Call Now to Set Up Tutoring:

(888) 888-0446

SAT Mathematics : SAT Math

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 #2 : Applying Number Properties

What is the greatest common factor of 15 and 75?

Possible Answers:

Correct answer:

Explanation:

The greatest common factor (GCF) refers to the largest factor for each number that is shared by all the numbers of a given set, so in this case, it is the greatest factor of 15 and 75. The best way to approach these problems is to factorize each number and calculate the GCF from the multiplication of these numbers. 15 can be factorized into 3 and 5. 75 can be factorized into 3, 5, and 5. Now, identify the factors they have in common. Both 15 and 75 share one 3 and one 5, so multiplied together, the GCF = 3 * 5 = 15.

Report an Error

Example Question #1 : Simplifying Fractions

Simplify $\frac{x}{2}-\frac{x}{5}$

Possible Answers:

$\frac{3x}{10}$

$\frac{5x}{3}$

$\frac{2x}{7}$

$\frac{3x}{7}$

Correct answer:

$\frac{3x}{10}$

Explanation:

Simplifying this expression is similar to $\frac{1}{2}-\frac{1}{5}$ . The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2*5=10 . So the problem becomes $\frac{1}{2}-\frac{1}{5}=\frac{5}{10}-\frac{2}{10}=\frac{3}{10}$ .

Report an Error

Example Question #21 : Sat Math

If $\frac{p}{6}$ is an integer, which of the following is a possible value of ?

Possible Answers:

Correct answer:

Explanation:

$\frac{0}{6}=0$ , which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

Report an Error

Example Question #3 : Simplifying Fractions

Simplify: $\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}$

Possible Answers:

$\frac{3x^{2}y^{3}}{z}$

$\frac{x^{2}}{8y^{3}z}$

$\frac{x^{2}}{3y^{3}z}$

$\frac{1}{3x^{2}y^{3}z}$

Correct answer:

$\frac{x^{2}}{3y^{3}z}$

Explanation:

$\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}=\frac{x^{2}}{3y^{3}z}$

First, let's simplify $\frac{4}{12}$ . The greatest common factor of 4 and 12 is 4. 4 divided by 4 is 1 and 12 divided by 4 is 3. Therefore $\frac{4}{12}=\frac{1}{3}$ .

To simply fractions with exponents, subtract the exponent in the numerator from the exponent in the denominator. That leaves us with $\frac{1}{3}x^{2}y^{-3}z^{-1}$ or $\frac{x^{2}}{3y^{3}z}$

Report an Error

Example Question #4 : Simplifying Fractions

Which of the following is not equal to $\frac{32}{24}$ ?

Possible Answers:

$\frac{224}{168}$

$\frac{160}{96}$

$\frac{4}{3}$

$\frac{16}{12}$

Correct answer:

$\frac{160}{96}$

Explanation:

$\frac{32}{24}=1.33$ , so the answer choice needs to be something that is not equal to 1.33 in order to be correct.

$\frac{16}{12}=1.33$

$\frac{224}{168}=1.33$

$\frac{4}{3}=1.33$

$\frac{160}{96}=1.67$

Report an Error

Example Question #5 : Simplifying Fractions

Find the root of:

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}$

Possible Answers:

$-\sqrt{5 }$

$-\sqrt3$

$\sqrt5$

$\sqrt3$

Correct answer:

$-\sqrt{5 }$

Explanation:

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}=\frac{(x-\sqrt3)(x+\sqrt5)}{x-\sqrt3}=x+\sqrt5$

The root occurs where y=0 . So we substitute 0 for .

$y=x+\sqrt{5}$

$0=x+\sqrt{5}$

This means that the root is at $x=-\sqrt5$ .

Report an Error

Example Question #21 : Sat Math

Simplify $\frac{32}{88}$

Possible Answers:

$\frac{4}{11}$

$\frac{1}{4}$

$\frac{2}{11}$

$\frac{8}{11}$

Correct answer:

$\frac{4}{11}$

Explanation:

Find the common factors of the numerator and denominator. They both share factors of 2,4, and 8. For simplicity, factor out an 8 from both terms and simplify.

$\frac{32}{88}=\frac{8\times 4}{8\times 11}=\frac{4}{11}$

Report an Error

Example Question #23 : Sat Math

Simply the following fraction:

$\frac{\frac{a^2}{b}}{\frac{a}{b}}$

Possible Answers:

$\frac{a^3}{b^2}$

$\frac{a^2}{b}$

$\infty$

Correct answer:

Explanation:

Remember that when you divide a fraction by a fraction, that is the same as multiplying the fraction in the numerator by the reciprocal of the fraction in the denominator.

In other words,

$\frac{\frac{a^2}{b}}{\frac{a}{b}} = \frac{a^2}{b}\cdot\frac{b}{a}=\frac{a^2b}{ab}$

Simplifying this final fraction gives us our correct answer, .

Report an Error

Example Question #8 : Simplifying Fractions

Solve for .

$\frac{\frac{x-2}{4^2}}{\frac{x^2-4}{2}}=1$

Possible Answers:

$x=-\frac{15}{8}$

$x=-\frac{8}{15}$

$x=\frac{15}{8}$

$x=\frac{8}{15}$

Correct answer:

$x=-\frac{15}{8}$

Explanation:

To solve for , simplify the fraction. In order to do this, recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, rewrite the equation as follows.

$\frac{\frac{x-2}{4^2}}{\frac{x^2-4}{2}}=1\Rightarrow \frac{x-2}{4^2}\times \frac{2}{x^2-4}=1$

Now, simplify the first fraction by calculating four squared.

$\frac{x-2}{16}\times \frac{2}{x^2-4}=1$

From here, factor the denominator of the second fraction.

$\frac{x-2}{16}\times \frac{2}{(x-2)(x+2)}=1$

Next, factor the 16.

$\frac{x-2}{2(8)}\times \frac{2}{(x-2)(x+2)}=1$

From here, cancel out like terms that are in both the numerator and denominator. In this particular case that includes (x-2) and 2.

$\frac{1}{8(x+2)}=1$

Now, distribute the eight.

$\frac{1}{8x+16}=1$

Next, multiply both sides by the denominator.

$(8x+16)\times \frac{1}{8x+16}=1\times (8x+16)$

The (8x+16) cancels out and leaves the following equation.

1=8x+16

Now to solve for perform opposite operations to move all numerical values to one side of the equation leaving by itself on the other side of the equation.

$\\1=8x+16 \\-15=8x \\\\\frac{-15}{8}=x$

Report an Error

Example Question #9 : Simplifying Fractions

Which of the following fractions is not equivalent to $\frac{6}{45}$ ?

Possible Answers:

$\frac{3}{22.5}$

$\frac{2}{15}$

$\frac{4}{30}$

$\frac{12}{89}$

Correct answer:

$\frac{12}{89}$

Explanation:

Let us simplify $\frac{6}{45}$ :

$\frac{6}{45}=\frac{3\times 2}{3\times 15}=\frac{2}{15}$

We can get alternate forms of the same fraction by multiplying the denominator and the numerator by the same number:

$\frac{2\times 2}{15\times 2}=\frac{4}{30}$

$\frac{2\times 1.5}{15\times 1.5}=\frac{3}{22.5}$

Now let's look at $\frac{12}{89}$ :

$6 \times 2 = 12$ , but $45 \times 2 = 90$ .

Therefore, $\frac{12}{89}$ is the correct answer, as it is not equivalent to $\frac{6}{45}$ .

Report an Error

View Tutors

Brooke
Certified Tutor

New York University, Bachelor in Arts, Drama and Dance Teacher Education. Georgia State University, Master of Arts, Communica...

View Tutors

Nicole
Certified Tutor

Western Governors University, Bachelor of Education, Special Education.

View Tutors

Travis
Certified Tutor

Delaware State University, Bachelor of Science, Mathematics.

All SAT Mathematics Resources

137 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Spanish Tutors in Atlanta, GRE Tutors in San Francisco-Bay Area, Physics Tutors in Miami, SSAT Tutors in Washington DC, Algebra Tutors in Dallas Fort Worth, Spanish Tutors in Seattle, Spanish Tutors in San Diego, Chemistry Tutors in Philadelphia, GMAT Tutors in Los Angeles, Statistics Tutors in Denver

Popular Courses & Classes

GMAT Courses & Classes in Boston, ISEE Courses & Classes in Washington DC, GMAT Courses & Classes in Dallas Fort Worth, SAT Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Denver, GMAT Courses & Classes in Atlanta, LSAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Philadelphia

Popular Test Prep

GMAT Test Prep in Chicago, LSAT Test Prep in New York City, GMAT Test Prep in Philadelphia, LSAT Test Prep in Washington DC, MCAT Test Prep in Chicago, SSAT Test Prep in San Diego, GRE Test Prep in San Francisco-Bay Area, ISEE Test Prep in Seattle, GRE Test Prep in Atlanta, LSAT Test Prep in Dallas Fort Worth

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 : SAT Math

Study concepts, example questions & explanations for SAT Mathematics

All SAT Mathematics Resources

Example Questions

Example Question #2 : Applying Number Properties

Example Question #1 : Simplifying Fractions

Example Question #21 : Sat Math

Example Question #3 : Simplifying Fractions

Example Question #4 : Simplifying Fractions

Example Question #5 : Simplifying Fractions

Example Question #21 : Sat Math

Example Question #23 : Sat Math

Example Question #8 : Simplifying Fractions

Example Question #9 : Simplifying Fractions

All SAT Mathematics Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: