Call Now to Set Up Tutoring:

(888) 888-0446

SAT Mathematics : Divisibility & Number Fluency

Study concepts, example questions & explanations for SAT Mathematics

Create An Account Create Tests & Flashcards

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3. 4 Next →

Example Question #1 :Divisibility & Number Fluency

Jesse has a large movie collection containingmovies. $\frac{1}{3}$ 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:

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

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

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

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

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:

$\frac{13}{6}$

$\frac{6}{5}$

$\frac{5}{6}$

Correct answer:

$\frac{13}{6}$

Explanation:

Substitute the values ofandinto 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:

$-\frac{47}{60}$

$\frac{43}{60}$

$\frac{17}{60}$

$\frac{47}{60}$

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 letrange fromtoto 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, whenis raised to an even power, the result is. Conversely, ifis 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. Becauseis 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 :Working With Fractions

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=2

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

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

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

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:

$\frac{47}{140}$

$\frac{3}{39}$

$\frac{43}{140}$

$\frac{3}{28}$

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 #6 :Divisibility & Number Fluency

Add:

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

Possible Answers:

$\frac{6}{27x}$

$\frac{10}{27x}$

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

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

Correct answer:

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

Explanation:

Find the least common denominator to solve this problem

Multiply 27 with, and multiplywith 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 #7 :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:

117

232

156

Correct answer:

117

Explanation:

首先,我们必须找到嘻哈的分数记录s 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 isand $\frac{3}{7}$ of 364 is 156 , knowing that we need the amount remaining, we can subtract 91+156 from 364 and get 117 .

Answer choiceis 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 #8 :Divisibility & Number Fluency

Jackson wrote a song with equal parts pre-chorus, chorus, and bridge. The song ends up beingminutes andseconds with a beat occurring everyseconds. 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 addseconds 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 byand get 48.67 seconds of chorus.
Since a beat occurs every five seconds, we divide 48.67 seconds byseconds 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 choiceis incorrect because it is finding the total number of beats in the song.

Answer choiceis incorrect because it rounds up to the nearest beat.

Report an Error

Example Question #2 :Sat Math

Please simplify the following:

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

Possible Answers:

$\frac{ad}{bc}$

$\frac{cb}{ad}$

$\frac{ac}{db}$

$\frac{a}{bdc}$

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” meaningis 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, thenis labeled top so it moves to the top.

Report an Error

Example Question #10 :Divisibility & Number Fluency

找到的价值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 subtractfrom 15x

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

x=6

Report an Error

← Previous 1 2 3. 4 Next →

View Tutors

Andrew
Certified Tutor

University of South Florida-Main Campus, Bachelors, Biomedical Sciences. New York Medical College, PHD, Doctor of Medicine.

View Tutors

Janine
Certified Tutor

Towson University, Bachelor of Science, Elementary School Teaching. Towson University, Master of Arts Teaching, Reading Teach...

View Tutors

Jessica
Certified Tutor

Johns Hopkins University, Bachelor of Science, Nursing (RN). American Sentinel University, Doctor of Education, Nursing (RN).

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Biology Tutors in San Francisco-Bay Area,Reading Tutors in Denver,LSAT Tutors in Washington DC,LSAT Tutors in Philadelphia,Spanish Tutors in Dallas Fort Worth,Physics Tutors in Phoenix,Calculus Tutors in Chicago,GRE Tutors in Boston,English Tutors in Denver,ISEE Tutors in Boston

Popular Courses & Classes

ISEE Courses & Classes in Philadelphia,LSAT Courses & Classes in San Diego,ACT Courses & Classes in Denver,SSAT Courses & Classes in Washington DC,Spanish Courses & Classes in Denver,GMAT Courses & Classes in Seattle,GRE Courses & Classes in Denver,MCAT Courses & Classes in New York City,GRE Courses & Classes in New York City,ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

MCAT Test Prep in Miami,SSAT Test Prep in Seattle,GMAT Test Prep in Miami,ISEE Test Prep in Washington DC,MCAT Test Prep in Philadelphia,SAT Test Prep in Denver,SAT Test Prep in Washington DC,ACT Test Prep in Denver,ACT Test Prep in Dallas Fort Worth,GRE Test Prep in Los Angeles

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 : Divisibility & Number Fluency

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 :Working With Fractions

Example Question #5 :Divisibility & Number Fluency

Example Question #6 :Divisibility & Number Fluency

Example Question #7 :Divisibility & Number Fluency

Example Question #8 :Divisibility & Number Fluency

Example Question #2 :Sat Math

Example Question #10 :Divisibility & Number Fluency

All SAT Mathematics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
Your name:
Feedback: