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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 #21 : Grade 7

David walks $\frac{1}{8}$ of a mile in $\frac{1}{2}$ of an hour. If he continues this rate, what is David's speed in miles per hour $(\textup{mph})?$

Possible Answers:

$\frac{1}{5}\textup{ mph}$

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

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

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

$\frac{5}{8}\textup{ mph}$

Correct answer:

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

Explanation:

The phrase "miles 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 miles, $\frac{1}{8}$ , divided by hours, $\frac{1}{2}$ :

$\frac{\ \frac{1}{8}\ \textup{miles}}{\ \frac{1}{2}\ \textup{hours}}$

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

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

Therefore:

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

David can walk at a speed of:

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

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Example Question #21 : Ratios & Proportional Relationships

Jenni drinks $\frac{1}{3}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues this rate, how many liters per hour does Jenni drink?

Possible Answers:

$\frac{2}{3}\textup{ liters per hour}$

$\frac{1}{5}\textup{ liters per hour}$

$\frac{2}{5}\textup{ liters per hour}$

$\frac{1}{3}\textup{ liters per hour}$

$\frac{3}{5}\textup{ liters per hour}$

Correct answer:

$\frac{2}{3}\textup{ liters per hour}$

Explanation:

The phrase "liters 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 liters, $\frac{1}{3}$ , divided by hours, $\frac{1}{2}$ :

$\frac{\ \frac{1}{3}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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

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

Therefore:

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

Jenni drinks $\frac{2}{3}\textup{ liters per hour}$

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Example Question #22 : Ratios & Proportional Relationships

Lisa drinks $\frac{1}{4}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues this rate, how many liters per hour does Lisa drink?

Possible Answers:

$\frac{1}{3}\textup{ liter per hour}$

$\frac{3}{4}\textup{ liter per hour}$

$\frac{1}{2}\textup{ liter per hour}$

$\frac{2}{3}\textup{ liter per hour}$

$\frac{1}{4}\textup{ liter per hour}$

Correct answer:

$\frac{1}{2}\textup{ liter per hour}$

Explanation:

$\frac{\ \frac{1}{4}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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

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

Therefore:

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

Lisa drinks $\frac{1}{2}\textup{ liter per hour}$

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Example Question #22 : Grade 7

Molly drinks $\frac{1}{5}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues this rate, how many liters per hour does Molly drink?

Possible Answers:

$\frac{2}{5}\textup{ liters per hour}$

$\frac{3}{5}\textup{ liters per hour}$

$\frac{2}{3}\textup{ liters per hour}$

$\frac{1}{5}\textup{ liters per hour}$

$\frac{4}{5}\textup{ liters per hour}$

Correct answer:

$\frac{2}{5}\textup{ liters per hour}$

Explanation:

$\frac{\ \frac{1}{5}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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

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

Therefore:

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

Molly drinks $\frac{2}{5}\textup{ liters per hour}$

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Example Question #24 : Ratios & Proportional Relationships

Emily drinks $\frac{1}{6}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues this rate, how many liters per hour does Emily drink?

Possible Answers:

$\frac{1}{2}\textup{ liters per hour}$

$\frac{1}{3}\textup{ liters per hour}$

$\frac{5}{6}\textup{ liters per hour}$

$\frac{1}{6}\textup{ liters per hour}$

$\frac{2}{3}\textup{ liters per hour}$

Correct answer:

$\frac{1}{3}\textup{ liters per hour}$

Explanation:

$\frac{\ \frac{1}{6}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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

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

Therefore:

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

Emily drinks $\frac{1}{3}\textup{ liters per hour}$

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Example Question #23 : Grade 7

Leah drinks $\frac{1}{7}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues this rate, how many liters per hour does Leah drink?

Possible Answers:

$\frac{3}{7}\textup{ liters per hour}$

$\frac{2}{7}\textup{ liters per hour}$

$\frac{4}{7}\textup{ liters per hour}$

$\frac{5}{7}\textup{ liters per hour}$

$\frac{1}{7}\textup{ liters per hour}$

Correct answer:

$\frac{2}{7}\textup{ liters per hour}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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

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

Therefore:

$\frac{1}{7}\times\frac{2}{1}=\frac{2}{7}$

Leah drinks $\frac{2}{7}\textup{ liters per hour}$

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Example Question #21 : Grade 7

Judy eats $\frac{1}{5}$ of a bag of chips in $\frac{1}{3}$ of an hour. If she continues this rate, how much of the bag can she eat per hour?

Possible Answers:

$\frac{2}{5}\textup{ of a bag of chips per hour}$

$\frac{2}{3}\textup{ of a bag of chips per hour}$

$\frac{1}{5}\textup{ of a bag of chips per hour}$

$\frac{3}{5}\textup{ of a bag of chips per hour}$

$\frac{4}{5}\textup{ of a bag of chips per hour}$

Correct answer:

$\frac{3}{5}\textup{ of a bag of chips per hour}$

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 amount of chips, $\frac{1}{5}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{5}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

$\frac{1}{5}\times\frac{3}{1}=\frac{3}{5}$

Judy can eat $\frac{3}{5}\textup{ of a bag of chips per hour}$

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Example Question #24 : Grade 7

Nancy eats $\frac{1}{6}$ of a bag of chips in $\frac{1}{3}$ of an hour. If she continues this rate, how much of the bag can she eat per hour?

Possible Answers:

$\frac{5}{6}\textup{ of a bag of chips per hour}$

$\frac{3}{4}\textup{ of a bag of chips per hour}$

$\frac{1}{2}\textup{ of a bag of chips per hour}$

$\frac{1}{6}\textup{ of a bag of chips per hour}$

$\frac{1}{4}\textup{ of a bag of chips per hour}$

Correct answer:

$\frac{1}{2}\textup{ of a bag of chips per hour}$

Explanation:

$\frac{\ \frac{1}{6}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Nancy can eat $\frac{1}{2}\textup{ of a bag of chips per hour}$

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Example Question #25 : Grade 7

Shellie eats $\frac{1}{7}$ of a bag of chips in $\frac{1}{3}$ of an hour. If she continues this rate, how much of the bag can she eat per hour?

Possible Answers:

$\frac{2}{7}\textup{ of a bag of chips per hour}$

$\frac{4}{7}\textup{ of a bag of chips per hour}$

$\frac{6}{7}\textup{ of a bag of chips per hour}$

$\frac{3}{7}\textup{ of a bag of chips per hour}$

$\frac{5}{7}\textup{ of a bag of chips per hour}$

Correct answer:

$\frac{3}{7}\textup{ of a bag of chips per hour}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Shellie can eat $\frac{3}{7}\textup{ of a bag of chips per hour}$

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Example Question #30 : Ratios & Proportional Relationships

Lilly eats $\frac{1}{8}$ of a bag of chips in $\frac{1}{3}$ of an hour. If she continues this rate, how much of the bag can she eat per hour?

Possible Answers:

$\frac{1}{8}\textup{ of a bag of chips per hour}$

$\frac{5}{8}\textup{ of a bag of chips per hour}$

$\frac{1}{4}\textup{ of a bag of chips per hour}$

$\frac{3}{8}\textup{ of a bag of chips per hour}$

$\frac{1}{2}\textup{ of a bag of chips per hour}$

Correct answer:

$\frac{3}{8}\textup{ of a bag of chips per hour}$

Explanation:

$\frac{\ \frac{1}{8}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Lilly can eat $\frac{3}{8}\textup{ of a bag of chips per hour}$

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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 #21 : Grade 7

Example Question #21 : Ratios & Proportional Relationships

Example Question #22 : Ratios & Proportional Relationships

Example Question #22 : Grade 7

Example Question #24 : Ratios & Proportional Relationships

Example Question #23 : Grade 7

Example Question #21 : Grade 7

Example Question #24 : Grade 7

Example Question #25 : Grade 7

Example Question #30 : Ratios & Proportional Relationships

All Common Core: 7th Grade Math Resources

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