GRE Math : How to order fractions from least to greatest or from greatest to least

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 Order Fractions From Least To Greatest Or From Greatest To Least

Which fraction is the SMALLEST?

Possible Answers:

6/11

35/50

4/9

1/2

47/100

Correct answer:

4/9

Explanation:

estimate or calculate decimals after simplifying

Report an Error

Example Question #1 : Ordering

8/9 > x > 6/7

Quantity A: x

Quantity B: 7/8

Possible Answers:

Quantity A is greater.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined from the information given.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

At first glance, it appears that both values are equal.7/8 and x will be between 6/7 and 8/9.

However do a quick calculation on the GRE calculator to figure out that 6/7 is approximately 0.857 and and 8/9 is approximately 0.889. 7/8 (Quantity B) is 0.875. x could equal 0.86 and be less than Quantity B or x could equal 0.88 and be greater than Quantity B. Because at least two possibilities exist (x could also equal 7/8), there is not enough information given to determine the relationship.

Report an Error

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Which of the following fractions is the greatest?

Possible Answers:

17/23

19/25

1/2

15/21

8/11

Correct answer:

19/25

Explanation:

The trick here is to set 1/2 as a baseline; all other choices are greater than 1/2.

Next is to see how much the difference is between each numerator and denominator (if you multiply 8/11 by 2/2, it will become 16/22) - each fraction besides 1/2 has a numerator that is 6 units less than the denominator. The trick is that the largest numerator will be the largest fraction when the numerator and denominator are the same units apart on all fractions.

Report an Error

Example Question #2 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Which is greater, $\frac{3}{4} + \frac{3}{4}$ or $\left ( \frac{3}{4} \right )^{2}$ ?

Possible Answers:

$\left ( \frac{3}{4} \right )^{2}$ is greater

The quantities are equal.

$\frac{3}{4} +\frac{3}{4}$ is greater

The relationship cannot be determined from the information given.

Correct answer:

$\frac{3}{4} +\frac{3}{4}$ is greater

Explanation:

To add fractions with the same denominator, add their numerators and leave the denominator the same: $\frac{3}{4} + \frac{3}{4} = \frac{6}{4}$

To square a fraction, square its numerator and denominator: $\left ( \frac{3}{4} \right )^{2} = \frac{3^{2}}{4^{2}} = \frac{9}{16}$

For comparison, rewrite the first fraction with 16 as its denominator also: $\dpi{100} \small \frac{6}{4}= \frac{6\times 4}{4\times 4} = \frac{24}{16}$

$\frac{24}{16} > \frac{9}{16}$ so $\frac{3}{4} + \frac{3}{4} > \left ( \frac{3}{4} \right ) ^{2}$

Report an Error

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Quantitative Comparison

Quantity A: $\frac{3}{7}+\frac{3}{8}$

Quantity B: $\frac{13}{4}+\frac{4}{5}$

Possible Answers:

The relationship cannot be determined form the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

One option is to do the actual math to find the answer. Quantity A = 3/7 + 3/8 = 45/56. Quantity B = 13/14 + 4/5 = 121/70. Here Quantity A < 1 and Quantity B > 1, so it is easy to tell which is bigger. This isn't always the case however, so often doing the math is NOT the quickest or easiest way to solve GRE questions. For example, if the two answers had been 45/56 and 72/83, it would have been very difficult to tell which was the larger fraction just by looking at them.

Instead of computationally figuring this question out, we can break it into parts.

Let's look at the first fraction in the two columns: 3/7 < 1/2 and 13/14 > 1/2, so the first fraction in Quantity B is bigger.

Next look at the second fraction: 3/8 < 1/2 and 4/5 > 1/2, so the second fraction in Quantity B is bigger.

Now we know that Quantity B is bigger without having to do any real math!

Report an Error

Example Question #2 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Which of these fractions is the LARGEST?

Possible Answers:

$\frac{7}{9}$

$\frac{15}{20}$

$\frac{40}{50}$

$\frac{25}{30}$

$\frac{6}{7}$

Correct answer:

$\frac{6}{7}$

Explanation:

Now that the GRE has a built-in calculator, simply find the decimal equivalent of each of the answer choices to see which is the largest!

Report an Error

Example Question #5 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Which of the following is the greatest fraction:

$\frac{1}{3}, \frac{4}{3}, \frac{5}{6}, \frac{3}{12}, \frac{11}{12}$

Possible Answers:

$\frac{4}{3}$

$\frac{1}{3}$

$\frac{5}{6}$

$\frac{11}{12}$

$\frac{3}{12}$

Correct answer:

$\frac{4}{3}$

Explanation:

Since the fraction $\frac{4}{3}$ is the only one with a numerator larger than its denominator, it is the only one greater than one. That means it is the largest fraction.

Report an Error

All GRE Math Resources

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

Popular Subjects

SSAT Tutors in Phoenix, SAT Tutors in Chicago, Statistics Tutors in Atlanta, Chemistry Tutors in Phoenix, Calculus Tutors in Denver, English Tutors in Philadelphia, GRE Tutors in Denver, Computer Science Tutors in Atlanta, Physics Tutors in San Diego, Reading Tutors in New York City

Popular Courses & Classes

GRE Courses & Classes in Phoenix, LSAT Courses & Classes in San Diego, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Boston, GRE Courses & Classes in Washington DC, SAT Courses & Classes in Philadelphia, MCAT Courses & Classes in New York City, LSAT Courses & Classes in Miami, MCAT Courses & Classes in Chicago

Popular Test Prep

LSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Houston, SAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Miami, SAT Test Prep in Los Angeles, MCAT Test Prep in Chicago, GRE Test Prep in Washington DC, MCAT Test Prep in New York City, SSAT Test Prep in Los Angeles, GMAT 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 order fractions from least to greatest or from greatest to least

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 : Ordering

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #2 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #2 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #5 : How To Order Fractions From Least To Greatest Or From Greatest To Least

All GRE Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details