Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Middle Level Math : Operations

Study concepts, example questions & explanations for ISEE Middle Level Math

Create An Account

All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : How To Divide Variables

Gina can chop 2 carrots in a minute. Bob can chop 3 carrots in a minute. How long (in minutes) will it take them to chop 60 carrots, if they work together?

Possible Answers:

$\frac{1}{5}$

Correct answer:

Explanation:

Given that Gina can chop 2 carrots in a minute, and that Bob can chop 3 carrots in a minute, they will be able to chop 5 carrots in a minute if they work together.

If there are 60 carrots, it will take 12 minutes for them to chop up all the carrots, because 60 divided by 5 is 12.

Therefore, 12 is the correct answer.

Report an Error

Example Question #14 : How To Divide Variables

Which of the following numbers is divisible by 60?

Possible Answers:

3,600

3,500

3,700

3,606

Correct answer:

3,600

Explanation:

Given that 36 is divisible by 6, it follows that 360 would be divisble by 60 (as both numbers are multiplied by 10). A multiple of 360, such as 3,600 would also be divisible by 60.

Given that none of the other answer choices listed are divisble by 60, the correct answer is 3,600.

Report an Error

Example Question #93 : Algebraic Concepts

Simplify the following expression:

$\frac{6x5y2z}{3x}$

Possible Answers:

$\frac{2*5yz}{x}$

20yz

The expression is already reduced.

10y

2x5y2z

Correct answer:

20yz

Explanation:

When dividing by variables you must deal with the like variables first.

Since there are variables on the numerator and denominator, you would divide them together.

The constants will divide regularly and the variables will cancel out

$\frac{6x}{3x}=2$ .

The other variables are left alone so the final answer will just be

2*5y*2z=20yz .

Report an Error

Example Question #93 : Variables

Simplify the following expression:

$\frac{t^4x^5p^{26}}{t^2x^4p^{20}}$

Possible Answers:

$t^2x^{10}p^6$

t^2xp^6

$\frac{1}{t^2xp^6}$

tx^3p^6

Correct answer:

t^2xp^6

Explanation:

Simplify the following expression:

$\frac{t^4x^5p^{26}}{t^2x^4p^{20}}$

When we are dividing variables, we can simpligy by subtracting the exponent of the variable on bottom from the variable on the top.

So because t has an exponent of 4 on top and 2 on the bottom, the new exponent will be:

$t^4-t^2=t^{4-2}=t^2$

Do the same for our other two exponents (x and p) to get the following

$\frac{t^4x^5p^{26}}{t^2x^4p^{20}}=t^2xp^6$

Making our answer:

t^2xp^6

Report an Error

Example Question #93 : Algebraic Concepts

Reduce the expression:

$\frac{4x^{3}y^{2}}{2x}$

Possible Answers:

$2y^{2}$

$2x^{2}y^{2}$

Cannot be reduced

$y^{5}$

Correct answer:

$2x^{2}y^{2}$

Explanation:

For this division problem, you must deal with the like terms.

You will divide the constants and then divide the variables.

$4\div2=2$

and then

$x^{3}\div x=x^{2}$

because when dividing exponents with common bases, you just subtract the exponents.

The variable remains unchanged and your answer is,

$2x^{2}y^{2}$ .

Report an Error

Example Question #94 : Algebraic Concepts

$7^{4} \div (18-11) =$

Possible Answers:

343

Correct answer:

343

Explanation:

To solve

$7^{4} \div (18-11) =$

First, use the order of operations.

$7^{4} \div 7 =$

When dividing with variables and the coefficients are the same, subtract the exponents.

