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

← Previous 1 2 3 Next →

Example Question #1 : Algebraic Fractions

The expression $(\frac{a^{2}}{b^{3}})(\frac{a^{-2}}{b^{-3}}) = ?$

Possible Answers:

$1$

$\frac{b^{9}}{a^{4}}$

$b^{-9}$

$\frac{a^{-4}}{b^{-9}}$

$0$

Correct answer:

$1$

Explanation:

A negative exponent in the numerator of a fraction can be rewritten with a positive exponent in the denominator. The same is true for a negative exponent in the denominator. Thus, $\frac{a^{-2}}{b^{-3}} =\frac{b^{3}}{a^{2}}$ .

When $\frac{a^{2}}{b^{3}}$ is multiplied by $\frac{b^{3}}{a^{2}}$ , the numerators and denominators cancel out, and you are left with 1.

Report an Error

Example Question #1 : Algebraic Fractions

Two two-digit numbers, 'AB' and 'BA' , sum to produce a three-digit number in which the second digit is equal to . The addition is represented below. (Note that the variables are used to represent individual digits; no multiplication is taking place).

AB + BA = 1A2

What is ?

Possible Answers:

Correct answer:

Explanation:

Another way to represent this question is:

$\begin{matrix} & \ \ AB\\ +& \ \ BA\\ & 1A2 \end{matrix}$

In the one's column, and add to produce a number with a two in the one's place. In the ten's column, we can see that a one must carry in order to get a digit in the hundred's place. Together, we can combine these deductions to see that the sum of and must be twelve (a one in the ten's place and a two in the one's place).

In the one's column: B+A=12

The one carries to the ten's column.

In the ten's column: (1)+A+B=(1)+12=13

The three goes into the answer and the one carries to the hundred's place. The final answer is 132. From this, we can see that {A=3} because 1A2=132 .

Using this information, we can solve for .

$A+B=12\ \text{and}\ A=3$

3+B=12

B=9

You can check your answer by returning to the original addition and plugging in the values of and .

$AB=39\ \text{and}\ BA=93$

AB+BA=39+93=132

Report an Error

Example Question #1 : Algebraic Fractions

Let $\frac{\frac{1}{4}+\frac{1}{3}-\frac{1}{5}}{\frac{1}{2}-\frac{1}{6}+1}$ = $\frac{a}{b}$ , where and are both positive integers whose greatest common factor is one. What is the value of a + b ?

Possible Answers:

103

115

Correct answer:

103

Explanation:

First we want to simplify the expression: $\frac{\frac{1}{4}+\frac{1}{3}-\frac{1}{5}}{\frac{1}{2}-\frac{1}{6}+1}$ .

One way to simplify this complex fraction is to find the least common multiple of all the denominators, i.e. the least common denominator (LCD). If we find this, then we can multiply every fraction by the LCD and thereby be left with only whole numbers. This will make more sense in a little bit.

The denominators we are dealing with are 2, 3, 4, 5, and 6. We want to find the smallest multiple that these numbers have in common. First, it will help us to notice that 6 is a multiple of both 2 and 3. Thus, if we find the least common multiple of 4, 5, and 6, it will automatically be a multiple of both 2 and 3. Let's list out the first several multiples of 4, 5, and 6.

4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

The smallest multiple that 4, 5, and 6 have in common is 60. Thus, the least common multiple of 4, 5, and 6 is 60. This also means that the least common multiple of 2, 3, 4, 5, and 6 is 60. Therefore, the LCD of all the fractions is 60.

Let's think of the expression we want to simplify as one big fraction. The numerator contains the fractions 1/4, 1/3, and –1/5. The denominator of the fraction is 1/2, –1/6 and 1. Remember that if we have a fraction, we can multiply the numerator and denominator by the same number without changing the value of the fraction. In other words, x/y = (xz)/(yz). This will help us because we can multiply the numerator (which consists of 1/4, 1/3, and –1/5) by 60, and then mutiply the denominator (which consists of 1/2, –1/6, and 1) by 60, thereby ridding us of fractions in the numerator and denominator. This process is shown below:

$\frac{\frac{1}{4}+\frac{1}{3}-\frac{1}{5}}{\frac{1}{2}-\frac{1}{6}+1}$ = $\frac{60}{60}\cdot$ $\frac{\frac{1}{4}+\frac{1}{3}-\frac{1}{5}}{\frac{1}{2}-\frac{1}{6}+1}$ = $\frac{60\cdot \frac{1}{4}+60\cdot \frac{1}{3}-60\cdot \frac{1}{5}}{60\cdot \frac{1}{2}-60\cdot \frac{1}{6}+60\cdot 1}$

= $\frac{15+20-12}{30-10+60}=\frac{23}{80}$

This means that a/b = 23/80. We are told that a and b are both positive and that their greatest common factor is 1. In other words, a/b must be the simplified form of 23/80. When a fraction is in simplest form, the greatest common factor of the numerator and denominator equals one. Since 23/80 is simplified, a = 23, and b = 80. The sum of a and b is thus 23 + 80 = 103.

The answer is 103.

Report an Error

Example Question #1 : How To Simplify A Fraction

Simplify:

$\frac{8x^3y^2z^2}{4xy^4z^3}$

Possible Answers:

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

2x^2y^2z

2x^4y^6z^4

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

Correct answer:

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

Explanation:

$\frac{8x^3y^2z^2}{4xy^4z^3}$

To simply a fraction with variables, subtract exponents of like bases:

x: 3-1=2

y: 2-4=-2

z: 2-3=-1

This leaves us with the expression:

$2x^2y^{-2}z^{-1}$

Next, we know that to change negative exponents in the numerator into positive exponents, we place them in the denominator. Thus, our expression simplifies to:

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

Report an Error

Example Question #2 : How To Simplify A Fraction

Simplify the expression, $\left(\frac{x^2}{y^{-3}}\right)\left(\frac{x^{-1}}{y^3}\right)$ .

Possible Answers:

Can't be simplified

x^3

$\frac{x}{y^6}$

Correct answer:

Explanation:

The and variables with negative exponents can be rewritten with positive exponents by moving them from the denominator to the numerator, and vice versa. Therefore, the expression can be rewritten as

$\left(x^2y^3 \right) \left(\frac{1}{xy^3}\right) = \frac{x^2y^3}{xy^3}$ .

The exponents on the denominator can then be subtracted from the exponent in the numerator to give

$x^{2-1}y^{3-3} = x^1y^0 = x \cdot1 = x$

Report an Error

Example Question #3 : How To Simplify A Fraction

Simplify the expression $\left(\frac{2x^2}{ab^4}\right)(a^5b^2x^{-1})$ .

Possible Answers:

$\frac{2x^3a^4}{b^2}$

$\frac{xa^4}{b^2}$

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

$\frac{2a^4x}{b^2}$

Correct answer:

$\frac{2a^4x}{b^2}$

Explanation:

The expression can be rewritten as

$\left(\frac{2x^2}{ab^4}\right)\left(\frac{a^5b^2}{x}\right)$

Now the expression can be combined by adding and subtracting exponents

$\left(\frac{2x^2a^5b^2}{ab^4x}\right) = 2x^{(2-1)}a^{(5-1)}b^{(2-4)} = 2xa^4b^{-2} = \frac{2xa^4}{b^2} = \frac{2a^4x}{b^2}$

Report an Error

Example Question #4 : How To Simplify A Fraction

Simplify the expression

$(12X^2Y^{-3}Z^2)\left(\frac{X^3Y^4Z^{-3}}{4}\right)$ .

Possible Answers:

$\frac{3}{XYZ}$

$\frac{3Y}{XZ}$

$\frac{3X^5Y}{Z}$

3X^5Z

Correct answer:

$\frac{3X^5Y}{Z}$

Explanation:

We can combine the expression into

$\left(\frac{12X^2X^3Y^{-3}Y^4Z^2Z^{-3}}{4}\right) = \frac{12}{4} X^{(2+3)}Y^{(-3+4)}Z^{(2-3)}$

The combined expression can then be simplified to

$3X^5Y^1Z^{-1} = \frac{3X^5Y}{Z}$

Report an Error

Example Question #1 : How To Simplify A Fraction

Simplify the expression

$\left(\frac{A^{\frac{3}{2}}\sqrt{B}}{C^{-\frac{1}{2}}}\right)\left(\frac{B^{-\frac{1}{2}}}{2\sqrt{AC}}\right)$ .

Possible Answers:

2A^2

$\frac{A^2}{2}$

$\frac{A}{2}$

A^2

Correct answer:

$\frac{A}{2}$

Explanation:

The expression can be rewritten as

$\left(\frac{A^{\frac{3}{2}}B^\frac{1}{2}}{C^{-\frac{1}{2}}}\right)\left(\frac{B^{-\frac{1}{2}}}{2A^\frac{1}{2}C^\frac{1}{2}}\right)$

We can now move the variables to the numerator and combine alike variables

$(A^\frac{3}{2}B^\frac{1}{2}C^\frac{1}{2})\left(\frac{A^{-\frac{1}{2}}B^{-\frac{1}{2}}C^{-\frac{1}{2}}}{2}\right) = \frac{A^{(\frac{3}{2}-\frac{1}{2})}B^{(\frac{1}{2}-\frac{1}{2})}C^{(\frac{1}{2}-\frac{1}{2})}}{2}$

This becomes

$\frac{A^{\frac{2}{2}}B^0C^0}{2} = \frac{A^1}{2} = \frac{A}{2}$

Report an Error

Example Question #51 : Algebraic Fractions

Simplify the expression

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

Possible Answers:

Cannot be simplified

a+b

a^2 + b^2

$\frac{a}{b}-\frac{b}{a}$

Correct answer:

a+b

Explanation:

The numerator of this expression can be factored, giving the expression

$\frac{(a+b)(a-b)}{(a-b)}$

The (a-b) will cancel itself out leaving,

$\frac{a+b\cdot1}{1} = a+b$

Report an Error

Example Question #2 : How To Simplify A Fraction

Simplify the expression

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

Possible Answers:

x^2 - 3

x +3

x-3

x+6

Correct answer:

x-3

Explanation:

The expression can be factored to the expression

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

The $\small (x+3)$ in the numerator and denominator will then cancel each other out to give,

$\small \frac{(x-3)\cdot1}{1} = x -3$

Report an Error

← Previous 1 2 3 Next →

View PSAT Mathematics Tutors

Shakeel
Certified Tutor

View PSAT Mathematics Tutors

Joseph
Certified Tutor

CUNY College of Staten Island, Bachelor in Arts, Applied Psychology. New York University, Master of Arts, Applied Psychology.

View PSAT Mathematics Tutors

Swagatika
Certified Tutor

Regional Institute of Education Bhubaneswar, Bachelor of Economics, Mathematics.

All PSAT Math Resources

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

Popular Subjects

Computer Science Tutors in Boston, Statistics Tutors in Denver, Biology Tutors in Phoenix, Algebra Tutors in San Francisco-Bay Area, GMAT Tutors in Los Angeles, Biology Tutors in Denver, Computer Science Tutors in New York City, GMAT Tutors in Phoenix, Computer Science Tutors in Denver, GMAT Tutors in Boston

Popular Courses & Classes

GMAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Dallas Fort Worth, SSAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Boston, GMAT Courses & Classes in Dallas Fort Worth, GMAT Courses & Classes in Houston, ACT Courses & Classes in Chicago, GMAT Courses & Classes in Washington DC, LSAT Courses & Classes in San Diego, MCAT Courses & Classes in Dallas Fort Worth

Popular Test Prep

GMAT Test Prep in Philadelphia, LSAT Test Prep in Chicago, SSAT Test Prep in New York City, SAT Test Prep in Houston, GMAT Test Prep in Houston, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Denver, SAT Test Prep in Denver, LSAT Test Prep in Atlanta, GRE Test Prep in San Diego

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 #1 : Algebraic Fractions

Example Question #1 : Algebraic Fractions

Example Question #1 : Algebraic Fractions

Example Question #1 : How To Simplify A Fraction

Example Question #2 : How To Simplify A Fraction

Example Question #3 : How To Simplify A Fraction

Example Question #4 : How To Simplify A Fraction

Example Question #1 : How To Simplify A Fraction

Example Question #51 : Algebraic Fractions

Example Question #2 : How To Simplify A Fraction

All PSAT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: