Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: 6th Grade Math : Grade 6

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

Create An Account

All Common Core: 6th Grade Math Resources

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

Example Questions

Example Question #1 : Ratios & Proportional Relationships

If candidate A receives $\displaystyle 1$ vote for every $\displaystyle 3$ votes that candidate B receives. At the end of the election candidate B has 320 $\displaystyle 320$ votes. How many votes did candidate A get?

Possible Answers:

960 $\displaystyle 960$

$\displaystyle 3$

$\displaystyle 1$

$106\tfrac{2}{3}$ $\displaystyle 106\tfrac{2}{3}$

320 $\displaystyle 320$

Correct answer:

$106\tfrac{2}{3}$ $\displaystyle 106\tfrac{2}{3}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 1$ vote cast for candidate A, candidate B got $\displaystyle 3$ votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:3\rightarrow \frac{1}{3}$ $\displaystyle 1:3\rightarrow \frac{1}{3}$

We know that candidate B received 320 $\displaystyle 320$ votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$ $\displaystyle A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{3}=\frac{A}{320}$ $\displaystyle \frac{1}{3}=\frac{A}{320}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 3(A)=320(1)$

Simplify.

3A=320 $\displaystyle 3A=320$

Divide both sides of the equation by $\displaystyle 3$ .

$\frac{3A}{3}=\frac{320}{3}$ $\displaystyle \frac{3A}{3}=\frac{320}{3}$

Solve.

$A=106\tfrac{2}{3}$ $\displaystyle A=106\tfrac{2}{3}$

Report an Error

Example Question #2 : Ratios & Proportional Relationships

If candidate A receives $\displaystyle 2$ votes for every $\displaystyle 5$ votes that candidate B receives. At the end of the election candidate B has 320 $\displaystyle 320$ votes. How many votes did candidate A get?

Possible Answers:

128 $\displaystyle 128$

160 $\displaystyle 160$

132 $\displaystyle 132$

155 $\displaystyle 155$

282 $\displaystyle 282$

Correct answer:

128 $\displaystyle 128$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 2$ votes cast for candidate A, candidate B got $\displaystyle 5$ votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$2:5\rightarrow \frac{2}{5}$ $\displaystyle 2:5\rightarrow \frac{2}{5}$

We know that candidate B received 320 $\displaystyle 320$ votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$ $\displaystyle A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{2}{5}=\frac{A}{320}$ $\displaystyle \frac{2}{5}=\frac{A}{320}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 5(A)=320(2)$

Simplify.

5A=640 $\displaystyle 5A=640$

Divide both sides of the equation by $\displaystyle 5$ .

$\frac{5A}{5}=\frac{640}{5}$ $\displaystyle \frac{5A}{5}=\frac{640}{5}$

Solve.

A=128 $\displaystyle A=128$

Report an Error

Example Question #3 : Ratios & Proportional Relationships

If candidate A receives $\displaystyle 1$ vote for every $\displaystyle 5$ votes that candidate B receives. At the end of the election candidate B has 320 $\displaystyle 320$ votes. How many votes did candidate A get?

Possible Answers:

410 $\displaystyle 410$

$\displaystyle 75$

335 $\displaystyle 335$

$\displaystyle 5$

$\displaystyle 64$

Correct answer:

$\displaystyle 64$

Explanation:

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:5\rightarrow \frac{1}{5}$ $\displaystyle 1:5\rightarrow \frac{1}{5}$

We know that candidate B received 320 $\displaystyle 320$ votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$ $\displaystyle A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{5}=\frac{A}{320}$ $\displaystyle \frac{1}{5}=\frac{A}{320}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 5(A)=320(1)$

Simplify.

5A=320 $\displaystyle 5A=320$

Divide both sides of the equation by $\displaystyle 5$ .

$\frac{5A}{5}=\frac{320}{5}$ $\displaystyle \frac{5A}{5}=\frac{320}{5}$

Solve.

A=64 $\displaystyle A=64$

Report an Error

Example Question #4 : Grade 6

If candidate A receives $\displaystyle 3$ votes for every $\displaystyle 5$ votes that candidate B receives. At the end of the election candidate B has 300 $\displaystyle 300$ votes. How many votes did candidate A get?

Possible Answers:

100 $\displaystyle 100$

190 $\displaystyle 190$

$\displaystyle 99$

$\displaystyle 90$

180 $\displaystyle 180$

Correct answer:

180 $\displaystyle 180$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 3$ votes cast for candidate A, candidate B got $\displaystyle 5$ votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:5\rightarrow \frac{3}{5}$ $\displaystyle 3:5\rightarrow \frac{3}{5}$

We know that candidate B received 300 $\displaystyle 300$ votes. Write a new ratio.

$A:300\rightarrow\frac{A}{300}$ $\displaystyle A:300\rightarrow\frac{A}{300}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{3}{5}=\frac{A}{300}$ $\displaystyle \frac{3}{5}=\frac{A}{300}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 5(A)=300(3)$

Simplify.

5A=900 $\displaystyle 5A=900$

Divide both sides of the equation by $\displaystyle 5$ .

$\frac{5A}{5}=\frac{900}{5}$ $\displaystyle \frac{5A}{5}=\frac{900}{5}$

Solve.

A=180 $\displaystyle A=180$

Report an Error

Example Question #5 : Grade 6

If candidate A receives $\displaystyle 3$ votes for every $\displaystyle 6$ votes that candidate B receives. At the end of the election candidate B has 255 $\displaystyle 255$ votes. How many votes did candidate A get?

Possible Answers:

123 $\displaystyle 123$

$127\tfrac{1}{2}$ $\displaystyle 127\tfrac{1}{2}$

255 $\displaystyle 255$

$\displaystyle 6$

237 $\displaystyle 237$

Correct answer:

$127\tfrac{1}{2}$ $\displaystyle 127\tfrac{1}{2}$

Explanation:

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:6\rightarrow \frac{3}{6}$ $\displaystyle 3:6\rightarrow \frac{3}{6}$

Reduce.

$\frac{3}{6}=\frac{1}{2}$ $\displaystyle \frac{3}{6}=\frac{1}{2}$

We know that candidate B received 255 $\displaystyle 255$ votes. Write a new ratio.

$A:320\rightarrow\frac{A}{255}$ $\displaystyle A:320\rightarrow\frac{A}{255}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{2}=\frac{A}{255}$ $\displaystyle \frac{1}{2}=\frac{A}{255}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 2(A)=255(1)$

Simplify.

2A=255 $\displaystyle 2A=255$

Divide both sides of the equation by $\displaystyle 2$ .

$\frac{2A}{2}=\frac{255}{2}$ $\displaystyle \frac{2A}{2}=\frac{255}{2}$

Solve.

$A=127\tfrac{1}{2}$ $\displaystyle A=127\tfrac{1}{2}$

Report an Error

Example Question #2 : Grade 6

If candidate A receives $\displaystyle 1$ vote for every $\displaystyle 2$ votes that candidate B receives. At the end of the election candidate B has 300 $\displaystyle 300$ votes. How many votes did candidate A get?

Possible Answers:

160 $\displaystyle 160$

$\displaystyle 75$

310 $\displaystyle 310$

302 $\displaystyle 302$

150 $\displaystyle 150$

Correct answer:

150 $\displaystyle 150$

Explanation:

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:2\rightarrow \frac{1}{2}$ $\displaystyle 1:2\rightarrow \frac{1}{2}$

We know that candidate B received 300 $\displaystyle 300$ votes. Write a new ratio.

$A:300\rightarrow\frac{A}{300}$ $\displaystyle A:300\rightarrow\frac{A}{300}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{2}=\frac{A}{300}$ $\displaystyle \frac{1}{2}=\frac{A}{300}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 2(A)=300(1)$

Simplify.

2A=300 $\displaystyle 2A=300$

Divide both sides of the equation by $\displaystyle 2$ .

$\frac{2A}{2}=\frac{300}{2}$ $\displaystyle \frac{2A}{2}=\frac{300}{2}$

Solve.

A=150 $\displaystyle A=150$

Report an Error

Example Question #3 : Grade 6

If candidate A receives $\displaystyle 5$ votes for every $\displaystyle 3$ votes that candidate B receives. At the end of the election candidate B has 320 $\displaystyle 320$ votes. How many votes did candidate A get?

Possible Answers:

500 $\displaystyle 500$

525 $\displaystyle 525$

$533\tfrac{1}{3}$ $\displaystyle 533\tfrac{1}{3}$

$325\tfrac{2}{3}$ $\displaystyle 325\tfrac{2}{3}$

357 $\displaystyle 357$

Correct answer:

$533\tfrac{1}{3}$ $\displaystyle 533\tfrac{1}{3}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 5$ votes cast for candidate A, candidate B got $\displaystyle 3$ votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$5:3\rightarrow \frac{5}{3}$ $\displaystyle 5:3\rightarrow \frac{5}{3}$

We know that candidate B received 320 $\displaystyle 320$ votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$ $\displaystyle A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{5}{3}=\frac{A}{320}$ $\displaystyle \frac{5}{3}=\frac{A}{320}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 3(A)=320(5)$

Simplify.

3A=1600 $\displaystyle 3A=1600$

Divide both sides of the equation by $\displaystyle 3$ .

$\frac{3A}{3}=\frac{1600}{3}$ $\displaystyle \frac{3A}{3}=\frac{1600}{3}$

Solve.

$A=533\tfrac{1}{3}$ $\displaystyle A=533\tfrac{1}{3}$

Report an Error

Example Question #2 : Ratios & Proportional Relationships

If candidate A receives $\displaystyle 5$ votes for every $\displaystyle 1$ vote that candidate B receives. At the end of the election candidate B has $\displaystyle 37$ votes. How many votes did candidate A get?

Possible Answers:

137 $\displaystyle 137$

135 $\displaystyle 135$

185 $\displaystyle 185$

$\displaystyle 42$

155 $\displaystyle 155$

Correct answer:

185 $\displaystyle 185$

Explanation:

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$5:1\rightarrow \frac{5}{1}$ $\displaystyle 5:1\rightarrow \frac{5}{1}$

We know that candidate B received $\displaystyle 37$ votes. Write a new ratio.

$A:37\rightarrow\frac{A}{37}$ $\displaystyle A:37\rightarrow\frac{A}{37}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{5}{1}=\frac{A}{37}$ $\displaystyle \frac{5}{1}=\frac{A}{37}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 1(A)=37(5)$

Simplify and solve.

A=185 $\displaystyle A=185$

Report an Error

Example Question #9 : Grade 6

If candidate A receives $\displaystyle 7$ votes for every $\displaystyle 4$ votes that candidate B receives. At the end of the election candidate B has $\displaystyle 38$ votes. How many votes did candidate A get?

Possible Answers:

$\displaystyle 42$

$\displaystyle 68$

$66\tfrac{1}{2}$ $\displaystyle 66\tfrac{1}{2}$

$\displaystyle 39$

125 $\displaystyle 125$

Correct answer:

$66\tfrac{1}{2}$ $\displaystyle 66\tfrac{1}{2}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 7$ votes cast for candidate A, candidate B got $\displaystyle 4$ votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$7:4\rightarrow \frac{7}{4}$ $\displaystyle 7:4\rightarrow \frac{7}{4}$

We know that candidate B received $\displaystyle 38$ votes. Write a new ratio.

$A:38\rightarrow\frac{A}{38}$ $\displaystyle A:38\rightarrow\frac{A}{38}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{7}{4}=\frac{A}{38}$ $\displaystyle \frac{7}{4}=\frac{A}{38}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 4(A)=38(7)$

Simplify.

4A=266 $\displaystyle 4A=266$

Divide both sides of the equation by $\displaystyle 4$ .

$\frac{4A}{4}=\frac{266}{4}$ $\displaystyle \frac{4A}{4}=\frac{266}{4}$

Solve.

$A=66\tfrac{1}{2}$ $\displaystyle A=66\tfrac{1}{2}$

Report an Error

Example Question #31 : Ratio And Proportion

If candidate A receives $\displaystyle 19$ votes for every $\displaystyle 9$ votes that candidate B receives. At the end of the election candidate B has $\displaystyle 77$ votes. How many votes did candidate A get?

Possible Answers:

$162\tfrac{5}{9}$ $\displaystyle 162\tfrac{5}{9}$

169 $\displaystyle 169$

216 $\displaystyle 216$

129 $\displaystyle 129$

219 $\displaystyle 219$

Correct answer:

$162\tfrac{5}{9}$ $\displaystyle 162\tfrac{5}{9}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every $\displaystyle 19$ votes cast for candidate A, candidate B got $\displaystyle 9$ votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$ $\displaystyle A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$19:9\rightarrow \frac{19}{9}$ $\displaystyle 19:9\rightarrow \frac{19}{9}$

We know that candidate B received $\displaystyle 77$ votes. Write a new ratio.

$A:77\rightarrow\frac{A}{77}$ $\displaystyle A:77\rightarrow\frac{A}{77}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{19}{9}=\frac{A}{77}$ $\displaystyle \frac{19}{9}=\frac{A}{77}$

Cross multiply and solve for $\displaystyle A$ .

$\displaystyle 9(A)=77(19)$

Simplify.

9A=1463 $\displaystyle 9A=1463$

Divide both sides of the equation by $\displaystyle 9$ .

$\frac{9A}{9}=\frac{1463}{9}$ $\displaystyle \frac{9A}{9}=\frac{1463}{9}$

Solve.

$A=162\tfrac{5}{9}$ $\displaystyle A=162\tfrac{5}{9}$

Report an Error

View Tutors

Patrick
Certified Tutor

LeTourneau University, Bachelors, Electrical Engineering. LeTourneau University, Masters, Electrical Engineering.

View Tutors

Jamie
Certified Tutor

East Central University, Bachelors, Special Education.

View Tutors

Rainier
Certified Tutor

Norfolk State University, Bachelors, Physics.

All Common Core: 6th Grade Math Resources

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

Popular Subjects

Algebra Tutors in Los Angeles, SAT Tutors in Denver, Biology Tutors in Phoenix, MCAT Tutors in Denver, Algebra Tutors in Phoenix, Chemistry Tutors in Denver, Spanish Tutors in Miami, Physics Tutors in Chicago, LSAT Tutors in Boston, ISEE Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, LSAT Courses & Classes in San Diego, GRE Courses & Classes in Boston, ACT Courses & Classes in Washington DC, ACT Courses & Classes in San Diego, ACT Courses & Classes in Boston, GMAT Courses & Classes in Seattle, GRE Courses & Classes in Miami, ACT Courses & Classes in Phoenix, ACT Courses & Classes in Houston

Popular Test Prep

ACT Test Prep in Miami, LSAT Test Prep in Seattle, GMAT Test Prep in Seattle, ACT Test Prep in Boston, ACT Test Prep in Houston, MCAT Test Prep in Houston, SSAT Test Prep in Boston, MCAT Test Prep in Phoenix, ACT Test Prep in Phoenix, SSAT 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

Common Core: 6th Grade Math : Grade 6

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

All Common Core: 6th Grade Math Resources

Example Questions

Example Question #1 : Ratios & Proportional Relationships

Example Question #2 : Ratios & Proportional Relationships

Example Question #3 : Ratios & Proportional Relationships

Example Question #4 : Grade 6

Example Question #5 : Grade 6

Example Question #2 : Grade 6

Example Question #3 : Grade 6

Example Question #2 : Ratios & Proportional Relationships

Example Question #9 : Grade 6

Example Question #31 : Ratio And Proportion

All Common Core: 6th Grade Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: