We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Mathematics : Working with Fractions

Study concepts, example questions & explanations for SAT Mathematics

Create An Account

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Divisibility & Number Fluency

Jesse has a large movie collection containing movies. $\frac{1}{3}$ of his movies are action movies, $\frac{3}{5}$ of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?

Possible Answers:

$\left ( \frac{11}{15} \right )*x$

$\left ( \frac{4}{15} \right )*x$

$\left ( \frac{2}{5} \right )*x$

$\left ( \frac{7}{12} \right )*x$

Correct answer:

$\left ( \frac{4}{15} \right )*x$

Explanation:

$\frac{1}{3}$ of the movies are action movies. $\frac{3}{5}$ of $\frac{2}{3}$ of the movies are comedies, or $\frac{3}{5}*\frac{2}{3}$ , or $\frac{6}{15}$ . Combining the comedies and the action movies ( $\frac{1}{3}$ or $\frac{5}{15}$ ), we get $\frac{11}{15}$ of the movies being either action or comedy. Thus, $\frac{4}{15}$ of the movies remain and all of them have to be historical.

Report an Error

Example Question #2 : Divisibility & Number Fluency

If $x=\frac{1}{3}$ and $y=\frac{1}{2}$ , find the value of 2x+3y .

Possible Answers:

$\frac{5}{6}$

$\frac{13}{6}$

$\frac{6}{5}$

Correct answer:

$\frac{13}{6}$

Explanation:

Substitute the values of and into the given expression:

$2(\frac{1}{3})+3\left ( \frac{1}{2} \right )$

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

$=\frac{4}{6}+\frac{9}{6}$

$=\frac{13}{6}$

Report an Error

Example Question #3 : Divisibility & Number Fluency

Let the nth term of a sequence be denoted as $a_{n}$ and given by the following equation:

$a_{n}=\frac{\left ( -1 \right )^{n-1}}{n}$

For example, the tenth term of the sequence is $a_{10}=\frac{\left ( -1 \right )^{10-1}}{10}$ .

What is the sum of the first five terms of the sequence?

Possible Answers:

$\frac{43}{60}$

$-\frac{47}{60}$

$\frac{47}{60}$

$\frac{17}{60}$

Correct answer:

$\frac{47}{60}$

Explanation:

In order to find the sum of the first five terms, we will need to find the values of each of the first five terms using the equation given above. Essentially, we will let range from to to determine each term.

$a_{1}=\frac{\left ( -1 \right )^{1-1}}{1}=\frac{\left ( -1 \right )^{0}}{1}=\frac{1}{1}=1$

Remember that anything to the power of zero is equal to 1. Therefore, raised to the zero power is also .

$a_{2}=\frac{\left ( -1 \right )^{2-1}}{2}=\frac{\left ( -1 \right )^{1}}{2}=-\frac{1}{2}$

$a_{3}=\frac{\left ( -1 \right )^{3-1}}{3}=\frac{\left ( -1 \right )^{2}}{3}=\frac{\left (-1 \right )\left ( -1 \right )}{3}=\frac{1}{3}$

In general, when is raised to an even power, the result is . Conversely, if is raised to an odd power, the result is .

$a_{4}=\frac{\left ( -1 \right )^{4-1}}{4}=\frac{\left ( -1 \right )^{3}}{4}=\frac{\left (-1 \right )\left ( -1 \right )\left ( -1 \right )}{4}=-\frac{1}{4}$

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

Thus, the first five terms of the sequence are $1, -\frac{1}{2},\frac{1}{3},-\frac{1}{4}, and\, \frac{1}{5}$ . We must now add these all together. Because we are adding fractions with unlike denominators, we need to find the smallest multiple that $2, 3, 4, and\, 5$ have in common. Because is a multiple of , we really only need to worry about $3, 4, and \, 5$ . If we were to list out the multiple of $3, 4, and \, 5$ , e would see that the smallest one they have in common is . Sometimes, the easiest way to find the least common multiple of several numbers is o multiply them together. The products of $3, 4, and \, 5$ is .

We will now convert each fraction to an equivalent form with a denominator of . For example, if we were to convert $\frac{1}{2}$ to a fraction with a denominator of , we would multiple both the numerator and denominator by , as shown below:

$\frac{1}{2}=\frac{\left ( 1 \right )\left ( 30 \right )}{\left ( 2 \right )\left ( 30 \right )}=\frac{30}{60}$

$1+\frac{1}{2}+\frac{1}{3}+-\frac{1}{4}+\frac{1}{5}=\frac{60}{60}-\frac{30}{60}+\frac{20}{60}-\frac{15}{60}+\frac{12}{60}=\frac{60-30+20-15+12}{60}=\frac{47}{60}$

The answer is $\frac{47}{60}$ .

Report an Error

Example Question #1 : Divisibility & Number Fluency

What is the solution, reduced to its simplest form, for $x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}}$ ?

Possible Answers:

$x=\frac{7}{15}$

x=2

$x=\frac{75}{45}$

$x=\frac{5}{3}$

Correct answer:

$x=\frac{5}{3}$

Explanation:

$x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$

Report an Error

Example Question #5 : Divisibility & Number Fluency

What is the result of adding 20% of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{3}{28}$

$\frac{43}{140}$

$\frac{3}{39}$

$\frac{47}{140}$

Correct answer:

$\frac{43}{140}$

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of $\frac{2}{7}$ is found by multiplying $\frac{2}{7}$ by $\frac{2}{10}$ (or, simplified, $\frac{1}{5}$ ): $\frac{2}{7}*\frac{1}{5}=\frac{2}{35}$

Our addition is therefore $\frac{2}{35}+\frac{1}{4}$ . There are no common factors, so the least common denominator will be 35*4 or 140 . Multiply the numerator and denominator of $\frac{2}{35}$ by $\frac{4}{4}$ and the numerator of $\frac{1}{4}$ by $\frac{35}{35}$

This yields:

$\frac{8}{140}+\frac{35}{140}=\frac{43}{140}$ , which cannot be reduced.

Report an Error

Example Question #1 : Working With Fractions

Add:

$\frac{2}{9x}+\frac{4}{27}$

Possible Answers:

$\frac{6}{27x}$

$\frac{4x+6}{27x}$

$\frac{4x+6}{27}$

$\frac{10}{27x}$

Correct answer:

$\frac{4x+6}{27x}$

Explanation:

Find the least common denominator to solve this problem

Multiply 27 with , and multiply with 3 to obtain common denominators.

Convert the fractions.

$\frac{2}{9x}+\frac{4}{27}=\frac{6}{27x}+\frac{4x}{27x}$

Combine the terms as one fraction.

The answer is: $\frac{4x+6}{27x}$

Report an Error

Example Question #6 : Divisibility & Number Fluency

A record store has stocked up on new supplies so that their current inventory consists of pop, rock, and hip-hop. $\frac{1}{4}$ of their records are pop records and $\frac{3}{7}$ of their records are rock records. If the store has a total of 364 records, how many hip-hop records are stocked in the store?

Possible Answers:

156

232

117

Correct answer:

117

Explanation:

First we must find what fraction of hip-hop records are there in the store. We find a common denominator for the faction of pop records and rock records by multiplying $\frac{1}{4}$ by $\frac{7}{7}$ and $\frac{3}{7}$ by $\frac{4}{4}$ to get $\frac{7}{28}$ records being pop records and $\frac{12}{28}$ records being rock records.

In order to get the faction of hip-hop records remaining in the store, we must write out:

$\frac{7}{28}+\frac{12}{28}+\frac{x}{28}=\frac{28}{28}$ since the sum total of the fractions must add up to . We solve to get x=9 .

This tells us that fraction of hip-hop records must be $\frac{9}{28}$ .

The question is asking how many records are stocked in the store, therefore we need a denominator of 364 . We can write out $\frac{9}{28}=\frac{h}{364}$ and solve for h=117 .

Similarly, this question can be solved using deduction. If $\frac{1}{4}$ of 364 is and $\frac{3}{7}$ of 364 is 156 , knowing that we need the amount remaining, we can subtract 91+156 from 364 and get 117 .

Answer choice is wrong because it is finding the total amount of Pop records.

Answer choice 156 is wrong because it is finding the total amount of rock records.

Answer choice 156 is wrong because the factions were added incorrectly $\frac{1}{4}+\frac{3}{7}\neq \frac{4}{11}$ .

Report an Error

Example Question #7 : Divisibility & Number Fluency

Jackson wrote a song with equal parts pre-chorus, chorus, and bridge. The song ends up being minutes and seconds with a beat occurring every seconds. How many beats are there in the chorus?

Possible Answers:

Correct answer:

Explanation:

First, we must convert the song length from minutes and seconds to simply seconds.
$\frac{2\, minutes}{x\, seconds}=\frac{1\, minute}{60\, seconds}$ . We add seconds to 120 seconds and get 146 seconds total song length.

If the song is equal parts pre-chorus, chorus, and bridge that means $\frac{1}{3}$ of the song is composed of pre-chorus, $\frac{1}{3}$ of the song is composed of chorus, and $\frac{1}{3}$ of the song is composed of bridges. Therefore, we divide 146 by and get 48.67 seconds of chorus.
Since a beat occurs every five seconds, we divide 48.67 seconds by seconds to get the amount of beats in that time frame. $\frac{48.67\, seconds}{5\, seconds}=9.73\, beats$ . Since a beat can not be sectioned, the answer is rounded down to .

Answer choice is incorrect because it is finding the total number of beats in the song.

Answer choice is incorrect because it rounds up to the nearest beat.

Report an Error

Example Question #8 : Divisibility & Number Fluency

Please simplify the following:

$\frac{(\frac{a}{b})}{(\frac{c}{d})}$

Possible Answers:

$\frac{cb}{ad}$

$\frac{a}{bdc}$

$\frac{ac}{db}$

$\frac{ad}{bc}$

Correct answer:

$\frac{ad}{bc}$

Explanation:

The rule for dividing fractions is invert the second fraction and multiply. We keep the $\frac{a}{b}$ as it is then change the division sign to a multiplication sign and invert $\frac{c}{d}$ into $\frac{d}{c}$ .
$\frac{a}{b}\div\frac{c}{d}$ becomes $\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$ .

Similarly, you can memorize, “top, bottom, bottom, top” meaning is on top and it stays on top, is labeled bottom and it stays on the bottom, is labeled bottom and it moved to the bottom, then is labeled top so it moves to the top.

Report an Error

Example Question #1 : Working With Fractions

Find the value of if $\frac{x}{x+4}=\frac{9}{15}$

Possible Answers:

Correct answer:

Explanation:

To find the answer we must cross multiply. When we cross multiply we get:

$x\times 15=9\times (x+4)$ or 15x=9x+36

We subtract from 15x

6x=36 Then we solve for x by dividing by 6,

x=6

Report an Error

View Tutors

Oselen
Certified Tutor

UNIVERSITY OF BENIN, Bachelor of Science, Mechanical Engineering. University of Windsor, Master of Science, Mechanical Engine...

View Tutors

George
Certified Tutor

Pensacola State College, Bachelor in Arts, Mathematics.

View Tutors

Krittika
Certified Tutor

University of Dhaka, Master's/Graduate, Statistics. University of Waterloo, Master's/Graduate, Biostatistics.

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

LSAT Tutors in Dallas Fort Worth, GRE Tutors in Boston, ISEE Tutors in Phoenix, Math Tutors in San Diego, Physics Tutors in Chicago, ACT Tutors in Washington DC, Spanish Tutors in Los Angeles, English Tutors in Miami, LSAT Tutors in New York City, ISEE Tutors in Washington DC

Popular Courses & Classes

SAT Courses & Classes in Phoenix, GRE Courses & Classes in Chicago, Spanish Courses & Classes in Houston, GRE Courses & Classes in Houston, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in Los Angeles, MCAT Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Houston, LSAT Test Prep in Chicago, SAT Test Prep in Atlanta, MCAT Test Prep in Atlanta, SAT Test Prep in Miami, ACT Test Prep in San Francisco-Bay Area, SAT Test Prep in Dallas Fort Worth, ISEE Test Prep in Washington DC, SSAT Test Prep in Atlanta, GRE Test Prep in Washington DC

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)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

SAT Mathematics : Working with Fractions

Study concepts, example questions & explanations for SAT Mathematics

All SAT Mathematics Resources

Example Questions

Example Question #1 : Divisibility & Number Fluency

Example Question #2 : Divisibility & Number Fluency

Example Question #3 : Divisibility & Number Fluency

Example Question #1 : Divisibility & Number Fluency

Example Question #5 : Divisibility & Number Fluency

Example Question #1 : Working With Fractions

Example Question #6 : Divisibility & Number Fluency

Example Question #7 : Divisibility & Number Fluency

Example Question #8 : Divisibility & Number Fluency

Example Question #1 : Working With Fractions

All SAT Mathematics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: