Call Now to Set Up Tutoring:

(888) 888-0446

PSAT Math : How to simplify a fraction

Study concepts, example questions & explanations for PSAT Math

Create An Account

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #51 : Algebraic Fractions

Simplify the expression

$\small \frac{x^2-4x+4}{x-2}$ .

Possible Answers:

$\small x-4$

$\small x^2$

$\small x-2$

$\small x+2$

Correct answer:

$\small x-2$

Explanation:

The expression is factorable into the expression

$\small \frac{(x-2)(x-2)}{(x-2)}$

Cancelling the $\small x-2$ in the numerator and the denominator leaves

$\small x-2$

Report an Error

Example Question #52 : Algebraic Fractions

Simplify the expression,

$\small \frac{a^2+b^2}{a+b}$ .

Possible Answers:

$\small \frac{a}{b}+\frac{b}{a}$

Cannot be simplified

$\small a- b$

$\small a+b$

Correct answer:

Cannot be simplified

Explanation:

The numerator of the expression cannot be factored. Therefore, the denominator cannot divide into the numerator, and the expression is in its simplest form.

Report an Error

Example Question #53 : Algebraic Fractions

Simplify the expression

$\small \frac{x^2+x-6}{x+3}$ .

Possible Answers:

$\small x +3$

$\small x - 2$

$\small 2x$

Cannot be simplified

Correct answer:

$\small x - 2$

Explanation:

The expression's numerator can be factored. Factoring the expression gives,

$\small \frac{(x-2)(x+3)}{(x+3)}$

The numerator and denominator can then both be divided by $\small (x+3)$ to give,

$\small \frac{(x-2)(1)}{(1)} = x-2$

Report an Error

Example Question #54 : Algebraic Fractions

Simplify the expression

$\small \frac{x^3-2x^2+9x-18}{x^2+9}$ .

Possible Answers:

Cannot be simplified

x + 2

$\small x-2$

$\small x - 3$

Correct answer:

$\small x-2$

Explanation:

The expression can be factored to give

$\small \frac{(x-2)(x^2+9)}{(x^2+9)}$ .

$\small (x^2+9)$ can then be divded from the numerator and the denominator to give,

$\small \frac{(x-2)(1)}{(1)} = x -2$

Report an Error

Example Question #15 : How To Simplify A Fraction

Simplify the expression

$\small \frac{x^2-7x+10}{x^2-9x+20}$ .

Possible Answers:

$\small 2$

$\small 2x$

$\small \frac{x-2}{x-4}$

$\small \frac{x-3}{x-5}$

Correct answer:

$\small \frac{x-2}{x-4}$

Explanation:

The expression must first be factored in order to be solvable. Both the numerator and the denominator can be factored, which would give

$\small \frac{(x-2)(x-5)}{(x-5)(x-4)}$ .

$\small x-5$ can be divided from both the numerator and the denominator to give

$\small \frac{(x-2)(1)}{(1)(x-4)} = \frac{x-2}{x-4}$

Report an Error

Example Question #55 : Algebraic Fractions

Simplify the expression

$\small \frac{x^3y^{-2}z^2}{xy^3z^2}$ .

Possible Answers:

$\small \frac{x^2}{y^5}$

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

$\small \frac{x^2}{y}$

$\small \frac{x^2z^4}{y}$

Correct answer:

$\small \frac{x^2}{y^5}$

Explanation:

The expression can be rewritten as

$\small x^{(3-1)}y^{(-2-3)}z^{(2-2)} = x^2y^{-5}z^0 = \frac{x^2}{y^5}$

Report an Error

Example Question #3 : Algebraic Fractions

A train travels at a constant rate of meters per second. How many kilometers does it travel in minutes? $(1\ km=1000\ m)$

Possible Answers:

Correct answer:

Explanation:

Set up the conversions as fractions and solve:

$\dpi{100} \small \frac{20m}{1sec}\times \frac{60sec^}{1min}\times \frac{1km}{1000m}\times \frac{10min}{1}$

Report an Error

Example Question #4 : Algebraic Fractions

Simplify. $\frac{4x^{4}z^{3}}{2xz^{2}}$

Possible Answers:

$\frac{2x^{4}z^{3}}{xz}$

$2x^{3}z$

Can't be simplified

$2x^{4}z^{3}$

$4x^{3}z$

Correct answer:

$2x^{3}z$

Explanation:

To simplify exponents which are being divided, subtract the exponents on the bottom from exponents on the top. Remember that only exponents with the same bases can be simplified

Report an Error

Example Question #5 : Algebraic Fractions

Simplify:

$\frac{x^2-y^2}{x+y}$

Possible Answers:

x-y

2xy

$x-y,\ x+y$

x+y

Correct answer:

x-y

Explanation:

x² – y² can be also expressed as (x + y)(x – y).

Therefore, the fraction now can be re-written as (x + y)(x – y)/(x + y).

This simplifies to (x – y).

Report an Error

Example Question #6 : Algebraic Fractions

Simplify:

$\frac{x\sqrt{2}-2\sqrt{2}}{\sqrt{2x}+2}$

Possible Answers:

$\frac{x+2}{\sqrt{x-2}}$

$x+\sqrt{2}$

$\sqrt{x}+\sqrt{2}$

$\sqrt{x}-\sqrt{2}$

$x-\sqrt{2}$

Correct answer:

$\sqrt{x}-\sqrt{2}$

Explanation:

Notice that the $\sqrt{2}$ term appears frequently. Let's try to factor that out:

$\frac{x\sqrt{2}-2\sqrt{2}}{\sqrt{2x}+2} = \frac{\sqrt{2}*(x-2)}{\sqrt{2}*(\sqrt{x} +\sqrt{2})} = \frac{x-2}{\sqrt{x} +\sqrt{2}}$

Now multiply both the numerator and denominator by the conjugate of the denominator:

$\frac{x-2}{\sqrt{x} +\sqrt{2}} * \frac{\sqrt{x} -\sqrt{2}}{\sqrt{x} -\sqrt{2}} =\frac{(x-2)*(\sqrt{x} -\sqrt{2})}{x-2} =\sqrt{x} -\sqrt{2}$

Report an Error

View PSAT Mathematics Tutors

Joseph
Certified Tutor

Bank Street College of Education , Master's/Graduate, Early Childhood and Childhood General Education.

View PSAT Mathematics Tutors

Yongmao
Certified Tutor

Nankai University, Bachelor of Science, Chemistry. Washington University in St Louis, Doctor of Philosophy, Organic Chemistry.

View PSAT Mathematics Tutors

Joy
Certified Tutor

Boston University, Bachelor in Arts, Conservation Biology.

All PSAT Math Resources

10 Diagnostic Tests 421 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in Boston, GMAT Tutors in Houston, SAT Tutors in Philadelphia, Biology Tutors in San Diego, ISEE Tutors in Los Angeles, SSAT Tutors in San Diego, GRE Tutors in Los Angeles, SSAT Tutors in Los Angeles, Biology Tutors in Houston, French Tutors in Seattle

Popular Courses & Classes

Spanish Courses & Classes in Los Angeles, SSAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Washington DC, MCAT Courses & Classes in Miami, LSAT Courses & Classes in Atlanta, SAT Courses & Classes in New York City, SSAT Courses & Classes in Philadelphia, SAT Courses & Classes in Los Angeles, SAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

SAT Test Prep in Miami, LSAT Test Prep in Dallas Fort Worth, LSAT Test Prep in New York City, GMAT Test Prep in Washington DC, SSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Chicago, ISEE Test Prep in Houston, SSAT Test Prep in Chicago, LSAT Test Prep in Denver, SSAT Test Prep in Atlanta

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

PSAT Math : How to simplify a fraction

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #51 : Algebraic Fractions

Example Question #52 : Algebraic Fractions

Example Question #53 : Algebraic Fractions

Example Question #54 : Algebraic Fractions

Example Question #15 : How To Simplify A Fraction

Example Question #55 : Algebraic Fractions

Example Question #3 : Algebraic Fractions

Example Question #4 : Algebraic Fractions

Example Question #5 : Algebraic Fractions

Example Question #6 : Algebraic Fractions

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: