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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 #71 : Ratios & Proportional Relationships

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{8}$ of his workout in $\frac{1}{6}$ of an hour. If he continues this rate, how much of his workout does Andrew complete per hour?

Possible Answers:

$\frac{1}{2}\textup{ of his workout}$

$\frac{3}{4}\textup{ of his workout}$

$\frac{1}{3}\textup{ of his workout}$

$\frac{1}{4}\textup{ of his workout}$

$\frac{3}{8}\textup{ of his workout}$

Correct answer:

$\frac{3}{4}\textup{ of his workout}$

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 his workout, $\frac{1}{8}$ , divided by hours, $\frac{1}{6}$ :

$\frac{\ \frac{1}{8}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

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

$\frac{1}{6}\rightarrow \frac{6}{1}$

Therefore:

$\frac{1}{8}\times\frac{6}{1}=\frac{6}{8}=\frac{3}{4}$

Andrew can complete $\frac{3}{4}$ of his workout per hour.

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Example Question #72 : Ratios & Proportional Relationships

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{7}$ of his workout in $\frac{1}{6}$ of an hour. If he continues this rate, how much of his workout does Andrew complete per hour?

Possible Answers:

$\frac{5}{7}\textup{ of his workout}$

$\frac{3}{7}\textup{ of his workout}$

$\frac{6}{7}\textup{ of his workout}$

$\frac{2}{7}\textup{ of his workout}$

$\frac{4}{7}\textup{ of his workout}$

Correct answer:

$\frac{6}{7}\textup{ of his workout}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

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

$\frac{1}{6}\rightarrow \frac{6}{1}$

Therefore:

$\frac{1}{7}\times\frac{6}{1}=\frac{6}{7}$

Andrew can complete $\frac{6}{7}$ of his workout per hour.

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Example Question #73 : Ratios & Proportional Relationships

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{11}$ of his workout in $\frac{1}{6}$ of an hour. If he continues this rate, how much of his workout does Andrew complete per hour?

Possible Answers:

$\frac{8}{11}\textup{ of his workout}$

$\frac{5}{11}\textup{ of his workout}$

$\frac{4}{11}\textup{ of his workout}$

$\frac{7}{11}\textup{ of his workout}$

$\frac{6}{11}\textup{ of his workout}$

Correct answer:

$\frac{6}{11}\textup{ of his workout}$

Explanation:

$\frac{\ \frac{1}{11}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

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

$\frac{1}{6}\rightarrow \frac{6}{1}$

Therefore:

$\frac{1}{11}\times\frac{6}{1}=\frac{6}{11}$

Andrew can complete $\frac{6}{11}$ of his workout per hour.

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Example Question #74 : Ratios & Proportional Relationships

A company that produces medicine for children in the United States wants to see if kids like their new medicine flavor. Select the option that best represents a population.

Possible Answers:

Everyone in the United States

Every adult in the United States

Everyone in Florida

Every child in the United States

Correct answer:

Every child in the United States

Explanation:

In order to answer this question, we first need to know what "population" means. A population is the entire group that is being studied.. In this case, it's all of the kids in the United States.

Because the medicine company is only concerned about what kids think of their new flavor, we can eliminate all of the options that say "everyone" or "every adult", leaving us with "Every child in the United states" as our correct answer.

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Example Question #75 : Ratios & Proportional Relationships

A janitor can clean $\frac{1}{9}$ of a stadium in $\frac{1}{3}$ of an hour. If he continues at this rate, how much of the stadium can he clean per hour?

Possible Answers:

$\frac{2}{9}\textup{ of the stadium}$

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

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

$\frac{1}{9}\textup{ of the stadium}$

$\frac{4}{9}\textup{ of the stadium}$

Correct answer:

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

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, $\frac{1}{9}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{9}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

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:

$\frac{1}{9}\times\frac{3}{1}=\frac{3}{9}=\frac{1}{3}$

The janitor can clean $\frac{1}{3}$ of the stadium per hour.

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Example Question #76 : Ratios & Proportional Relationships

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{12}$ of his workout in $\frac{1}{6}$ of an hour. If he continues at this rate, how much of his workout does Andrew complete per hour?

Possible Answers:

$\frac{1}{2}\textup{ of his workout}$

$\frac{1}{4}\textup{ of his workout}$

$\frac{5}{12}\textup{ of his workout}$

$\frac{1}{6}\textup{ of his workout}$

$\frac{1}{3}\textup{ of his workout}$

Correct answer:

$\frac{1}{2}\textup{ of his workout}$

Explanation:

$\frac{\ \frac{1}{12}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

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

$\frac{1}{6}\rightarrow \frac{6}{1}$

Therefore:

$\frac{1}{12}\times\frac{6}{1}=\frac{6}{12}=\frac{1}{2}$

Andrew can complete $\frac{1}{2}$ of his workout per hour.

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Example Question #74 : Grade 7

Drew walks $\frac{1}{3}$ of a mile in $\frac{1}{2}$ of an hour. If he continues at this rate, what is Drew's speed in miles per hour $(\textup{mph})?$

Possible Answers:

$1\textup{ mph}$

$3\textup{ mph}$

$\frac{1}{3}\textup{ mph}$

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

$2\textup{ mph}$

Correct answer:

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

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, $\frac{1}{3}$ , divided by hours, $\frac{1}{2}$ :

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

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:

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

Drew can walk at a speed of:

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

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Example Question #75 : Grade 7

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

Possible Answers:

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

$1\textup{ liter per hour}$

$2\textup{ liters per hour}$

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

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

Correct answer:

$1\textup{ liter per hour}$

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, $\frac{1}{2}$ , divided by hours, $\frac{1}{2}$ :

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

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:

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

Sarah drinks $1\textup{ liter per hour}$

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Example Question #76 : Grade 7

Kalea eats $\frac{1}{4}$ of a bag of chips in $\frac{1}{3}$ of an hour. If she continues at this rate, how much of the bag can she eat per hour?

Possible Answers:

$\frac{1}{3}\textup{ of a bag of chips per hour}$

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

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

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

$1\textup{ bag of chips per hour}$

Correct answer:

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

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, $\frac{1}{4}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{4}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

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

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Example Question #77 : Ratios & Proportional Relationships

Megan can clean $\frac{1}{7}$ of a house in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the house can Megan clean per hour?

Possible Answers:

$\frac{4}{7}\textup{ of the house per hour}$

$\frac{3}{7}\textup{ of the house per hour}$

$\frac{5}{7}\textup{ of the house per hour}$

$1\textup{ house per hour}$

$\frac{6}{7}\textup{ of the house per hour}$

Correct answer:

$\frac{4}{7}\textup{ of the house per hour}$

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 the portion of the house, $\frac{1}{7}$ , divided by hours, $\frac{1}{4}$ :

$\frac{\ \frac{1}{7}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

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

Megan can clean $\frac{4}{7}$ of the house 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 #71 : Ratios & Proportional Relationships

Example Question #72 : Ratios & Proportional Relationships

Example Question #73 : Ratios & Proportional Relationships

Example Question #74 : Ratios & Proportional Relationships

Example Question #75 : Ratios & Proportional Relationships

Example Question #76 : Ratios & Proportional Relationships

Example Question #74 : Grade 7

Example Question #75 : Grade 7

Example Question #76 : Grade 7

Example Question #77 : Ratios & Proportional Relationships

All Common Core: 7th Grade Math Resources

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