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Common Core: 7th Grade Math : Grade 7

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

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All Common Core: 7th Grade Math Resources

7 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Ratios & Proportional Relationships

Chloe eats $\frac{1}{9}$ 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:

$\frac{4}{9}\textup{ of a bag of chips per hour}$

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

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

$\frac{1}{9}\textup{ of a bag of chips per hour}$

$\frac{2}{9}\textup{ of a bag of chips per hour}$

Correct answer:

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

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

$\frac{\ \frac{1}{9}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

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

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Example Question #32 : Ratios & Proportional Relationships

Stuart used $\frac{1}{6}$ of a bag of oranges to squeeze $\frac{1}{6}$ of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?

Possible Answers:

$1\frac{2}{5}\textup{ bags of oranges }$

$1\frac{1}{5}\textup{ bags of oranges }$

$1\textup{ bag of oranges }$

$1\frac{4}{5}\textup{ bags of oranges }$

$1\frac{3}{5}\textup{ bags of oranges }$

Correct answer:

$1\textup{ bag of oranges }$

Explanation:

The phrase "bags of oranges does he use per gallon" 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 bags of oranges, $\frac{1}{6}$ , divided by gallons, $\frac{1}{6}$ :

$\frac{\ \frac{1}{6}\ \textup{bag of oranges}}{\ \frac{1}{6}\ \textup{gallons}}$

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:

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

Stuart will use bag of oranges to fill a gallon of juice.

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Example Question #33 : Ratios & Proportional Relationships

Andy used $\frac{1}{7}$ of a bag of oranges to squeeze $\frac{1}{6}$ of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?

Possible Answers:

$\frac{5}{7}\textup{ bag of oranges }$

$\frac{3}{7}\textup{ bag of oranges }$

$\frac{4}{7}\textup{ bag of oranges }$

$\frac{6}{7}\textup{ bag of oranges }$

$\frac{2}{7}\textup{ bag of oranges }$

Correct answer:

$\frac{6}{7}\textup{ bag of oranges }$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{bag of oranges}}{\ \frac{1}{6}\ \textup{gallons}}$

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:

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

Andy will use $\frac{6}{7}$ bags of oranges to fill a gallon of juice.

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Example Question #34 : Ratios & Proportional Relationships

Matt used $\frac{1}{8}$ of a bag of oranges to squeeze $\frac{1}{6}$ of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?

Possible Answers:

$\frac{1}{8}\textup{ bags of oranges }$

$\frac{5}{8}\textup{ bags of oranges }$

$\frac{3}{4}\textup{ bags of oranges }$

$\frac{1}{4}\textup{ bags of oranges }$

$\frac{1}{2}\textup{ bags of oranges }$

Correct answer:

$\frac{3}{4}\textup{ bags of oranges }$

Explanation:

$\frac{\ \frac{1}{8}\ \textup{bag of oranges}}{\ \frac{1}{6}\ \textup{gallons}}$

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:

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

Matt will use $\frac{3}{4}$ bags of oranges to fill a gallon of juice.

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Example Question #35 : Ratios & Proportional Relationships

Dan used $\frac{1}{9}$ of a bag of oranges to squeeze $\frac{1}{6}$ of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?

Possible Answers:

$\frac{2}{9}\textup{ bags of oranges }$

$\frac{1}{3}\textup{ bags of oranges }$

$\frac{1}{9}\textup{ bags of oranges }$

$\frac{4}{9}\textup{ bags of oranges }$

$\frac{2}{3}\textup{ bags of oranges }$

Correct answer:

$\frac{2}{3}\textup{ bags of oranges }$

Explanation:

$\frac{\ \frac{1}{9}\ \textup{bag of oranges}}{\ \frac{1}{6}\ \textup{gallons}}$

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:

$\frac{1}{9}\times\frac{6}{1}=\frac{6}{9}=\frac{2}{3}$

Dan will use $\frac{2}{3}$ bags of oranges to fill a gallon of juice.

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Example Question #36 : Ratios & Proportional Relationships

Justin used $\frac{1}{10}$ of a bag of oranges to squeeze $\frac{1}{6}$ of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?

Possible Answers:

$\frac{4}{5}\textup{ bags of oranges }$

$\frac{1}{5}\textup{ bags of oranges }$

$\frac{2}{5}\textup{ bags of oranges }$

$\frac{3}{5}\textup{ bags of oranges }$

$\frac{1}{2}\textup{ bags of oranges }$

Correct answer:

$\frac{3}{5}\textup{ bags of oranges }$

Explanation:

$\frac{\ \frac{1}{10}\ \textup{bag of oranges}}{\ \frac{1}{6}\ \textup{gallons}}$

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:

$\frac{1}{10}\times\frac{6}{1}=\frac{6}{10}=\frac{3}{5}$

Justin will use $\frac{3}{5}$ bags of oranges to fill a gallon of juice.

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Example Question #37 : Ratios & Proportional Relationships

Kris can clean $\frac{1}{8}$ of a house in $\frac{1}{4}$ of an hour. If she continues this rate, how much of the house can Kris clean per hour?

Possible Answers:

$\frac{1}{2}\textup{ of the house per hour}$

$\frac{2}{5}\textup{ of the house per hour}$

$\frac{1}{5}\textup{ of the house per hour}$

$\frac{3}{5}\textup{ of the house per hour}$

$\frac{3}{10}\textup{ of the house per hour}$

Correct answer:

$\frac{1}{2}\textup{ of the house per hour}$

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, $\frac{1}{8}$ , divided by hours, $\frac{1}{4}$ :

$\frac{\ \frac{1}{8}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

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

Kris can clean $\frac{1}{2}$ of the house per hour.

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Example Question #38 : Ratios & Proportional Relationships

Maggie can clean $\frac{1}{9}$ of a house in $\frac{1}{4}$ of an hour. If she continues this rate, how much of the house can Maggie clean per hour?

Possible Answers:

$\frac{8}{9}\textup{ of the house per hour}$

$\frac{5}{9}\textup{ of the house per hour}$

$\frac{4}{9}\textup{ of the house per hour}$

$\frac{7}{9}\textup{ of the house per hour}$

$\frac{6}{9}\textup{ of the house per hour}$

Correct answer:

$\frac{4}{9}\textup{ of the house per hour}$

Explanation:

$\frac{\ \frac{1}{9}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

$\frac{1}{9}\times\frac{4}{1}=\frac{4}{9}$

Maggie can clean $\frac{4}{9}$ of the house per hour.

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Example Question #39 : Ratios & Proportional Relationships

Linda can clean $\frac{1}{10}$ of a house in $\frac{1}{4}$ of an hour. If she continues this rate, how much of the house can Linda clean per hour?

Possible Answers:

$\frac{4}{5}\textup{ of the house per hour}$

$\frac{2}{5}\textup{ of the house per hour}$

$\frac{3}{5}\textup{ of the house per hour}$

$\frac{1}{5}\textup{ of the house per hour}$

$1\textup { house per hour}$

Correct answer:

$\frac{2}{5}\textup{ of the house per hour}$

Explanation:

$\frac{\ \frac{1}{10}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

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

Linda can clean $\frac{2}{5}$ of the house per hour.

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Example Question #40 : Ratios & Proportional Relationships

Kendall can clean $\frac{1}{11}$ of a house in $\frac{1}{4}$ of an hour. If she continues this rate, how much of the house can Kendall clean per hour?

Possible Answers:

$\frac{5}{11}\textup{ of the house per hour}$

$\frac{3}{11}\textup{ of the house per hour}$

$\frac{4}{11}\textup{ of the house per hour}$

$\frac{7}{11}\textup{ of the house per hour}$

$\frac{6}{11}\textup{ of the house per hour}$

Correct answer:

$\frac{4}{11}\textup{ of the house per hour}$

Explanation:

$\frac{\ \frac{1}{11}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

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

Kendall can clean $\frac{4}{11}$ of the house per hour.

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Common Core: 7th Grade Math : Grade 7

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

All Common Core: 7th Grade Math Resources

Example Questions

Example Question #31 : Ratios & Proportional Relationships

Example Question #32 : Ratios & Proportional Relationships

Example Question #33 : Ratios & Proportional Relationships

Example Question #34 : Ratios & Proportional Relationships

Example Question #35 : Ratios & Proportional Relationships

Example Question #36 : Ratios & Proportional Relationships

Example Question #37 : Ratios & Proportional Relationships

Example Question #38 : Ratios & Proportional Relationships

Example Question #39 : Ratios & Proportional Relationships

Example Question #40 : Ratios & Proportional Relationships

All Common Core: 7th Grade Math Resources

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