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Common Core: 6th Grade Math : Grade 6

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

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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 vote for every votes that candidate B receives. At the end of the election candidate B has 320 votes. How many votes did candidate A get?

Possible Answers:

$106\tfrac{2}{3}$

320

960

Correct answer:

$106\tfrac{2}{3}$

Explanation:

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

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

Now substitute in the given numbers.

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

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

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

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

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

Cross multiply and solve for .

3(A)=320(1)

Simplify.

3A=320

Divide both sides of the equation by .

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

Solve.

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

Report an Error

Example Question #1 : Ratios & Proportional Relationships

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

Possible Answers:

132

282

128

160

155

Correct answer:

128

Explanation:

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

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

Now substitute in the given numbers.

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

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

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

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

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

Cross multiply and solve for .

5(A)=320(2)

Simplify.

5A=640

Divide both sides of the equation by .

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

Solve.

A=128

Report an Error

Example Question #2 : Ratios & Proportional Relationships

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

Possible Answers:

335

410

Correct answer:

Explanation:

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

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

Now substitute in the given numbers.

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

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

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

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

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

Cross multiply and solve for .

5(A)=320(1)

Simplify.

5A=320

Divide both sides of the equation by .

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

Solve.

A=64

Report an Error

Example Question #2 : Ratios & Proportional Relationships

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

Possible Answers:

190

100

180

Correct answer:

180

Explanation:

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

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

Now substitute in the given numbers.

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

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

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

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

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

Cross multiply and solve for .

5(A)=300(3)

Simplify.

5A=900

Divide both sides of the equation by .

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

Solve.

A=180

Report an Error

Example Question #3 : Ratios & Proportional Relationships

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

Possible Answers:

255

237

$127\tfrac{1}{2}$

123

Correct answer:

$127\tfrac{1}{2}$

Explanation:

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

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

Now substitute in the given numbers.

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

Reduce.

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

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

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

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

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

Cross multiply and solve for .

2(A)=255(1)

Simplify.

2A=255

Divide both sides of the equation by .

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

Solve.

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

Report an Error

Example Question #4 : Ratios & Proportional Relationships

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

Possible Answers:

302

150

310

160

Correct answer:

150

Explanation:

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

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

Now substitute in the given numbers.

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

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

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

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

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

Cross multiply and solve for .

2(A)=300(1)

Simplify.

2A=300

Divide both sides of the equation by .

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

Solve.

A=150

Report an Error

Example Question #21 : Ratio And Proportion

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

Possible Answers:

500

357

$533\tfrac{1}{3}$

525

$325\tfrac{2}{3}$

Correct answer:

$533\tfrac{1}{3}$

Explanation:

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

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

Now substitute in the given numbers.

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

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

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

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

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

Cross multiply and solve for .

3(A)=320(5)

Simplify.

3A=1600

Divide both sides of the equation by .

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

Solve.

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

Report an Error

Example Question #2 : Understand The Concept Of A Ratio: Ccss.Math.Content.6.Rp.A.1

If candidate A receives votes for every vote that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Possible Answers:

137

135

185

155

Correct answer:

185

Explanation:

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

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

Now substitute in the given numbers.

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

We know that candidate B received votes. Write a new ratio.

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

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

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

Cross multiply and solve for .

1(A)=37(5)

Simplify and solve.

A=185

Report an Error

Example Question #7 : Ratios & Proportional Relationships

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Possible Answers:

125

$66\tfrac{1}{2}$

Correct answer:

$66\tfrac{1}{2}$

Explanation:

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

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

Now substitute in the given numbers.

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

We know that candidate B received votes. Write a new ratio.

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

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

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

Cross multiply and solve for .

4(A)=38(7)

Simplify.

4A=266

Divide both sides of the equation by .

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

Solve.

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

Report an Error

Example Question #4 : Ratios & Proportional Relationships

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has votes. How many votes did candidate A get?

Possible Answers:

216

169

219

$162\tfrac{5}{9}$

129

Correct answer:

$162\tfrac{5}{9}$

Explanation:

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

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

Now substitute in the given numbers.

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

We know that candidate B received votes. Write a new ratio.

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

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

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

Cross multiply and solve for .

9(A)=77(19)

Simplify.

9A=1463

Divide both sides of the equation by .

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

Solve.

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

Report an Error

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All Common Core: 6th Grade Math Resources

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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 #1 : Ratios & Proportional Relationships

Example Question #2 : Ratios & Proportional Relationships

Example Question #2 : Ratios & Proportional Relationships

Example Question #3 : Ratios & Proportional Relationships

Example Question #4 : Ratios & Proportional Relationships

Example Question #21 : Ratio And Proportion

Example Question #2 : Understand The Concept Of A Ratio: Ccss.Math.Content.6.Rp.A.1

Example Question #7 : Ratios & Proportional Relationships

Example Question #4 : Ratios & Proportional Relationships

All Common Core: 6th Grade Math Resources

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