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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 #21 : Rational Numbers

On a map, $4\textup{ centimeters}=20\textup{ miles}$ . If two cities are $10\textup{ cm}$ apart on the map, how many miles apart are they in reality?

Possible Answers:

Correct answer:

Explanation:

Set up the following proportion:

$\frac{4}{10}=\frac{20}{x}$ ,

where is the number of miles the cities are apart.

Now, solve for .

4x=200

x=50

The two cities are miles apart.

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Example Question #22 : Rational Numbers

Chuck is building a driveway that measures feet by feet. He needs to use pounds of cement for every square foot of driveway. How many pounds of cement does he need to complete the driveway?

Possible Answers:

300

400

6000

500

Correct answer:

6000

Explanation:

First, find the area of the driveway.

$15\times20=300 ft^2$

Since it takes pounds of cement per square feet,

$300\times20=6000$ pounds will be needed to complete the driveway.

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Example Question #11 : How To Find Rate

Joanna can finish math problems in minutes. How many minutes would it take her to finish math problems?

Possible Answers:

$300\textup { min}$

$270\textup { min}$

$315\textup { min}$

$245\textup { min}$

Correct answer:

$270\textup { min}$

Explanation:

First, find out how long it will take her to finish math problem.

$45\div10=4.5$

Since it takes Joanna 4.5 minutes to finish one problem, multiply this number by the amount of questions she needs to do.

$4.5\times60=270$

It will take her 270 minutes to finish questions.

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Example Question #22 : Numbers And Operations

A car travels 684 miles in hours. At what rate does the car travel?

Possible Answers:

$57\textup { mph}$

$47\textup { mph}$

$67\textup { mph}$

$52\textup { mph}$

$62\textup { mph}$

Correct answer:

$57\textup { mph}$

Explanation:

Divide the number of miles by the number of hours to get the number of miles per hour.

$\textup {rate}=\frac{\textup {distance}}{\textup {time}}=\frac{\textup {miles}}{\textup {hours}}$

$\frac{684\textup { miles}}{12\textup { hours}} = 57\textup { miles per hour}$

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Example Question #11 : Grade 7

Joe used $\frac{1}{5}$ 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:

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

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

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

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

$2\textup{ bags of oranges }$

Correct answer:

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

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, $\frac{1}{5}$ , divided by gallons, $\frac{1}{6}$ :

$\frac{\ \frac{1}{5}\ \textup{bag of oranges}}{\ \frac{1}{6}\ \textup{gallons}}$

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:

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

Joe will use $1\frac{1}{5}$ bags of oranges to fill a gallon of juice.

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Example Question #12 : Grade 7

A landscaper can mow $\frac{1}{3}$ 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:

$2\textup{ yards}$

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

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

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

$3\textup{ yards}$

Correct answer:

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

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, $\frac{1}{3}$ , divided by hours, $\frac{1}{8}$ :

$\frac{\ \frac{1}{3}\ \textup{of a yard}}{\ \frac{1}{8}\ \textup{hours}}$

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:

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

The landscaper can mow $2\frac{2}{3}$ yards per hour.

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Example Question #13 : Grade 7

Hannah loves to shop. She can shop in $\frac{1}{9}$ of the mall in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the mall can she shop per hour?

Possible Answers:

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

$\frac{5}{9}\textup{ of the mall}$

$\frac{8}{9}\textup{ of the mall}$

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

$\frac{7}{9}\textup{ of the mall}$

Correct answer:

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

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

$\frac{\ \frac{1}{9}\ \textup{of the mall}}{\ \frac{1}{4}\ \textup{hours}}$

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:

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

Hannah can shop in $\frac{4}{9}$ of the mall per hour.

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Example Question #14 : Grade 7

Charlie walks $\frac{1}{5}$ of a mile in $\frac{1}{2}$ of an hour. If he continues this rate, what is Charlie's speed in miles per hour $(\textup{mph})?$

Possible Answers:

$\frac{2}{5}\textup{ mph}$

$\frac{3}{5}\textup{ mph}$

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

$\frac{4}{5}\textup{ mph}$

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

Correct answer:

$\frac{2}{5}\textup{ mph}$

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, $\frac{1}{5}$ , divided by hours, $\frac{1}{2}$ :

$\frac{\ \frac{1}{5}\ \textup{miles}}{\ \frac{1}{2}\ \textup{hours}}$

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:

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

Charlie can walk at a speed of:

$\frac{2}{5}\textup{ mph}$

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Example Question #15 : Grade 7

Alan walks $\frac{1}{6}$ of a mile in $\frac{1}{2}$ of an hour. If he continues this rate, what is Alan's speed in miles per hour $(\textup{mph})?$

Possible Answers:

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

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

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

$\frac{5}{6}\textup{ mph}$

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

Correct answer:

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

Explanation:

$\frac{\ \frac{1}{6}\ \textup{miles}}{\ \frac{1}{2}\ \textup{hours}}$

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:

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

Alan can walk at a speed of:

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

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Example Question #13 : Ratios & Proportional Relationships

Jake walks $\frac{1}{7}$ of a mile in $\frac{1}{2}$ of an hour. If he continues this rate, what is Jake's speed in miles per hour $(\textup{mph})?$

Possible Answers:

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

$\frac{5}{7}\textup{ mph}$

$\frac{4}{7}\textup{ mph}$

$\frac{3}{7}\textup{ mph}$

$\frac{2}{7}\textup{ mph}$

Correct answer:

$\frac{2}{7}\textup{ mph}$

Explanation:

$\frac{\ \frac{1}{7}\ \textup{miles}}{\ \frac{1}{2}\ \textup{hours}}$

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:

$\frac{1}{7}\times\frac{2}{1}=\frac{2}{7}$

Jake can walk at a speed of:

$\frac{2}{7}\textup{ mph}$

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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 #21 : Rational Numbers

Example Question #22 : Rational Numbers

Example Question #11 : How To Find Rate

Example Question #22 : Numbers And Operations

Example Question #11 : Grade 7

Example Question #12 : Grade 7

Example Question #13 : Grade 7

Example Question #14 : Grade 7

Example Question #15 : Grade 7

Example Question #13 : Ratios & Proportional Relationships

All Common Core: 7th Grade Math Resources

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