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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 #41 : Grade 7

Kylie can clean $\frac{1}{12}$ of a house in $\frac{1}{4}$ of an hour. If she continues this rate, how much of the house can Kylie clean per hour?

Possible Answers:

$\frac{1}{12}\textup{ of the house per hour}$

$\frac{2}{3}\textup{ of the house per hour}$

$\frac{1}{6}\textup{ of the house per hour}$

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

$\frac{1}{3}\textup{ of the house per hour}$

Correct answer:

$\frac{1}{3}\textup{ of the house per hour}$

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, $\frac{1}{12}$ , divided by hours, $\frac{1}{4}$ :

$\frac{\ \frac{1}{12}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

$\frac{1}{12}\times\frac{4}{1}=\frac{4}{12}=\frac{1}{3}$

Kylie can clean $\frac{1}{3}$ of the house per hour.

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Example Question #42 : Grade 7

Greg can complete $\frac{1}{6}$ of his homework in $\frac{1}{3}$ of an hour. If he continues this rate, how much of his homework can Greg complete per hour?

Possible Answers:

$\frac{1}{4}\textup{ of homework}$

$\frac{1}{5}\textup{ of homework}$

$\frac{1}{3}\textup{ of homework}$

$\frac{1}{6}\textup{ of homework}$

$\frac{1}{2}\textup{ of homework}$

Correct answer:

$\frac{1}{2}\textup{ of homework}$

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 homework, $\frac{1}{6}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{6}\ \textup{homework}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Greg can complete $\frac{1}{2}$ of his homework per hour.

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Example Question #43 : Grade 7

Aubtin can complete $\frac{1}{7}$ of his homework in $\frac{1}{3}$ of an hour. If he continues this rate, how much of his homework can Aubtin complete per hour?

Possible Answers:

$\frac{3}{7}\textup{ of homework}$

$\frac{1}{7}\textup{ of homework}$

$\frac{2}{7}\textup{ of homework}$

$\frac{5}{7}\textup{ of homework}$

$\frac{4}{7}\textup{ of homework}$

Correct answer:

$\frac{3}{7}\textup{ of homework}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{homework}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Aubtin can complete $\frac{3}{7}$ of his homework per hour.

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Example Question #44 : Grade 7

Tim can complete $\frac{1}{8}$ of his homework in $\frac{1}{3}$ of an hour. If he continues this rate, how much of his homework can Tim complete per hour?

Possible Answers:

$\frac{3}{8}\textup{ of homework}$

$\frac{1}{8}\textup{ of homework}$

$\frac{2}{8}\textup{ of homework}$

$\frac{5}{8}\textup{ of homework}$

$\frac{4}{8}\textup{ of homework}$

Correct answer:

$\frac{3}{8}\textup{ of homework}$

Explanation:

$\frac{\ \frac{1}{8}\ \textup{homework}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Tim can complete $\frac{3}{8}$ of his homework per hour.

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Example Question #45 : Grade 7

James can complete $\frac{1}{9}$ of his homework in $\frac{1}{3}$ of an hour. If he continues this rate, how much of his homework can James complete per hour?

Possible Answers:

$\frac{2}{3}\textup{ of homework}$

$\frac{1}{3}\textup{ of homework}$

$\frac{4}{9}\textup{ of homework}$

$\frac{1}{9}\textup{ of homework}$

$\frac{2}{9}\textup{ of homework}$

Correct answer:

$\frac{1}{3}\textup{ of homework}$

Explanation:

$\frac{\ \frac{1}{9}\ \textup{homework}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

James can complete $\frac{1}{3}$ of his homework per hour.

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Example Question #46 : Grade 7

Michael can complete $\frac{1}{10}$ of his homework in $\frac{1}{3}$ of an hour. If he continues this rate, how much of his homework can Michael complete per hour?

Possible Answers:

$\frac{1}{5}\textup{ of homework}$

$\frac{2}{5}\textup{ of homework}$

$\frac{1}{10}\textup{ of homework}$

$\frac{3}{10}\textup{ of homework}$

$\frac{1}{2}\textup{ of homework}$

Correct answer:

$\frac{3}{10}\textup{ of homework}$

Explanation:

$\frac{\ \frac{1}{10}\ \textup{homework}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Michael can complete $\frac{3}{10}$ of his homework per hour.

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Example Question #41 : Ratios & Proportional Relationships

A baker can decorate $\frac{1}{9}$ of a wedding cake in $\frac{1}{4}$ of an hour. If the baker continues this rate, how much of the wedding cake can he decorate per hour?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 cake decorated, $\frac{1}{9}$ , divided by hours, $\frac{1}{4}$ :

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

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:

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

The baker can decorate $\frac{4}{9}$ of the wedding cake per hour.

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Example Question #48 : Grade 7

A baker can decorate $\frac{1}{10}$ of a wedding cake in $\frac{1}{4}$ of an hour. If the baker continues this rate, how much of the wedding cake can he decorate per hour?

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

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:

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

The baker can decorate $\frac{2}{5}$ of the wedding cake per hour.

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Example Question #49 : Grade 7

A baker can decorate $\frac{1}{11}$ of a wedding cake in $\frac{1}{4}$ of an hour. If the baker continues this rate, how much of the wedding cake can he decorate per hour?

Possible Answers:

$\frac{7}{11}\textup{ of the cake}$

$\frac{8}{11}\textup{ of the cake}$

$\frac{6}{11}\textup{ of the cake}$

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

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

Correct answer:

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

Explanation:

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

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:

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

The baker can decorate $\frac{4}{11}$ of the wedding cake per hour.

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Example Question #50 : Grade 7

A baker can decorate $\frac{1}{12}$ of a wedding cake in $\frac{1}{4}$ of an hour. If the baker continues this rate, how much of the wedding cake can he decorate per hour?

Possible Answers:

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

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

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

$\frac{1}{12}\textup{ of the cake}$

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

Correct answer:

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

Explanation:

$\frac{\ \frac{1}{12}\ \textup{of a cake}}{\ \frac{1}{4}\ \textup{hours}}$

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:

$\frac{1}{12}\times\frac{4}{1}=\frac{4}{12}=\frac{1}{3}$

The baker can decorate $\frac{1}{3}$ of the wedding cake 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 #41 : Grade 7

Example Question #42 : Grade 7

Example Question #43 : Grade 7

Example Question #44 : Grade 7

Example Question #45 : Grade 7

Example Question #46 : Grade 7

Example Question #41 : Ratios & Proportional Relationships

Example Question #48 : Grade 7

Example Question #49 : Grade 7

Example Question #50 : Grade 7

All Common Core: 7th Grade Math Resources

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