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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 #51 : Ratios & Proportional Relationships

A baker can decorate $\frac{1}{13}$ 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:

$\frac{3}{13}\textup{ of the cake}$

$\frac{5}{13}\textup{ of the cake}$

$\frac{7}{13}\textup{ of the cake}$

$\frac{4}{13}\textup{ of the cake}$

$\frac{6}{13}\textup{ of the cake}$

Correct answer:

$\frac{4}{13}\textup{ of the cake}$

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, $\frac{1}{13}$ , divided by hours, $\frac{1}{4}$ :

$\frac{\ \frac{1}{13}\ \textup{of a cake}}{\ \frac{1}{4}\ \textup{hours}}$

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:

$\frac{1}{13}\times\frac{4}{1}=\frac{4}{13}$

The baker can decorate $\frac{4}{13}$ of the wedding cake per hour.

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Example Question #52 : Ratios & Proportional Relationships

A painter can paint $\frac{1}{8}$ of a house in $\frac{1}{5}$ of an hour. If he continues this rate, how much of the house can he paint per hour?

Possible Answers:

$\frac{3}{8}\textup{ of a house}$

$\frac{7}{8}\textup{ of a house}$

$\frac{5}{8}\textup{ of a house}$

$\frac{1}{2}\textup{ of a house}$

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

Correct answer:

$\frac{5}{8}\textup{ of a house}$

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 portion of the house painted, $\frac{1}{8}$ , divided by hours, $\frac{1}{5}$ :

$\frac{\ \frac{1}{8}\ \textup{of a house}}{\ \frac{1}{5}\ \textup{hours}}$

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

$\frac{1}{5}\rightarrow \frac{5}{1}$

Therefore:

$\frac{1}{8}\times\frac{5}{1}=\frac{5}{8}$

The painter can paint $\frac{5}{8}$ of a house per hour.

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Example Question #53 : Ratios & Proportional Relationships

A painter can paint $\frac{1}{7}$ of a house in $\frac{1}{5}$ of an hour. If he continues this rate, how much of the house can he paint per hour?

Possible Answers:

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

$\frac{3}{7}\textup{ of a house}$

$\frac{6}{7}\textup{ of a house}$

$\frac{2}{7}\textup{ of a house}$

$\frac{5}{7}\textup{ of a house}$

Correct answer:

$\frac{5}{7}\textup{ of a house}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{of a house}}{\ \frac{1}{5}\ \textup{hours}}$

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

$\frac{1}{5}\rightarrow \frac{5}{1}$

Therefore:

$\frac{1}{7}\times\frac{5}{1}=\frac{5}{7}$

The painter can paint $\frac{5}{7}$ of a house per hour.

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Example Question #54 : Ratios & Proportional Relationships

A painter can paint $\frac{1}{6}$ of a house in $\frac{1}{5}$ of an hour. If he continues this rate, how much of the house can he paint per hour?

Possible Answers:

$\frac{1}{3}\textup{ of a house}$

$\frac{2}{3}\textup{ of a house}$

$\frac{1}{2}\textup{ of a house}$

$\frac{5}{6}\textup{ of a house}$

$\frac{1}{6}\textup{ of a house}$

Correct answer:

$\frac{5}{6}\textup{ of a house}$

Explanation:

$\frac{\ \frac{1}{6}\ \textup{of a house}}{\ \frac{1}{5}\ \textup{hours}}$

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

$\frac{1}{5}\rightarrow \frac{5}{1}$

Therefore:

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

The painter can paint $\frac{5}{6}$ of a house per hour.

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Example Question #55 : Ratios & Proportional Relationships

A painter can paint $\frac{1}{5}$ of a house in $\frac{1}{5}$ of an hour. If he continues this rate, how much of the house can he paint per hour?

Possible Answers:

$\frac{4}{5}\textup{ of a house}$

$1\textup{ house}$

$\frac{3}{5}\textup{ of a house}$

$\frac{2}{5}\textup{ of a house}$

$2\textup{ houses}$

Correct answer:

$1\textup{ house}$

Explanation:

$\frac{\ \frac{1}{5}\ \textup{of a house}}{\ \frac{1}{5}\ \textup{hours}}$

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

$\frac{1}{5}\rightarrow \frac{5}{1}$

Therefore:

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

The painter can paint of a house per hour.

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Example Question #56 : Ratios & Proportional Relationships

A painter can paint $\frac{1}{4}$ of a house in $\frac{1}{5}$ of an hour. If he continues this rate, how much of the house can he paint per hour?

Possible Answers:

$1\frac{3}{5}\textup{ houses}$

$\frac{4}{5}\textup{ of a house}$

$\frac{3}{5}\textup{ of a house}$

$1\frac{2}{5}\textup{ houses}$

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

Correct answer:

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

Explanation:

$\frac{\ \frac{1}{4}\ \textup{of a house}}{\ \frac{1}{5}\ \textup{hours}}$

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

$\frac{1}{5}\rightarrow \frac{5}{1}$

Therefore:

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

The painter can paint $1\frac{1}{5}$ of a house per hour.

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Example Question #57 : Ratios & Proportional Relationships

A landscaper can mow $\frac{1}{4}$ 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:

$2\textup{ yards}$

$2\frac{1}{4}\textup{ yards}$

$2\frac{1}{8}\textup{ yards}$

$1\textup{ yard}$

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

Correct answer:

$2\textup{ yards}$

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

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

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:

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

The landscaper can mow yards per hour.

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Example Question #58 : Ratios & Proportional Relationships

A landscaper can mow $\frac{1}{5}$ 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:

$1\textup{ yard}$

$1\frac{2}{5}\textup{ yards}$

$1\frac{3}{5}\textup{ yards}$

$1\frac{4}{5}\textup{ yards}$

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

Correct answer:

$1\frac{3}{5}\textup{ yards}$

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, $\frac{1}{5}$ , divided by hours, $\frac{1}{8}$ :

$\frac{\ \frac{1}{5}\ \textup{of a yard}}{\ \frac{1}{8}\ \textup{hours}}$

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:

$\frac{1}{5}\times\frac{8}{1}=\frac{8}{5}=1\frac{3}{5}$

The landscaper can mow $1\frac{3}{5}$ yards per hour.

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Example Question #59 : Ratios & Proportional Relationships

A landscaper can mow $\frac{1}{6}$ 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:

$1\frac{5}{6}\textup{ yards}$

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

$1\frac{2}{3}\textup{ yards}$

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

$1\frac{1}{6}\textup{ yards}$

Correct answer:

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

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

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

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:

$\frac{1}{6}\times\frac{8}{6}=\frac{8}{6}=1\frac{2}{6}=1\frac{1}{3}$

The landscaper can mow $1\frac{1}{3}$ yards per hour.

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Example Question #60 : Ratios & Proportional Relationships

A landscaper can mow $\frac{1}{7}$ 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:

$1\frac{4}{7}\textup{ yards}$

$1\frac{2}{7}\textup{ yards}$

$1\frac{5}{7}\textup{ yards}$

$1\frac{3}{7}\textup{ yards}$

$1\frac{1}{7}\textup{ yards}$

Correct answer:

$1\frac{1}{7}\textup{ yards}$

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, $\frac{1}{7}$ , divided by hours, $\frac{1}{8}$ :

$\frac{\ \frac{1}{7}\ \textup{of a yard}}{\ \frac{1}{8}\ \textup{hours}}$

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:

$\frac{1}{7}\times\frac{8}{1}=\frac{8}{7}=1\frac{1}{7}$

The landscaper can mow $1\frac{1}{7}$ yards 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 #51 : Ratios & Proportional Relationships

Example Question #52 : Ratios & Proportional Relationships

Example Question #53 : Ratios & Proportional Relationships

Example Question #54 : Ratios & Proportional Relationships

Example Question #55 : Ratios & Proportional Relationships

Example Question #56 : Ratios & Proportional Relationships

Example Question #57 : Ratios & Proportional Relationships

Example Question #58 : Ratios & Proportional Relationships

Example Question #59 : Ratios & Proportional Relationships

Example Question #60 : Ratios & Proportional Relationships

All Common Core: 7th Grade Math Resources

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