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Common Core: 7th Grade Math : Ratios & Proportional Relationships

Study concepts, example questions & explanations for Common Core: 7th Grade Math

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All Common Core: 7th Grade Math Resources

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Example Questions

Example Question #61 : Ratios & Proportional Relationships

A landscaper can mow $\frac{1}{8}$ of a yard in $\frac{1}{8}$ of an hour. If he continues at this rate, how many yards can the landscaper mow per hour?

Possible Answers:

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

$1\frac{1}{8}\textup{ yards}$

$1\frac{3}{8}\textup{ yards}$

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

$1\textup{ yard}$

Correct answer:

$1\textup{ yard}$

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have yards, $\frac{1}{8}$ , divided by hours, $\frac{1}{8}$ :

$\frac{\ \frac{1}{8}\ \textup{of a yard}}{\ \frac{1}{8}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

$\frac{1}{8}\rightarrow \frac{8}{1}$

Therefore:

$\frac{1}{8}\times\frac{8}{1}=\frac{8}{8}=1$

The landscaper can mow yard per hour.

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Example Question #61 : Ratios & Proportional Relationships

A janitor can clean $\frac{1}{11}$ of a stadium in $\frac{1}{3}$ of an hour. If he continues this rate, how much of the stadium can he clean per hour?

Possible Answers:

$\frac{4}{11}\textup{ of the stadium}$

$\frac{3}{11}\textup{ of the stadium}$

$\frac{5}{11}\textup{ of the stadium}$

$\frac{2}{11}\textup{ of the stadium}$

$\frac{1}{11}\textup{ of the stadium}$

Correct answer:

$\frac{3}{11}\textup{ of the stadium}$

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of the stadium, $\frac{1}{11}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{11}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{11}\times\frac{3}{1}=\frac{3}{11}$

The janitor can clean $\frac{3}{11}$ of the stadium per hour.

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Example Question #62 : Ratios & Proportional Relationships

A janitor can clean $\frac{1}{10}$ of a stadium in $\frac{1}{3}$ of an hour. If he continues this rate, how much of the stadium can he clean per hour?

Possible Answers:

$\frac{2}{5}\textup{ of the stadium}$

$\frac{1}{5}\textup{ of the stadium}$

$\frac{1}{10}\textup{ of the stadium}$

$\frac{1}{2}\textup{ of the stadium}$

$\frac{3}{10}\textup{ of the stadium}$

Correct answer:

$\frac{3}{10}\textup{ of the stadium}$

Explanation:

$\frac{\ \frac{1}{10}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{10}\times\frac{3}{1}=\frac{3}{10}$

The janitor can clean $\frac{3}{10}$ of the stadium per hour.

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Example Question #61 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

A janitor can clean $\frac{1}{8}$ of a stadium in $\frac{1}{3}$ of an hour. If he continues this rate, how much of the stadium can he clean per hour?

Possible Answers:

$\frac{1}{2}\textup{ of the stadium}$

$\frac{1}{8}\textup{ of the stadium}$

$\frac{5}{8}\textup{ of the stadium}$

$\frac{1}{4}\textup{ of the stadium}$

$\frac{3}{8}\textup{ of the stadium}$

Correct answer:

$\frac{3}{8}\textup{ of the stadium}$

Explanation:

$\frac{\ \frac{1}{8}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{8}\times\frac{3}{1}=\frac{3}{8}$

The janitor can clean $\frac{3}{8}$ of the stadium per hour.

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Example Question #63 : Ratios & Proportional Relationships

A janitor can clean $\frac{1}{7}$ of a stadium in $\frac{1}{3}$ of an hour. If he continues this rate, how much of the stadium can he clean per hour?

Possible Answers:

$\frac{4}{7}\textup{ of the stadium}$

$\frac{5}{7}\textup{ of the stadium}$

$\frac{1}{7}\textup{ of the stadium}$

$\frac{3}{7}\textup{ of the stadium}$

$\frac{2}{7}\textup{ of the stadium}$

Correct answer:

$\frac{3}{7}\textup{ of the stadium}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

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

The janitor can clean $\frac{3}{7}$ of the stadium per hour.

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Example Question #61 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Hannah loves to shop. She can shop in $\frac{1}{10}$ of the mall in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Possible Answers:

$\frac{1}{5}\textup{ of the mall}$

$\frac{1}{2}\textup{ of the mall}$

$\frac{3}{5}\textup{ of the mall}$

$\frac{4}{5}\textup{ of the mall}$

$\frac{2}{5}\textup{ of the mall}$

Correct answer:

$\frac{2}{5}\textup{ of the mall}$

Explanation:

The phrase "per hour" gives us a clue that we are going to divide. In this problem, we can replace the word "per" with a division sign; therefore, we will have the portion of the mall, $\frac{1}{10}$ , divided by hours, $\frac{1}{4}$ :

$\frac{\ \frac{1}{10}\ \textup{of the mall}}{\ \frac{1}{4}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{10}\times\frac{4}{1}=\frac{4}{10}=\frac{2}{5}$

Hannah can shop in $\frac{2}{5}$ of the mall per hour.

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Example Question #64 : Grade 7

Hannah loves to shop. She can shop in $\frac{1}{11}$ of the mall in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Possible Answers:

$\frac{1}{11}\textup{ of the mall}$

$\frac{3}{11}\textup{ of the mall}$

$\frac{5}{11}\textup{ of the mall}$

$\frac{2}{11}\textup{ of the mall}$

$\frac{4}{11}\textup{ of the mall}$

Correct answer:

$\frac{4}{11}\textup{ of the mall}$

Explanation:

$\frac{\ \frac{1}{9}\ \textup{of the mall}}{\ \frac{1}{4}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{11}\times\frac{4}{1}=\frac{4}{11}$

Hannah can shop in $\frac{4}{11}$ of the mall per hour.

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Example Question #68 : Ratios & Proportional Relationships

Hannah loves to shop. She can shop in $\frac{1}{8}$ of the mall in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Possible Answers:

$\frac{1}{8}\textup{ of the mall}$

$\frac{1}{2}\textup{ of the mall}$

$\frac{3}{8}\textup{ of the mall}$

$\frac{1}{4}\textup{ of the mall}$

$\frac{3}{4}\textup{ of the mall}$

Correct answer:

$\frac{1}{2}\textup{ of the mall}$

Explanation:

$\frac{\ \frac{1}{8}\ \textup{of the mall}}{\ \frac{1}{4}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{8}\times\frac{4}{1}=\frac{4}{8}=\frac{1}{2}$

Hannah can shop in $\frac{1}{2}$ of the mall per hour.

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Example Question #64 : Ratios & Proportional Relationships

Hannah loves to shop. She can shop in $\frac{1}{7}$ of the mall in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Possible Answers:

$\frac{2}{7}\textup{ of the mall}$

$\frac{1}{7}\textup{ of the mall}$

$\frac{5}{7}\textup{ of the mall}$

$\frac{3}{7}\textup{ of the mall}$

$\frac{4}{7}\textup{ of the mall}$

Correct answer:

$\frac{4}{7}\textup{ of the mall}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{of the mall}}{\ \frac{1}{4}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

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

Hannah can shop in $\frac{4}{7}$ of the mall per hour.

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Example Question #66 : Grade 7

Hannah loves to shop. She can shop in $\frac{1}{6}$ of the mall in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Possible Answers:

$\frac{5}{6}\textup{ of the mall}$

$\frac{1}{3}\textup{ of the mall}$

$\frac{1}{6}\textup{ of the mall}$

$\frac{2}{3}\textup{ of the mall}$

$\frac{2}{5}\textup{ of the mall}$

Correct answer:

$\frac{2}{3}\textup{ of the mall}$

Explanation:

$\frac{\ \frac{1}{6}\ \textup{of the mall}}{\ \frac{1}{4}\ \textup{hours}}$

Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.

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

Therefore:

$\frac{1}{6}\times\frac{4}{1}=\frac{4}{6}=\frac{2}{3}$

Hannah can shop in $\frac{2}{3}$ of the mall per hour.

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Common Core: 7th Grade Math : Ratios & Proportional Relationships

Study concepts, example questions & explanations for Common Core: 7th Grade Math

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #61 : Ratios & Proportional Relationships

Example Question #61 : Ratios & Proportional Relationships

Example Question #62 : Ratios & Proportional Relationships

Example Question #61 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Example Question #63 : Ratios & Proportional Relationships

Example Question #61 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Example Question #64 : Grade 7

Example Question #68 : Ratios & Proportional Relationships

Example Question #64 : Ratios & Proportional Relationships

Example Question #66 : Grade 7

All Common Core: 7th Grade Math Resources

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