z^2+xyz}{xyz}$

$\frac{x+y+z+xyz}{xyz}$

$\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

$\frac{xy+xz+yz+xyz+x^2y^2z^2}{xyz}$

Correct answer:

$\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

Explanation:

Begin by finding the reciprocal of, the reciprocal of, and the reciprocal of:

$\frac{1}{x}$ , $\frac{1}{y}$ , $\frac{1}{z}$

In order to add the four terms together, we will need to find a common denominator. Find the common denominator by multiplying the three different terms in the denominator (x, y, and z). Our common denominator will be xyz . Put each term into terms of this common denominator:

$\frac{1}{x}*\frac{yz}{yz}=\frac{yz}{xyz}$

$\frac{1}{y}*\frac{xz}{xz}=\frac{xz}{xyz}$

$\frac{1}{z}*\frac{xy}{xy}=\frac{xy}{xyz}$

$xyz*\frac{xyz}{xyz}=\frac{x^2y^2z^2}{xyz}$

Now, add each term together:

$\frac{xy}{xyz}+\frac{xz}{xyz}+\frac{yz}{xyz}+\frac{x^2y^2z^2}{xyz}=\frac{xy+xz+yz+x^2y^2z^2}{xyz}$

Look for the answer choice that matches this.

Report an Error

Example Question #3 :How To Find The Reciprocal Of A Fraction

Find the reciprocal of the following expression:

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

Possible Answers:

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

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

$\frac{3b}{3b}$

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

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

Correct answer:

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

Explanation:

To find the reciprocal of a rational expression--any rational expression--all you need to do is flip the numerator and the denominator.

Therefore, the correct answer is:

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

You can check this by multiplying the two expressions together and ensuring that your answer is.

Report an Error

Example Question #4 :How To Find The Reciprocal Of A Fraction

Find the reciprocal of the following expression:

$22\frac{1}{2}$

Possible Answers:

$\frac{22}{33}$

$\frac{33}{22}$

$\frac{1}{22}$

$\frac{2}{45}$

$\frac{45}{2}$

Correct answer:

$\frac{2}{45}$

Explanation:

To find the reciprocal of any fraction, you merely need to invert the numerator and denominator.

In this case, first you have to convert the mixed number into a fraction:

$22\frac{1}{2} = \frac{2\cdot 22}{2}+\frac{1}{2}=\frac{44}{2} + \frac{1}{2} = \frac{45}{2}$

Therefore, the answer is:

$\frac{2}{45}$

Report an Error

All GRE Math Resources

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

Popular Subjects

Calculus Tutors in San Francisco-Bay Area,Calculus Tutors in Houston,MCAT Tutors in Houston,化学Tutors in San Diego,MCAT Tutors in Denver,Calculus Tutors in New York City,French Tutors in Washington DC,Calculus Tutors in Boston,SSAT Tutors in Miami,Algebra Tutors in San Francisco-Bay Area

Popular Courses & Classes

MCAT Courses & Classes in Miami,GMAT Courses & Classes in Denver,GMAT Courses & Classes in Philadelphia,GMAT Courses & Classes in Los Angeles,ISEE Courses & Classes in Dallas Fort Worth,ISEE Courses & Classes in Houston,ISEE Courses & Classes in Philadelphia,ACT Courses & Classes in Phoenix,LSAT Courses & Classes in Phoenix,MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GRE Test Prep in Houston,LSAT Test Prep in Boston,MCAT Test Prep in New York City,LSAT Test Prep in Phoenix,SSAT Test Prep in Washington DC,ISEE Test Prep in San Francisco-Bay Area,MCAT Test Prep in Miami,MCAT Test Prep in Chicago,ACT Test Prep in New York City,SAT Test Prep in Houston

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)

GRE Math : How to find the reciprocal of a fraction

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 :How To Find The Reciprocal Of A Fraction

Example Question #1 :How To Find The Reciprocal Of A Fraction

Example Question #3 :How To Find The Reciprocal Of A Fraction

Example Question #4 :How To Find The Reciprocal Of A Fraction

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:

Email address:
Your name:
Feedback: