We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

Create An Account Create Tests & Flashcards

All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 … 54 55 Next →

Example Question #1 :The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{5}\ miles$ in length and occupies an area of $\frac{7}{8}\ miles^2$ . How wide is this particular site?

Possible Answers:

$4\tfrac{5}{8}\ miles$

$4\tfrac{1}{8}\ miles$

$3\tfrac{3}{8}\ miles$

$4\tfrac{3}{8}\ miles$

$6\tfrac{3}{8}\ miles$

Correct answer:

$4\tfrac{3}{8}\ miles$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{7}{8}\ miles^2=\frac{1}{5}\ miles\times Width$

Divide both sides by $\frac{1}{5}\ miles$

$\frac{\frac{7}{8}\ miles^2}{\frac{1}{5}\ miles}=\frac{\frac{1}{5}\ miles \times Width}{\frac{1}{5}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{5}\ miles$

$\frac{1}{5}\ miles\rightarrow \frac{5}{1}\ miles$

Simplify and rewrite.

$Width=\frac{5}{1} \times \frac{7}{8}$

Multiply and solve.

$Width=\frac{35}{8}$

Reduce.

$Width=4\tfrac{3}{8}\ miles$

The width of the fracking site is $4\tfrac{3}{8}\ miles$

Report an Error

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{4}\ miles$ in length and occupies an area of $\frac{7}{9}\ miles^2$ . How wide is this particular site?

Possible Answers:

$3\tfrac{5}{9}\ miles$

$3\tfrac{1}{9}\ miles$

$9\tfrac{5}{9}\ miles$

$5\tfrac{1}{3}\ miles$

$9\tfrac{1}{3}\ miles$

Correct answer:

$3\tfrac{1}{9}\ miles$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{7}{9}\ miles^2=\frac{1}{4}\ miles\times Width$

Divide both sides by $\frac{1}{4}\ miles$

$\frac{\frac{7}{9}\ miles^2}{\frac{1}{4}\ miles}=\frac{\frac{1}{4}\ miles \times Width}{\frac{1}{4}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{4}\ miles$

$\frac{1}{4}\ miles\rightarrow \frac{4}{1}\ miles$

Simplify and rewrite.

$Width=\frac{4}{1} \times \frac{7}{9}$

Multiply and solve.

$Width=\frac{28}{9}$

Reduce.

$Width=3\tfrac{1}{9}\ miles$

The width of the fracking site is $3\tfrac{1}{9}\ miles$

Report an Error

Example Question #3 :The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{4}\ miles$ in length and occupies an area of $\frac{7}{8}\ miles^2$ . How wide is this particular site?

Possible Answers:

$3\tfrac{1}{3}\ miles$

$2\tfrac{1}{3}\ miles$

$2\tfrac{2}{3}\ miles$

$3\tfrac{1}{2}\ miles$

$3\tfrac{2}{3}\ miles$

Correct answer:

$3\tfrac{1}{2}\ miles$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{7}{8}\ miles^2=\frac{1}{4}\ miles\times Width$

Divide both sides by $\frac{1}{4}\ miles$

$\frac{\frac{7}{8}\ miles^2}{\frac{1}{4}\ miles}=\frac{\frac{1}{4}\ miles \times Width}{\frac{1}{4}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{4}\ miles$

$\frac{1}{4}\ miles\rightarrow \frac{4}{1}\ miles$

Simplify and rewrite.

$Width=\frac{4}{1} \times \frac{7}{8}$

Multiply and solve.

$Width=\frac{28}{8}$

Reduce.

$Width=3\tfrac{1}{2}\ miles$

The width of the fracking site is $3\tfrac{1}{2}\ miles$

Report an Error

Example Question #4 :The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{5}\ miles$ in length and occupies an area of $\frac{35}{41}\ miles^2$ . How wide is this particular site?

Possible Answers:

$5\tfrac{11}{41}\ miles$

$2\tfrac{11}{41}\ miles$

$4\tfrac{11}{41}\ miles$

$4\tfrac{21}{41}\ miles$

$11\tfrac{4}{41}\ miles$

Correct answer:

$4\tfrac{11}{41}\ miles$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{35}{41}\ miles^2=\frac{1}{5}\ miles\times Width$

Divide both sides by $\frac{1}{5}\ miles$

$\frac{\frac{35}{41}\ miles^2}{\frac{1}{5}\ miles}=\frac{\frac{1}{5}\ miles \times Width}{\frac{1}{5}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{5}\ miles$

$\frac{1}{5}\ miles\rightarrow \frac{5}{1}\ miles$

Simplify and rewrite.

$Width=\frac{5}{1} \times \frac{35}{41}$

Multiply and solve.

$Width=\frac{175}{41}$

Reduce.

$Width=4\tfrac{11}{41}\ miles$

The width of the fracking site is $4\tfrac{11}{41}\ miles$

Report an Error

Example Question #5 :The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collect pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{3}{4}\textup{ miles}$ in length and occupies an area of $\frac{1}{2}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{2}{3}\textup{ miles}$

$\frac{1}{3}\textup{ miles}$

$\frac{3}{5}\textup{ miles}$

$\frac{6}{7}\textup{ miles}$

$\frac{2}{5}\textup{ miles}$

Correct answer:

$\frac{2}{3}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{1}{2}\ miles^2=\frac{3}{4}\ miles\times Width$

Divide both sides by $\frac{3}{4}\ miles$

$\frac{\frac{1}{2}\ miles^2}{\frac{3}{4}\ miles}=\frac{\frac{3}{4}\ miles \times Width}{\frac{3}{4}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{3}{4}\ miles$

$\frac{3}{4}\ miles\rightarrow \frac{4}{3}\ miles$

Simplify and rewrite.

$Width=\frac{4}{3} \times \frac{1}{2}$

Multiply and solve.

$Width=\frac{4}{6}$

Reduce.

$Width=\frac{2}{3}\ miles$

The width of the fracking site is $\frac{2}{3}\ miles$

Report an Error

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{7}\textup{ miles}$ in length and occupies an area of $\frac{3}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$4\textup{ miles}$

$4\tfrac{2}{5}\textup{ miles}$

$4\tfrac{4}{5}\textup{ miles}$

$4\tfrac{1}{5}\textup{ miles}$

$4\tfrac{3}{5}\textup{ miles}$

Correct answer:

$4\tfrac{1}{5}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{3}{5}\ miles^2=\frac{1}{7}\ miles\times Width$

Divide both sides by $\frac{1}{7}\ miles$

$\frac{\frac{3}{5}\ miles^2}{\frac{1}{7}\ miles}=\frac{\frac{1}{7}\ miles \times Width}{\frac{1}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{7}\ miles$

$\frac{1}{7}\ miles\rightarrow \frac{7}{1}\ miles$

Simplify and rewrite.

$Width=\frac{7}{1} \times \frac{3}{5}$

Multiply and solve.

$Width=\frac{21}{5}$

Reduce.

$Width=4\tfrac{1}{5}\ miles$

The width of the fracking site is $4\tfrac{1}{5}\ miles$

Report an Error

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{2}{7}\textup{ miles}$ in length and occupies an area of $\frac{2}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{3}{5}\textup{ miles}$

$1\tfrac{3}{5}\textup{ miles}$

$1\tfrac{5}{7}\textup{ miles}$

$1\tfrac{2}{5}\textup{ miles}$

$2\tfrac{3}{5}\textup{ miles}$

Correct answer:

$1\tfrac{2}{5}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{2}{5}\ miles^2=\frac{2}{7}\ miles\times Width$

Divide both sides by $\frac{2}{7}\ miles$

$\frac{\frac{2}{5}\ miles^2}{\frac{2}{7}\ miles}=\frac{\frac{2}{7}\ miles \times Width}{\frac{2}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{2}{7}\ miles$

$\frac{2}{7}\ miles\rightarrow \frac{7}{2}\ miles$

Simplify and rewrite.

$Width=\frac{7}{2} \times \frac{2}{5}$

Multiply and solve.

$Width=\frac{14}{10}$

Reduce.

$Width=1\tfrac{2}{5}\ miles$

The width of the fracking site is $1\tfrac{2}{5}\ miles$

Report an Error

Example Question #1 :The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{5}{7}\textup{ miles}$ in length and occupies an area of $\frac{3}{5}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$\frac{24}{25}\textup{ miles}$

$\frac{21}{25}\textup{ miles}$

$\frac{21}{27}\textup{ miles}$

$\frac{31}{35}\textup{ miles}$

$\frac{11}{15}\textup{ miles}$

Correct answer:

$\frac{21}{25}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{3}{5}\ miles^2=\frac{5}{7}\ miles\times Width$

Divide both sides by $\frac{5}{7}\ miles$

$\frac{\frac{3}{5}\ miles^2}{\frac{5}{7}\ miles}=\frac{\frac{5}{7}\ miles \times Width}{\frac{5}{7}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{5}{7}\ miles$

$\frac{5}{7}\ miles\rightarrow \frac{7}{5}\ miles$

Simplify and rewrite.

$Width=\frac{7}{5} \times \frac{3}{5}$

Multiply and solve.

$Width=\frac{21}{25}$

The width of the fracking site is $\frac{21}{25}\ miles$

Report an Error

Example Question #1 :The Number System

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{8}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$3\tfrac{1}{3}\textup{ miles}$

$4\tfrac{1}{4}\textup{ miles}$

$5\tfrac{3}{4}\textup{ miles}$

$3\tfrac{5}{7}\textup{ miles}$

$3\tfrac{3}{4}\textup{ miles}$

Correct answer:

$3\tfrac{3}{4}\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{8}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{8}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{8}$

Multiply and solve.

$Width=\frac{30}{8}$

Reduce.

$Width=3\tfrac{3}{4}\ miles$

The width of the fracking site is $3\tfrac{3}{4}\ miles$

Report an Error

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Hydraulic fracturing is a process used by gas companies to rupture and collects pockets of gas trapped within pockets of shale rock. A particular shale fracking site is $\frac{1}{6}\textup{ miles}$ in length and occupies an area of $\frac{5}{6}\textup{ miles}^2$ . How wide is this particular site?

Possible Answers:

$5\tfrac{3}{5}\textup{ miles}$

$5\tfrac{1}{5}\textup{ miles}$

$4\textup{ miles}$

$5\tfrac{2}{5}\textup{ miles}$

$5\textup{ miles}$

Correct answer:

$5\textup{ miles}$

Explanation:

In order to solve this question, we need to first recall how to find the area of a rectangle.

$\text{Area}=\text{Length} \times \text{Width}$

Substitute in the given values in the equation and solve for $\text{Width}$ .

$\frac{5}{6}\ miles^2=\frac{1}{6}\ miles\times Width$

Divide both sides by $\frac{1}{6}\ miles$

$\frac{\frac{5}{6}\ miles^2}{\frac{1}{6}\ miles}=\frac{\frac{1}{6}\ miles \times Width}{\frac{1}{6}\ miles}$

Dividing by a fraction is the same as multiplying by its inverse or reciprocal.

Find the reciprocal of $\frac{1}{6}\ miles$

$\frac{1}{6}\ miles\rightarrow \frac{6}{1}\ miles$

Simplify and rewrite.

$Width=\frac{6}{1} \times \frac{5}{6}$

Multiply and solve.

$Width=\frac{30}{6}$

Reduce.

$Width=5\ miles$

The width of the fracking site is $5\ miles$

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 … 54 55 Next →

View Tutors

Yasmin
Certified Tutor

Saint Thomas University, Bachelors, Education. American Career College of Education, Masters, Curriculum and Instruction.

View Tutors

Sherry
Certified Tutor

St. John's University, Bachelor in Arts, Psychology. St. John's University, Master of Arts, Psychology.

View Tutors

Joscelyn
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Industrial Engineering.

All Common Core: 6th Grade Math Resources

6 Diagnostic Tests 186 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

MCAT Tutors in Washington DC,Physics Tutors in Denver,Computer Science Tutors in New York City,Calculus Tutors in Denver,Reading Tutors in Chicago,Statistics Tutors in Seattle,French Tutors in Philadelphia,Spanish Tutors in Los Angeles,Calculus Tutors in Houston,Math Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in Los Angeles,Spanish Courses & Classes in Chicago,LSAT Courses & Classes in Seattle,ACT Courses & Classes in Los Angeles,SAT Courses & Classes in New York City,SAT Courses & Classes in Miami,ISEE Courses & Classes in Boston,GRE Courses & Classes in Seattle,LSAT Courses & Classes in Miami,LSAT Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in Philadelphia,ACT Test Prep in Los Angeles,MCAT Test Prep in Phoenix,GMAT Test Prep in Chicago,SAT Test Prep in Seattle,SSAT Test Prep in San Diego,SSAT Test Prep in Dallas Fort Worth,MCAT Test Prep in Houston,LSAT Test Prep in Chicago,ACT 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.

哟ur 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:

哟u must include the following:

copyrigh的物理或电子签名t 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.

把你的投诉我们指定的代理:

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

Common Core: 6th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 6th Grade Math

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #1 :The Number System

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #3 :The Number System

Example Question #4 :The Number System

Example Question #5 :The Number System

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

Example Question #1 :The Number System

Example Question #1 :The Number System

Example Question #1 :Interpret And Compute Quotients Of Fractions: Ccss.Math.Content.6.Ns.A.1

All Common Core: 6th Grade Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Find the Best Tutors

Email address:
哟ur name:
Feedback: