We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : Simplifying Fractions

Study concepts, example questions & explanations for SAT Math

Create An Account

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Simplify A Fraction

Simplify x/2 – x/5

Possible Answers:

7x/10

5x/3

2x/7

3x/10

3x/7

Correct answer:

3x/10

Explanation:

Simplifying this expression is similar to 1/2 – 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 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

Report an Error

Example Question #1 : How To Simplify A Fraction

If $\dpi{100} \small \frac{p}{6}$ is an integer, which of the following is a possible value of $\dpi{100} \small p$ ?

Possible Answers:

$\dpi{100} \small 16$

$\dpi{100} \small 0$

$\dpi{100} \small 2$

$\dpi{100} \small 3$

$\dpi{100} \small 4$

Correct answer:

$\dpi{100} \small 0$

Explanation:

$\dpi{100} \small \frac{0}{6}=0$ , 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:

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

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

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

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

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 32/24?

Possible Answers:

16/12

224/168

160/96

96/72

4/3

Correct answer:

160/96

Explanation:

24/32 = 1.33

16/12 =1.33

224/168 =1.33

4/3 = 1.33

96/72 = 1.33

160/96 = 1.67

Report an Error

Example Question #1 : How To Simplify A Fraction

Find the root of

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

Possible Answers:

Can not be determined

$\sqrt3$

$-\sqrt3$

$\sqrt5$

$-\sqrt{5 }$

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 #5 : Simplifying Fractions

Simplify the fraction below:

$\frac{5}{125}$

Possible Answers:

$\frac{1}{25}$

$\frac{1}{20}$

$\frac{1}{4}$

$\frac{2}{13}$

Correct answer:

$\frac{1}{25}$

Explanation:

The correct approach to solve this problem is to first write factors for the numerator and the denominator:

5: 1, 5

125: 1, 5, 25, 125

The highest common factor is 5. Therefore, you can divide the numerator and denominator by 5 in order to get a simplified fraction.

Thus the numerator becomes,

$\frac{5}{5}=1$ and the denominator becomes $\frac{125}{5}=25$ .

Therefore the final answer is $\frac{1}{25}$ .

Report an Error

Example Question #631 : Arithmetic

Simplify: $\frac{32}{88}$

Possible Answers:

$\frac{4}{11}$

$\frac{8}{11}$

$\frac{2}{11}$

$\frac{1}{4}$

$\frac{3}{8}$

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 #7 : Simplifying Fractions

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 #1 : Simplifying Fractions

Solve for .

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

Possible Answers:

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

x=-2

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

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

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

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 #10 : How To Simplify A Fraction

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

Possible Answers:

$\frac{3}{22.5}$

$\frac{12}{89}$

$\frac{2}{15}$

$\frac{4}{30}$

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 SAT Mathematics Tutors

Liban
Certified Tutor

Emory University, Bachelor of Science, Mathematics/Economics.

View SAT Mathematics Tutors

Cole
Certified Tutor

UW Madison, Bachelors, Industrial Engineering. UW Madison, Masters, Industrial Engineering.

View SAT Mathematics Tutors

Amanda
Certified Tutor

Seattle University, Current Undergrad Student, Applied Mathematics.

All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

SAT Math Tutors in Top Cities:

Atlanta SAT Math Tutors, Austin SAT Math Tutors, Boston SAT Math Tutors, Chicago SAT Math Tutors, Dallas Fort Worth SAT Math Tutors, Denver SAT Math Tutors, Houston SAT Math Tutors, Kansas City SAT Math Tutors, Los Angeles SAT Math Tutors, Miami SAT Math Tutors, New York City SAT Math Tutors, Philadelphia SAT Math Tutors, Phoenix SAT Math Tutors, San Diego SAT Math Tutors, San Francisco-Bay Area SAT Math Tutors, Seattle SAT Math Tutors, St. Louis SAT Math Tutors, Tucson SAT Math Tutors, Washington DC SAT Math Tutors

Popular Courses & Classes

SAT Courses & Classes in Chicago, LSAT Courses & Classes in Boston, MCAT Courses & Classes in Seattle, GMAT Courses & Classes in Los Angeles, MCAT Courses & Classes in Washington DC, ACT Courses & Classes in Phoenix, Spanish Courses & Classes in Philadelphia, SAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Dallas Fort Worth

Popular Test Prep

MCAT Test Prep in Washington DC, SAT Test Prep in Chicago, ISEE Test Prep in Los Angeles, MCAT Test Prep in Chicago, LSAT Test Prep in New York City, ACT Test Prep in Dallas Fort Worth, LSAT Test Prep in Denver, SAT Test Prep in Washington DC, ACT Test Prep in Atlanta, SAT Test Prep in Philadelphia

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 Math : Simplifying Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Simplify A Fraction

Example Question #1 : How To Simplify A Fraction

Example Question #3 : Simplifying Fractions

Example Question #4 : Simplifying Fractions

Example Question #1 : How To Simplify A Fraction

Example Question #5 : Simplifying Fractions

Example Question #631 : Arithmetic

Example Question #7 : Simplifying Fractions

Example Question #1 : Simplifying Fractions

Example Question #10 : How To Simplify A Fraction

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: