GMAT Math : Understanding fractions

Study concepts, example questions & explanations for GMAT Math

Create An Account

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Understanding Fractions

$\frac{2}{3}+\frac{3}{4}+\frac{5}{6}=$

Possible Answers:

$\frac{9}{4}$

$\frac{14}{3}$

$\frac{11}{6}$

$\frac{7}3{}$

$\frac{27}{4}$

Correct answer:

$\frac{9}{4}$

Explanation:

In order to add these fractions, we must first find a common denominator for all three. Looking at our three different denominators, we can see that their lowest common denominator is 12. Therefore, we need to rewrite each fraction with a denominator of 12:

$\frac{2}{3}+\frac{3}{4}+\frac{5}{6}=\frac{2(4)}{3(4)}+\frac{3(3)}{4(3)}+\frac{5(2)}{6(2)}=\frac{8}{12}+\frac{9}{12}+\frac{10}{12}$

Now that the fractions all have a common denominator, we can simply add them together and then simplify the result, recognizing that 27 and 12 have a common factor of 3:

$\frac{8}{12}+\frac{9}{12}+\frac{10}{12}=\frac{27}{12}=\frac{9}{4}$

Report an Error

Example Question #11 : Fractions

Which of the following is less than $\frac{5}{8}$ ?

Possible Answers:

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{7}{6}$

$\frac{5}{6}$

$\frac{3}{4}$

Correct answer:

$\frac{1}{2}$

Explanation:

In order to determine which fractions are less than $\frac{5}{8}$ , it's best to convert them to decimals and compare:

$\frac{5}{8}=0.625$

$\frac{1}{2}=0.5$

$\frac{3}{4}=0.75$

$\frac{2}{3}=0.67$

$\frac{5}{6}=0.83$

$\frac{7}{6}=1.167$

Therefore, $\frac{1}2{}$ is the only choice that is less than $\frac{5}{8}$ .

Report an Error

Example Question #13 : Understanding Fractions

Define an operation $\ast$ as follows:

For all real numbers a ,b ,

$a \ast b = \frac{1}{4}a + b^{2}$

Evaluate $\frac{2}{3} \ast \frac{1}{3}$ .

Possible Answers:

$\frac{5}{18}$

$\frac{1}{16}$

$\frac{2}{15}$

$\frac{1}{4}$

None of the other responses is correct.

Correct answer:

$\frac{5}{18}$

Explanation:

$a \ast b = \frac{1}{4}a + b^{2}$

$\frac{2}{3} \ast \frac{1}{3}= \frac{1}{4} \cdot \frac{2}{3} + \left (\frac{1}{3} \right ) ^{2}$

$= \frac{2}{12} + \frac{1}{9}$

$= \frac{1}{6} + \frac{1}{9}$

$= \frac{3}{18} + \frac{2}{18}$

$= \frac{5}{18}$

Report an Error

Example Question #11 : Understanding Fractions

Casius has $\tiny \frac{1}{6}$ of a liter of water. Olivar has $\tiny \frac{4}{7}$ of the amount Casius has. How many liters of water does Olivar have?

Possible Answers:

$\tiny \tiny \frac{7}{6}$

$\tiny \tiny \frac{1}{4}$

$\tiny \tiny \frac{6}{7}$

$\tiny \frac{2}{21}$

$\tiny \frac{7}{24}$

Correct answer:

$\tiny \frac{2}{21}$

Explanation:

This question tests your ability to read word problems and multiply fractions. Because we know that Olivar has $\frac{4}{7}$ of what Casius has, we can see that we need to multiply. Perform the following operation to find the answer.

$\frac{1}{6}*\frac{4}{7}=\frac{4}{42}=\frac{2}{21}$

Report an Error

Example Question #15 : Understanding Fractions

Define an operation $\ast$ as follows:

For all real numbers a ,b ,

$a \ast b = 2a \div b$

Evaluate $5\frac{1}{6} \ast 3\frac{1}{3}$ , and round to the nearest whole number.

Possible Answers:

Correct answer:

Explanation:

$a \ast b = 2a \div b$

$5\frac{1}{6} \ast 3\frac{1}{3} = 2 \left ( 5\frac{1}{6} \right ) \div 3\frac{1}{3}$

$= 2 \left ( \frac{31}{6} \right ) \div \frac{10}{3}$

$= \frac{31}{3} \div \frac{10}{3}$

$= \frac{31}{3} \cdot \frac{3}{10}$

$= \frac{31} {10}$

$=3 \frac{1} {10}$

This rounds to 3.

Report an Error

Example Question #11 : Fractions

Seven thirds of eighteen seventieths is what?

Possible Answers:

Seven fifths

Five thirds

Three fifths

Seven sixths

Three sevenths

Correct answer:

Three fifths

Explanation:

Seven thirds of eighteen seventieths is

$\frac{7}{3} \times \frac{18 }{70} = \frac{7}{3} \times \frac{9}{35} = \frac{1}{1} \times \frac{3}{5}= \frac{3}{5}$

Report an Error

Example Question #12 : Fractions

One orange yields $\frac{1}{3}$ cup of juice; one gallon is equal to 16 cups. How many oranges are needed to yield one half gallon of orange juice?

Possible Answers:

Correct answer:

Explanation:

One half gallon comprises 8 cups. To find the number of oranges needed, divide:

$8 \div \frac{1}{3} = 24$

Report an Error

Example Question #11 : Fractions

Raise $\frac{15}{75}$ to the fourth power and express the result in lowest terms.

Possible Answers:

$\frac{1}{625}$

$\frac{1}{216}$

$\frac{1}{256}$

$\frac{1}{1,296}$

$\frac{1}{125}$

Correct answer:

$\frac{1}{625}$

Explanation:

$\frac{15}{75}$ reduces to $\frac{15 \div 15}{75 \div 15} = \frac{1}{5}$ . Raise this to the fourth power:

$\left ( \frac{1}{5} \right )^{4} = \frac{1}{5^{4}} = \frac{1}{625}$

Report an Error

Example Question #15 : Understanding Fractions

Evaluate: $\left (\frac{3}{7} \right )^{4} + \left (-\frac{3}{7} \right )^{4}$

Possible Answers:

$\frac{1,296}{2,401}$

$-\frac{162}{2,401}$

$-\frac{1,296}{2,401}$

$\frac{162}{2,401}$

Correct answer:

$\frac{162}{2,401}$

Explanation:

$\left (\frac{3}{7} \right )^{4} = \frac{3^{4} }{7^{4} } = \frac{81 }{2,401}$

$\left (-\frac{3}{7} \right )^{4} =\left (\frac{3}{7} \right )^{4} = \frac{81 }{2,401}$

$\left (\frac{3}{7} \right )^{4} + \left (-\frac{3}{7} \right )^{4}=\frac{81 }{2,401}+\frac{81 }{2,401}=\frac{162}{2,401}$

Report an Error

Example Question #18 : Understanding Fractions

Evaluate: $-\left (\frac{5}{8} \right )^{4} + \left (-\frac{5}{8} \right )^{4}$

Possible Answers:

$-\frac{625}{4,096}$

$\frac{625}{4,096}$

Correct answer:

Explanation:

This can actually be solved without any calculation.

A negative number raised to an even power is equal to its absolute value raised to that power, so

$\left (-\frac{5}{8} \right )^{4} = \left (\frac{5}{8} \right )^{4}$

Therefore, we can replace:

$-\left (\frac{5}{8} \right )^{4} + \left (\frac{5}{8} \right )^{4} = \left (\frac{5}{8} \right )^{4} -\left (\frac{5}{8} \right )^{4} =0$

Report an Error

All GMAT Math Resources

22 Diagnostic Tests 693 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Denver, Statistics Tutors in Philadelphia, MCAT Tutors in Boston, Biology Tutors in Miami, Physics Tutors in Atlanta, GRE Tutors in Boston, Spanish Tutors in Los Angeles, Statistics Tutors in Atlanta, Calculus Tutors in Los Angeles, Statistics Tutors in Houston

Popular Courses & Classes

LSAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Diego, SAT Courses & Classes in Philadelphia, GMAT Courses & Classes in Houston, SAT Courses & Classes in Atlanta, MCAT Courses & Classes in Miami, SSAT Courses & Classes in Atlanta, GMAT Courses & Classes in Miami, ACT Courses & Classes in Washington DC, SSAT Courses & Classes in San Francisco-Bay Area

Popular Test Prep

MCAT Test Prep in Atlanta, LSAT Test Prep in Philadelphia, SAT Test Prep in New York City, GMAT Test Prep in Atlanta, GRE Test Prep in Denver, GMAT Test Prep in Dallas Fort Worth, GRE Test Prep in Miami, SSAT Test Prep in Atlanta, GMAT Test Prep in Philadelphia, SSAT Test Prep in Boston

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:

GMAT Math : Understanding fractions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #11 : Understanding Fractions

Example Question #11 : Fractions

Example Question #13 : Understanding Fractions

Example Question #11 : Understanding Fractions

Example Question #15 : Understanding Fractions

Example Question #11 : Fractions

Example Question #12 : Fractions

Example Question #11 : Fractions

Example Question #15 : Understanding Fractions

Example Question #18 : Understanding Fractions

All GMAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details