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Common Core: 6th Grade Math : Ratios & Proportional Relationships

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

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All Common Core: 6th Grade Math Resources

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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:

282 $\displaystyle 282$

155 $\displaystyle 155$

132 $\displaystyle 132$

160 $\displaystyle 160$

128 $\displaystyle 128$

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 $\displaystyle 410$

$\displaystyle 5$

335 $\displaystyle 335$

$\displaystyle 64$

$\displaystyle 75$

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 #2 : Ratios & Proportional Relationships

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 $\displaystyle 100$

180 $\displaystyle 180$

$\displaystyle 90$

$\displaystyle 99$

190 $\displaystyle 190$

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 #3 : Ratios & Proportional Relationships

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:

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

237 $\displaystyle 237$

123 $\displaystyle 123$

255 $\displaystyle 255$

$\displaystyle 6$

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 #1 : Ratios & Proportional Relationships

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:

310 $\displaystyle 310$

302 $\displaystyle 302$

150 $\displaystyle 150$

$\displaystyle 75$

160 $\displaystyle 160$

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 #4 : Ratios & Proportional Relationships

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 $\displaystyle 500$

357 $\displaystyle 357$

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

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

525 $\displaystyle 525$

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 #5 : 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 $\displaystyle 135$

155 $\displaystyle 155$

185 $\displaystyle 185$

$\displaystyle 42$

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 #6 : Ratios & Proportional Relationships

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:

$\displaystyle 68$

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

125 $\displaystyle 125$

$\displaystyle 42$

$\displaystyle 39$

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 #7 : Ratios & Proportional Relationships

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:

129 $\displaystyle 129$

216 $\displaystyle 216$

169 $\displaystyle 169$

219 $\displaystyle 219$

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

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

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Common Core: 6th Grade Math : Ratios & Proportional Relationships

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 #2 : Ratios & Proportional Relationships

Example Question #3 : Ratios & Proportional Relationships

Example Question #1 : Ratios & Proportional Relationships

Example Question #4 : Ratios & Proportional Relationships

Example Question #5 : Ratios & Proportional Relationships

Example Question #6 : Ratios & Proportional Relationships

Example Question #7 : Ratios & Proportional Relationships

All Common Core: 6th Grade Math Resources

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