GRE Math : How to subtract complex 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 : How To Subtract Complex Fractions

Simplify the following:

$\frac{3+\frac{3}{7}}{\frac{2}{3}-4} - \frac{2 + \frac{1}{2}}{3}$

Possible Answers:

$-\frac{451}{7}$

$-\frac{391}{210}$

$\frac{211}{5}$

$\frac{21}{6}$

$-\frac{5}{3}$

Correct answer:

$-\frac{391}{210}$

Explanation:

This problem merely requires careful working out of each part. Begin by simplifying the first fraction:

$\frac{3+\frac{3}{7}}{\frac{2}{3}-4}$

The numerator will be:

$3+\frac{3}{7} = \frac{21}{7}+\frac{3}{7} = \frac{24}{7}$

The denominator will be:

$\frac{2}{3}-4 = \frac{2}{3}-\frac{12}{3} = -\frac{10}{3}$

Thus, we have the following fraction:

$\frac{\frac{24}{7}}{-\frac{10}{3}}$

Remember that you must multiply the numerator by the reciprocal of the denominator:

$\frac{24}{7} * -\frac{3}{10} = -\frac{72}{70}$

Now, work on the second fraction:

$\frac{2 + \frac{1}{2}}{3}$

This fraction is much easier. After simplifying the numerator, you get:

$\frac{\frac{5}{2}}{3}$

This is the same as:

$\frac{5}{2} \cdot \frac{1}{3} = \frac{5}{6}$

Thus, we come to our original expression! It is:

$-\frac{72}{70} - \frac{5}{6}$

The common denominator of these fractions is 210 . Thus, you have:

$\frac{-72 * 3 - 5 * 35}{210} = \frac{-216 -175}{210} = -\frac{391}{210}$

Report an Error

Example Question #2 : How To Subtract Complex Fractions

x >0

Quantity A: $\frac{x+2}{x+1}$

Quantity B: $\frac{x+3}{x+2}$

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The relationship between A and B cannot be determined.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

As it is, quantities A and B have different denominators, so making a comparison can be tricky. Making a common denominator will allow for comparison of just the numerators, so that would make a good first step:

Quantity A:

$\frac{x+2}{x+1}=\frac{(x+2)(x+2)}{(x+1)(x+2)}=\frac{x^2+4x+4}{x^2+3x+2}$

Quantity B:

$\frac{x+3}{x+2}=\frac{(x+3)(x+1)}{(x+2)(x+1)}=\frac{x^2+4x+3}{x^2+3x+2}$

Disregarding equal denominators, since they'll always have a positive value, compare the numerators. If x^2+4x is subtracted from quantity A and from quantity B, we're left with for the former and for the latter.

Quantity A is greater.

Report an Error

Example Question #3 : How To Subtract Complex Fractions

Quantity A: x^2+5x+ 4

Quantity B: x^2+10x+21

Possible Answers:

The relationship between A and B cannot be determined.

Quantity B is greater.

Quantity A is greater.

Quantity A and Quantity B are equal.

Correct answer:

The relationship between A and B cannot be determined.

Explanation:

One way to approach this question is to try to reduce the complexity of each quantity. By subtracting the value of Quantity A, x^2+5x+ 4 from both A and B, we can make a new comparison:

Quantity A': x^2+5x+ 4-(x^2+5x+ 4 )=0

Quantity B': x^2+10x+21-(x^2+5x+4)=5x+17

Now, it's easy to see that for different values of Quantity B may be greater, lesser, or equal to Quantity A.

Since is not restricted in its possible values, the relationship cannot be determined.

Report an Error

Example Question #1 : How To Subtract Complex Fractions

Rhoda can prune rhododendrons in hours, while Rhonda can prune in hours. If a work day is hours, how many rhododendrons will Rita have to prune per hour so that the team prunes the garden's 300 rhododendrons?

Possible Answers:

Correct answer:

Explanation:

To find out how many rhododendrons Rita will need to prune in an hour, we must first find out how many she needs to prune.

If Rhoda can prune rhododendrons in hours, then she can prune in hours, and if Rhonda can prune in hours, she can prune 120 in hours.

If this is not readily apparent, it can be found by finding out how many each prunes in one hour, then multiplying by .

Rhoda: $6(\frac{42}{3})=6(\frac{14}{1})=84$

Rhonda: $6(\frac{40}{2})=6(\frac{20}{1})=120$

Between Rhoda and Rhonda, 204 of the 300 rhododendrons can be pruned, leaving for Rita.

Since she has hours for the task, her rate of pruning can be found to be:

$\frac{96}{6}\frac{rhododendrons}{hours}=16\frac{rhododendrons}{hour}$

Report an Error

All GRE Math Resources

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

Popular Subjects

ACT Tutors in Atlanta, Calculus Tutors in Los Angeles, Statistics Tutors in Atlanta, SSAT Tutors in Boston, Physics Tutors in Chicago, SSAT Tutors in Miami, ISEE Tutors in San Diego, Computer Science Tutors in Seattle, English Tutors in San Diego, GRE Tutors in New York City

Popular Courses & Classes

MCAT Courses & Classes in New York City, GMAT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Houston, GRE Courses & Classes in Boston, ISEE Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in Denver, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Seattle, MCAT Test Prep in Miami, LSAT Test Prep in Chicago, MCAT Test Prep in San Diego, GMAT Test Prep in Denver, ACT Test Prep in Denver, SAT Test Prep in San Diego, ACT Test Prep in San Diego

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 : How to subtract complex fractions

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Subtract Complex Fractions

Example Question #2 : How To Subtract Complex Fractions

Example Question #3 : How To Subtract Complex Fractions

Example Question #1 : How To Subtract Complex Fractions

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details