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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 #81 : Ratios & Proportional Relationships

Armen can complete $\frac{1}{5}$ of his homework in $\frac{1}{3}$ of an hour. If he continues at this rate, how much of his homework can Armen complete per hour?

Possible Answers:

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

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

$\frac{4}{5}\textup{ of homework}$

$\frac{3}{5}\textup{ of homework}$

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

Correct answer:

$\frac{3}{5}\textup{ of homework}$

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

$\frac{\ \frac{1}{5}\ \textup{homework}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Armen can complete $\frac{3}{5}$ of his homework per hour.

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Example Question #81 : Ratios & Proportional Relationships

A baker can decorate $\frac{1}{8}$ of a wedding cake in $\frac{1}{4}$ of an hour. If the baker continues this at rate, how much of the wedding cake can he decorate per hour?

Possible Answers:

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

$\frac{3}{4}\textup{ of the cake}$

$\frac{3}{8}\textup{ of the cake}$

$\frac{1}{2}\textup{ of the cake}$

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

Correct answer:

$\frac{1}{2}\textup{ of the cake}$

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

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

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:

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

The baker can decorate $\frac{1}{2}$ of the wedding cake per hour.

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Example Question #83 : Ratios & Proportional Relationships

A painter can paint $\frac{1}{9}$ of a house in $\frac{1}{5}$ of an hour. If he continues at this rate, how much of the house can he paint per hour?

Possible Answers:

$\frac{3}{9}\textup{ of a house}$

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

$\frac{5}{9}\textup{ of a house}$

$\frac{2}{9}\textup{ of a house}$

$\frac{6}{9}\textup{ of a house}$

Correct answer:

$\frac{5}{9}\textup{ of a house}$

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, $\frac{1}{9}$ , divided by hours, $\frac{1}{5}$ :

$\frac{\ \frac{1}{9}\ \textup{of a house}}{\ \frac{1}{5}\ \textup{hours}}$

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:

$\frac{1}{9}\times\frac{5}{1}=\frac{5}{9}$

The painter can paint $\frac{5}{9}$ of a house per hour.

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Example Question #82 : Ratios & Proportional Relationships

A janitor can clean $\frac{1}{12}$ 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:

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

$\frac{3}{4}\textup{ of the stadium}$

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

$1\textup{ stadium}$

$\frac{5}{12}\textup{ of the stadium}$

Correct answer:

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

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, $\frac{1}{12}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{12}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

The janitor can clean $\frac{1}{4}$ of the stadium per hour.

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Example Question #81 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{10}$ 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:

$\frac{2}{5}\textup{ of his workout}$

$\frac{4}{5}\textup{ of his workout}$

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

$\frac{7}{10}\textup{ of his workout}$

$\frac{3}{5}\textup{ of his workout}$

Correct answer:

$\frac{3}{5}\textup{ of his workout}$

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, $\frac{1}{10}$ , divided by hours, $\frac{1}{6}$ :

$\frac{\ \frac{1}{10}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

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:

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

Andrew can complete $\frac{3}{5}$ of his workout per hour.

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Example Question #83 : Ratios & Proportional Relationships

Andrew spends every Saturday at the gym working out. He can complete $\frac{1}{9}$ 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:

$\frac{4}{9}\textup{ of his workout}$

$\frac{5}{9}\textup{ of his workout}$

$\frac{2}{9}\textup{ of his workout}$

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

$\frac{2}{3}\textup{ of his workout}$

Correct answer:

$\frac{2}{3}\textup{ of his workout}$

Explanation:

$\frac{\ \frac{1}{9}\ \textup{of a workout}}{\ \frac{1}{6}\ \textup{hours}}$

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:

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

Andrew can complete $\frac{2}{3}$ of his workout per hour.

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Example Question #82 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Eric walks one-fourth of a mile in half an hour. If he continues at this rate, what is Eric's speed in miles per hour $(\textup{mph})?$

Possible Answers:

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

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

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

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

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

Correct answer:

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

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, $\frac{1}{4}$ , divided by hours, $\frac{1}{2}$ :

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

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:

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

Eric can walk at a speed of:

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

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Example Question #81 : 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:

0.5

1.5

Correct answer:

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 #1 : Proportion / Ratio / Rate

In a class of students, the ratio of freshmen to sophomores to juniors is 2:3:5 . How many juniors are in the class?

Possible Answers:

Correct answer:

Explanation:

Let be the number of freshmen, be the number of sophomores, and be the number of juniors.

Now, since we have students,

2x+3x+5x=60

10x=60

x=6

Since we want to find the number of juniors, we need to find the value of .

5x=5(6)=30

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Example Question #61 : Number Concepts And Operations

In a zoo with 200 animals, the ratio of mammals to reptiles to birds is 5:6:9 . How many birds does the zoo have?

Possible Answers:

100

Correct answer:

Explanation:

Let be the number of mammals, be the number of reptiles, and be the number of birds.

Since the zoo has 200 animals,

5x+6x+9x=200

20x=200

x=10

Because we want the number of birds, we need to find the value of .

9x=9(10)=90

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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 #81 : Ratios & Proportional Relationships

Example Question #81 : Ratios & Proportional Relationships

Example Question #83 : Ratios & Proportional Relationships

Example Question #82 : Ratios & Proportional Relationships

Example Question #81 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Example Question #83 : Ratios & Proportional Relationships

Example Question #82 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Example Question #81 : Ratios & Proportional Relationships

Example Question #1 : Proportion / Ratio / Rate

Example Question #61 : Number Concepts And Operations

All Common Core: 7th Grade Math Resources

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