We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

SAT Math : How to evaluate a fraction

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 Evaluate A Fraction

Evaluate the following equation when x=5 and round your answer to the nearest hundredth.

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

Possible Answers:

4.33

5.00

2.32

-1.94

5.28

Correct answer:

2.32

Explanation:

$\frac{x^{3}-2x^{2}-3x+5}{5x+3}$

1. Plug in wherever there is an in the above equation.

$\frac{5^{3}-(2)(5^{2})-(3)(5)+5}{(5)(5)+3}$

2. Perform the above operations.

$\frac{5^{3}-(2)(25)-(3)(5)+5}{(5)(5)+3}$

$\frac{125-50-15+5}{25+3}$

$\frac{65}{28}=2.32$

Report an Error

Example Question #2 : How To Evaluate A Fraction

If $w=\frac{1}{8}$ then which of the following is equal to $w^\frac{2}{3}$ ?

Possible Answers:

$\frac{1}{64}$

$\frac{1}{4}$

$\frac{1}{16}$

$\frac{1}{2}$

$\frac{1}{32}$

Correct answer:

$\frac{1}{4}$

Explanation:

To raise $\frac{1}{8}$ to the exponent $\frac{2}{3}$ , square $\frac{1}{8}$ and then take the cube root.

$w^\frac{2}{3}=\sqrt[3]{w^2}$

$(\frac{1}{8})^\frac{2}{3}=\sqrt[3]{(\frac{1}{8})^2}=\sqrt[3]{\frac{1}{64}}$

$\sqrt[3]{\frac{1}{64}}=\frac{1}{4}$

$(\frac{1}{8})^{\frac{2}{3}}=\frac{1}{4}$

Report an Error

Example Question #3 : How To Evaluate A Fraction

Solve

Possible Answers:

–1

no solution

infinitely many solutions

Correct answer:

infinitely many solutions

Explanation:

The common denominator of the left side is x(x–1). Multiplying the top and bottom of 1/x by (x–1) yields

Since this statement is true, there are infinitely many solutions.

Report an Error

Example Question #4 : How To Evaluate A Fraction

Evaluate when x=11. Round to the nearest tenth.

Possible Answers:

0.3

1.9

0.2

1.8

Correct answer:

1.8

Explanation:

Wherever there is an x, plug in 11 and perform the given operations. The numerator will be equal to 83 and the denominator will be equal to 46. 83 divided by 46 is equal to 1.804… and since the second decimal place is not greater than or equal to 5, the first decimal place stays the same when rounding so the final answer is 1.8.

Report an Error

Example Question #5 : How To Evaluate A Fraction

For this question, the following trigonometric identities apply:

$\csc x=\frac{1}{\sin x}$ ,

$\sec x=\frac{1}{\cos x}$

$\cot x=\frac{1}{\tan x}$

Simplify: $\sin ^{2}x\csc x\cot x$

Possible Answers:

$\cos x$

$\sin x$

$\sec x$

$\sin x\cos x$

$\tan x$

Correct answer:

$\cos x$

Explanation:

To begin a problem like this, you must first convert everything to $\sin x$ and $\cos x$ alone. This way, you can begin to cancel and combine to its most simplified form.

Since $\csc x=\frac{1}{\sin x}$ and $\cot x=\frac{\cos x}{\sin x}$ , we insert those identities into the equation as follows.

$\sin ^{2}x\cdot \frac{1}{\sin x}\cdot \frac{\cos x}{\sin x}$

From here we combine the numerator and denominators of each fraction together to easily see what we can combine and cancel.

$\frac{\sin^{2}x\cdot \cos x}{\sin x\cdot \sin x}$

Since there is a $\sin ^{2}x$ in the numerator and the denominator, we can cancel them as they divide to equal 1. All we have left is $\cos x$ , the answer.

Report an Error

Example Question #2 : How To Evaluate A Fraction

If 3x = 12, y/4 = 10, and 4z = 9, what is the value of (10xyz)/xy?

Possible Answers:

4 ¹/₂

360

22 ¹/2

160

Correct answer:

22 ¹/2

Explanation:

Solve for the variables, the plug into formula.

x = 12/3 = 4

y = 10 * 4 = 40

z= 9/4 = 2 ¹/₄

10xyz = 3600

Xy = 160

3600/160 = 22 ¹/2

Report an Error

Example Question #3 : How To Evaluate A Fraction

If 5x=55 , x+y = 23 , and y-z=2 , find the value of $\frac{2x+y}{z}$ .

Possible Answers:

$\frac{9}{2}$

$\frac{19}{5}$

$\frac{16}{7}$

$\frac{17}{5}$

$\frac{13}{5}$

Correct answer:

$\frac{17}{5}$

Explanation:

In order to solve $\frac{2x+y}{z}$ , we must first find the values of , , and using the initial equations provided. Starting with 5x=55 :

$x=\frac{55}{5}=11$

Then:

x+y=23

11+y=23

y=12

Finally:

y-z=2

12-z=2

10=z

With the values of , , and in hand, we can solve the final equation:

$\frac{2x+y}{z}$

$=\frac{2(11)+12}{10}$

$=\frac{22+12}{10}$

$=\frac{34}{10}$

$=\frac{17}{5}$

Report an Error

Example Question #3 : How To Evaluate A Fraction

If $x =\frac{1}{2}$ and $y=\frac{2}{3}$ , then which of the following is equal to $\frac{2}{x+y}$ ?

Possible Answers:

$2 \frac{1}{3}$

$\frac{12}{7}$

$\frac{10}{3}$

$\frac{9}{7}$

Correct answer:

$\frac{12}{7}$

Explanation:

In order to solve $\frac{2}{x+y}$ , first substitute the values of and provided in the problem:

$\frac{2}{\frac{1}{2}+\frac{2}{3}}$

Find the Least Common Multiple (LCM) of the fractional terms in the denominator and find the equivalent fractions with the same common denominator:

$\frac{2}{\frac{1}{2}+\frac{2}{3}}$

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

$=\frac{2}{\frac{7}{6}}$

Finally, in order to divide by a fraction, we must multiply by the reciprocal of the fraction:

$=2\times \frac{6}{7}$

$=\frac{12}{7}$

Report an Error

Example Question #7 : How To Evaluate A Fraction

Find the value of if $w=\bigg(\frac{1}{3}+y\bigg)^{2}$ and $y=\frac{1}{9}$ .

Possible Answers:

$\frac{4}{27}$

$\frac{16}{81}$

$\frac{9}{10}$

$\frac{1}{12}$

$\frac{3}{55}$

Correct answer:

$\frac{16}{81}$

Explanation:

In order to solve for , first substitute $y=\frac{1}{9}$ into the equation for :

$w=\bigg(\frac{1}{3}+y\bigg)^{2}$

$w=\bigg(\frac{1}{3}+\frac{1}{9}\bigg)^{2}$

Then, find the Least Common Multiple (LCM) of the two fractions and generate equivalent fractions with the same denominator:

$w=\bigg(\frac{3}{9}+\frac{1}{9}\bigg)^{2}$

Finally, simplify the equation:

$w=\bigg(\frac{4}{9}\bigg)^{2}$

$w=\frac{16}{81}$

Report an Error

Example Question #21 : Algebraic Fractions

$\frac{7^{12}-7^{10}}{7^{11}-7^{9}}=$

Possible Answers:

343

Correct answer:

Explanation:

Factor out 7 from the numerator: $\frac{7(7^{11}-7^{9})}{7^{11}-7^{9}}$

This simplifies to 7.

Report an Error

View SAT Mathematics Tutors

Noah
Certified Tutor

Bard College, Bachelors, Philosophy and Creative Writing (Dual Major). Sarah Lawrence College, Master of Fine Arts, Creative ...

View SAT Mathematics Tutors

Priyanka
Certified Tutor

CUNY Hunter College, Bachelor in Arts, Economics.

View SAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

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 Phoenix, MCAT Courses & Classes in Denver, ISEE Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Houston, SSAT Courses & Classes in New York City, SAT Courses & Classes in Miami, GRE Courses & Classes in San Diego, GRE Courses & Classes in Atlanta, ISEE Courses & Classes in Houston, ACT Courses & Classes in Denver

Popular Test Prep

MCAT Test Prep in New York City, ISEE Test Prep in New York City, ISEE Test Prep in Phoenix, ISEE Test Prep in Houston, LSAT Test Prep in Chicago, ACT Test Prep in Denver, GMAT Test Prep in Chicago, SAT Test Prep in San Diego, GRE Test Prep in Houston, SSAT 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 Math : How to evaluate a fraction

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Evaluate A Fraction

Example Question #2 : How To Evaluate A Fraction

Example Question #3 : How To Evaluate A Fraction

Example Question #4 : How To Evaluate A Fraction

Example Question #5 : How To Evaluate A Fraction

Example Question #2 : How To Evaluate A Fraction

Example Question #3 : How To Evaluate A Fraction

Example Question #3 : How To Evaluate A Fraction

Example Question #7 : How To Evaluate A Fraction

Example Question #21 : Algebraic Fractions

All SAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: