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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

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

Example Questions

Example Question #81 : Ratio And Proportion

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 800 cars in the parking lot and $80\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

360

460

630

640

Correct answer:

640

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $80\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$80:100\rightarrow\frac{80}{100}$

Reduce.

$\frac{80}{100}\rightarrow \frac{8}{10}\rightarrow \frac{4}{5}$

We know that there are 800 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:800\rightarrow \frac{Red}{800}$

Now, we can create a proportion using our two ratios.

$\frac{4}{5}=\frac{Red}{800}$

Cross multiply and solve for Red .

$5 \times Red=4\times800$

Simplify.

5 Red=3200

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{3200}{5}$

Solve.

Red=640

There are 640 red cars in the parking lot.

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Example Question #111 : Ratio And Proportion

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 3200 cars in the parking lot and $8\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

182

218

256

188

800

Correct answer:

256

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $8\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$8:100\rightarrow\frac{8}{100}$

Reduce.

$\frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$

We know that there are 3200 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:3200\rightarrow \frac{Red}{3200}$

Now, we can create a proportion using our two ratios.

$\frac{2}{25}=\frac{Red}{3200}$

Cross multiply and solve for Red .

$25 \times Red=2\times3200$

Simplify.

25 Red=6400

Divide both sides of the equation by .

$\frac{25Red}{25}=\frac{6400}{25}$

Solve.

Red=256

There are 256 red cars in the parking lot.

Report an Error

Example Question #1 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $98\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$7 \tfrac{5}{6} \ feet$

$9 \tfrac{1}{6} \ feet$

$9 \tfrac{5}{6} \ feet$

$8 \tfrac{1}{6} \ feet$

$8 \tfrac{5}{6} \ feet$

Correct answer:

$8 \tfrac{1}{6} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $98\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$98\ inches:x\ feet\rightarrow \frac{98\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{98\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=98\ inches \times (1\ foot)$

Simplify.

12x=98

Divide both sides by .

$\frac{12x}{12}=\frac{98}{12}$

Solve.

$x=8 \tfrac{2}{12} \ feet$

Reduce.

$x=8 \tfrac{1}{6} \ feet$

The carpenter needs $8 \tfrac{1}{6} \ feet$ of material.

Report an Error

Example Question #2 : Solving Word Problems With One Unit Conversions

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $124\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$10 \tfrac{1}{3} \ feet$

$10 \tfrac{3}{5} \ feet$

$9 \tfrac{2}{3} \ feet$

$11 \tfrac{1}{3} \ feet$

$10 \tfrac{2}{3} \ feet$

Correct answer:

$10 \tfrac{1}{3} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $124\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$124\ inches:x\ feet\rightarrow \frac{124\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{124\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=124\ inches \times (1\ foot)$

Simplify.

12x=124

Divide both sides by .

$\frac{12x}{12}=\frac{124}{12}$

Solve.

$x=10 \tfrac{4}{12} \ feet$

Reduce.

$x=10 \tfrac{1}{3} \ feet$

The carpenter needs $10 \tfrac{1}{3} \ feet$ of material.

Report an Error

Example Question #2101 : Psat Mathematics

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $39\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

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

$3 \tfrac{2}{5} \ feet$

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

$3 \tfrac{3}{4} \ feet$

$3 \tfrac{1}{4} \ feet$

Correct answer:

$3 \tfrac{1}{4} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $39\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$39\ inches:x\ feet\rightarrow \frac{39\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{39\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=39\ inches \times (1\ foot)$

Simplify.

12x=39

Divide both sides by .

$\frac{12x}{12}=\frac{39}{12}$

Solve.

$x=3 \tfrac{3}{12} \ feet$

Reduce.

$x=3 \tfrac{1}{4} \ feet$

The carpenter needs $3 \tfrac{1}{4} \ feet$ of material.

Report an Error

Example Question #2102 : Psat Mathematics

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $87\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$7 \tfrac{2}{5} \ feet$

$8 \tfrac{1}{5} \ feet$

$7 \tfrac{1}{4} \ feet$

$6 \tfrac{3}{4} \ feet$

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

Correct answer:

$7 \tfrac{1}{4} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $87\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$87\ inches:x\ feet\rightarrow \frac{87\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{87\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=87\ inches \times (1\ foot)$

Simplify.

12x=87

Divide both sides by .

$\frac{12x}{12}=\frac{87}{12}$

Solve.

$x=7 \tfrac{3}{12} \ feet$

Reduce.

$x=7 \tfrac{1}{4} \ feet$

The carpenter needs $7 \tfrac{1}{4} \ feet$ of material.

Report an Error

Example Question #2103 : Psat Mathematics

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $144\ inches$ of the moulding for the house. How many additional feet of the material will he need to purchase to finish the model?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $144\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$144\ inches:x\ feet\rightarrow \frac{144\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{144\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=144\ inches \times (1\ foot)$

Simplify.

12x=144

Divide both sides by .

$\frac{12x}{12}=\frac{144}{12}$

Solve.

$x=12 \ feet$

The carpenter needs $12 \ feet$ of material. Since he already has 8 feet he will need to purchase more to finish the project.

Report an Error

Example Question #2104 : Psat Mathematics

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $164\ inches$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$13 \tfrac{1}{3} \ feet$

$11 \tfrac{2}{3} \ feet$

$12 \tfrac{1}{3} \ feet$

$13 \tfrac{2}{3} \ feet$

$13 \tfrac{1}{5} \ feet$

Correct answer:

$13 \tfrac{2}{3} \ feet$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $164\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$164\ inches:x\ feet\rightarrow \frac{164\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{164\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=164\ inches \times (1\ foot)$

Simplify.

12x=164

Divide both sides by .

$\frac{12x}{12}=\frac{164}{12}$

Solve.

$x=13 \tfrac{8}{12} \ feet$

Reduce.

$x=13 \tfrac{2}{3} \ feet$

The carpenter needs $13 \tfrac{2}{3} \ feet$ of material.

Report an Error

Example Question #1 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown molding to use as accent pieces. He needs $18\textup{ inches}$ of the molding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$1 \tfrac{1}{2} \textup{ feet}$

$3 \tfrac{1}{2} \textup{ feet}$

$2 \tfrac{1}{2} \textup{ feet}$

$2 \tfrac{3}{4} \textup{ feet}$

$1 \tfrac{2}{3} \textup{ feet}$

Correct answer:

$1 \tfrac{1}{2} \textup{ feet}$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $18\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$18\ inches:x\ feet\rightarrow \frac{18\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{18\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=18\ inches \times (1\ foot)$

Simplify.

12x=18

Divide both sides by .

$\frac{12x}{12}=\frac{18}{12}$

Solve.

$x=1 \tfrac{1}{2} \ feet$

The carpenter needs $1 \tfrac{1}{2} \ feet$ of material.

Report an Error

Example Question #2 : Solving Word Problems With One Unit Conversion

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown moulding to use as accent pieces. He needs $9\textup{ inches}$ of the moulding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$\frac {1}{2} \textup{ feet}$

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

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

$\frac {1}{4} \textup{ feet}$

$\frac {3}{4} \textup{ feet}$

Correct answer:

$\frac {3}{4} \textup{ feet}$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $9 \ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$9\ inches:x\ feet\rightarrow \frac{9\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{9\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=9\ inches \times (1\ foot)$

Simplify.

12x=9

Divide both sides by .

$\frac{12x}{12}=\frac{9}{12}$

Solve.

$x=\frac{9}{12} \ feet$

Reduce.

$x=\frac{3}{4} \ feet$

The carpenter needs $\frac {3}{4} \ feet$ of material.

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 #81 : Ratio And Proportion

Example Question #111 : Ratio And Proportion

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #2 : Solving Word Problems With One Unit Conversions

Example Question #2101 : Psat Mathematics

Example Question #2102 : Psat Mathematics

Example Question #2103 : Psat Mathematics

Example Question #2104 : Psat Mathematics

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #2 : Solving Word Problems With One Unit Conversion

All Common Core: 6th Grade Math Resources

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