$7^{4} \div 7^{1} = 7^{4-1}$

$7^{4-1} = 7^{3}$ $7^{3} = 7\times 7\times 7 = 343$

Report an Error

Example Question #21 : How To Divide Variables

$\frac{x^{8}}{x^{2}}$

Possible Answers:

$x^{10}$

$x^{6}$

$x^{\frac{1}{4}}$

$x^{4}$

Correct answer:

$x^{6}$

Explanation:

To solve, subtract the exponents

$\frac{x^{8}}{x^{2}} = x^{8-2}$

$x^{6}$

Report an Error

Example Question #91 : Operations

$\frac{n^{3}}{n^{6}}$

Possible Answers:

$\frac{1}{n^{3}}$

$n^{\frac{1}{2}}$

$n^{9}$

$n^{3}$

Correct answer:

$\frac{1}{n^{3}}$

Explanation:

To solve $\frac{n^{3}}{n^{6}}$ subtract the exponents

$n^{3-6} = n^{-3}$

$n^{-3} = n\div -3 =$

$\frac{1}{n^{3}}$

Report an Error

Example Question #97 : Algebraic Concepts

The area (A) of a rectangle is $36ab^{3}$ square units. The length is 6ab units. What is the width of this rectangle?

Possible Answers:

$6b^{2$ units

$216ab^{2}$ units

$6a^{2}b^{2}$ units

$216a^{2}b^{4}$ units

Correct answer:

$6b^{2$ units

Explanation:

The formula for the Area of a rectangle is:

A - length x width

Is this problem, you are given the amount of total area or A, which is $36ab^{3}$ square units, and you are given the measurement of the length, which is 6ab . In order to solve for the measurement of the width, divide. When dividing, exponents are subtracted.

$36\div6 =6$

$\frac{a^{1}}{a^{1}} = a^{1-1} = a^{0} = 1$

$\frac{b^{3}}{b^{1}} = b^{3-1} = b^{2}$

$6 (1) \times b^{2} = 6b^{2}$ units

Report an Error

Example Question #96 : Algebraic Concepts

$\frac{9x^{4}y^{6}}{3x^{2}y^{2}} =$

Possible Answers:

$6x^{2}y^{4}$ $3x^{2}y^{3}$

$6x^{8}y^{12}$

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

Correct answer:

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

Explanation:

To solve $\frac{9x^{4}y^{6}}{3x^{2}y^{2}}$ separate each part of the terms and divide. When dividing variables with exponents, subtract the exponents.

$9\div 3 = 3$

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

$\frac{y^{6}}{y^{2}}=y^{6-2} =y^{4}$

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

Report an Error

View Tutors

Magda
Certified Tutor

Heritage College, Bachelor of Science, Education.

View Tutors

Claire
Certified Tutor

Augustana College, Bachelor of Fine Arts, Music Teacher Education.

View Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in San Francisco-Bay Area, GRE Tutors in Chicago, ACT Tutors in Dallas Fort Worth, Computer Science Tutors in Phoenix, Algebra Tutors in Dallas Fort Worth, Math Tutors in Denver, French Tutors in Atlanta, Computer Science Tutors in Atlanta, MCAT Tutors in Denver, SSAT Tutors in San Diego

Popular Courses & Classes

ACT Courses & Classes in Atlanta, LSAT Courses & Classes in Phoenix, SAT Courses & Classes in Washington DC, MCAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Atlanta, ACT Courses & Classes in San Diego, LSAT Courses & Classes in Miami, LSAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Houston, LSAT Courses & Classes in Denver

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, ISEE Test Prep in Seattle, MCAT Test Prep in Seattle, ISEE Test Prep in New York City, GMAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Boston, MCAT Test Prep in Dallas Fort Worth, SSAT Test Prep in Philadelphia, ACT Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area

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

ISEE Middle Level Math : Operations

Study concepts, example questions & explanations for ISEE Middle Level Math

All ISEE Middle Level Math Resources

Example Questions

Example Question #13 : How To Divide Variables

Example Question #14 : How To Divide Variables

Example Question #93 : Algebraic Concepts

Example Question #93 : Variables

Example Question #93 : Algebraic Concepts

Example Question #94 : Algebraic Concepts

Example Question #21 : How To Divide Variables

Example Question #91 : Operations

Example Question #97 : Algebraic Concepts

Example Question #96 : Algebraic Concepts

All ISEE Middle Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: