Common Core: 7th Grade Math : Grade 7

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

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Example Questions

Example Question #1 : Ratios & Proportional Relationships

Write as a unit rate: \(\displaystyle 330\) revolutions in \(\displaystyle 15\) minutes

Possible Answers:

\(\displaystyle 22\) revolutions per minute

\(\displaystyle 21\) revolutions per minute

\(\displaystyle 24\) revolutions per minute

\(\displaystyle 19\) revolutions per minute

\(\displaystyle 18\) revolutions per minute

Correct answer:

\(\displaystyle 22\) revolutions per minute

Explanation:

Divide the number of revolutions by the number of minutes to get revolutions per minute:

\(\displaystyle 330\div 15 = 22\),

making \(\displaystyle 22\) revolutions per minute the correct choice.

Example Question #1 : Ratios & Proportional Relationships

A factory can make \(\displaystyle 300\) tents in \(\displaystyle 15\) minutes. At this rate, how long, in minutes, would it take the factory to make \(\displaystyle 9000\) tents?

Possible Answers:

\(\displaystyle 300\)

\(\displaystyle 550\)

\(\displaystyle 500\)

\(\displaystyle 450\)

Correct answer:

\(\displaystyle 450\)

Explanation:

First, find out how long it takes the factory to produce \(\displaystyle 1\) tent.

\(\displaystyle \frac{15}{300}=0.05\)

Since it takes the factory \(\displaystyle 0.05\) minutes to make \(\displaystyle 1\) tent, multiply this number by \(\displaystyle 9000\) to find how long it takes to make \(\displaystyle 9000\) tents.

\(\displaystyle 0.05\times9000=450\)

It will take the factory \(\displaystyle 450\) minutes to make \(\displaystyle 9000\) tents.

Example Question #1 : How To Find Rate

If Billy can drink \(\displaystyle 12\) cans of soda in \(\displaystyle 4\) days, how many cans of soda can he drink in \(\displaystyle 2\) days?

Possible Answers:

\(\displaystyle 4\)

\(\displaystyle 3\)

\(\displaystyle 6\)

\(\displaystyle 2\)

Correct answer:

\(\displaystyle 6\)

Explanation:

First, find how many cans of soda Billy can drink in 1 day.

\(\displaystyle \frac{12}{4}=3\)

Since, he can drink \(\displaystyle 3\) cans in \(\displaystyle 1\) day, then the following equation will tell us how many cans he drinks in \(\displaystyle 2\) days.

\(\displaystyle 3\times2=6\)

Example Question #1 : Ratios & Proportional Relationships

It costs \(\displaystyle \$45\) to buy \(\displaystyle 15\) markers. How much would it cost to buy \(\displaystyle 25\) markers?

Possible Answers:

\(\displaystyle \$60\)

\(\displaystyle \$50\)

\(\displaystyle \$65\)

\(\displaystyle \$75\)

Correct answer:

\(\displaystyle \$75\)

Explanation:

First, find the cost per marker.

\(\displaystyle 45\div15=3\)

Now, multiply this cost per marker by \(\displaystyle 25\), the number of markers we want.

\(\displaystyle 25\times3=75\)

Example Question #2 : How To Find Rate

\(\displaystyle 200\) gallon tank of water is leaking \(\displaystyle 2\) gallons every \(\displaystyle 30\) minutes. After how many hours will the tank be empty?

Possible Answers:

\(\displaystyle 45\)

\(\displaystyle 50\)

\(\displaystyle 3000\)

\(\displaystyle 30\)

Correct answer:

\(\displaystyle 50\)

Explanation:

Set up the following proportion:

\(\displaystyle \frac{2}{0.5}=\frac{200}{x}\),

where \(\displaystyle x\) is the number of hours it'll take to empty \(\displaystyle 200\) gallons.

Now solve for \(\displaystyle x\).

\(\displaystyle 2x=100\)

\(\displaystyle x=50\)

Example Question #3 : How To Find Rate

Julie can read \(\displaystyle 5\) pages in \(\displaystyle 2\) minutes. How long, in minutes, would it take Julie to read a book that had \(\displaystyle 120\) pages?

Possible Answers:

\(\displaystyle 72\)

\(\displaystyle 48\)

\(\displaystyle 60\)

\(\displaystyle 40\)

Correct answer:

\(\displaystyle 48\)

Explanation:

First, figure out how long it takes Julie to read 1 page.

\(\displaystyle 2\div5=0.4\)

It takes Julie \(\displaystyle 0.4\) minutes to read one page. Now, multiply this by the number of pages she needs to read to find out how long it will take her.

\(\displaystyle 0.4\times120=48\)

It will take Julie \(\displaystyle 48\) minutes to read \(\displaystyle 120\) pages.

Example Question #4 : How To Find Rate

If it takes Dennis \(\displaystyle 120\) minutes to paint \(\displaystyle 8\) walls, how many minutes does it take him to paint \(\displaystyle 1\) wall?

Possible Answers:

\(\displaystyle 18\)

\(\displaystyle 9\)

\(\displaystyle 12\)

\(\displaystyle 15\)

Correct answer:

\(\displaystyle 15\)

Explanation:

Divide the time it take Dennis to paint \(\displaystyle 8\) walls by the number of walls he painted to find how long it will take him to paint one wall.

\(\displaystyle 120\div8=15\)

It will take Dennis \(\displaystyle 15\) minutes to paint one wall.

Example Question #2 : Ratios & Proportional Relationships

An arcade charges players \(\displaystyle \$1.25\) to play on the machine for \(\displaystyle 3\) minutes. How much money would it cost a player if she wanted to play for an hour?

Possible Answers:

\(\displaystyle \$20\)

\(\displaystyle \$35\)

\(\displaystyle \$30\)

\(\displaystyle \$25\)

Correct answer:

\(\displaystyle \$25\)

Explanation:

First, find out how much money it costs to play for one minute.

\(\displaystyle 1.25\div3=0.41667\)

Now, multiply this amount by the number of minutes in an hour to find how much it will cost for the player to play for one hour.

\(\displaystyle 0.41667\times60=25\)

It will cost her \(\displaystyle \$25\) to play for one hour.

Example Question #3 : Ratios & Proportional Relationships

If a doctor charges \(\displaystyle \$500\) per hour for her services, how much would it cost to hire this doctor for \(\displaystyle 45\) minutes?

Possible Answers:

\(\displaystyle \$350\)

\(\displaystyle \$250\)

\(\displaystyle \$400\)

\(\displaystyle \$375\)

Correct answer:

\(\displaystyle \$375\)

Explanation:

First, convert the minutes to hours.

\(\displaystyle 45\div60=0.75\)

Since \(\displaystyle 45\) minutes is \(\displaystyle 0.75\) hours, multiply this by the doctor's hourly rate to find how much it will cost to hire this doctor for \(\displaystyle 45\) minutes.

\(\displaystyle 500\times0.75=375\)

Example Question #4 : Ratios & Proportional Relationships

A dentist charges \(\displaystyle \$50\) per hour for the first three hours of an appointment. Any amount of time greater than three hours is charged at \(\displaystyle \$25\) per hour. If a patient had a \(\displaystyle 8\) hour long appointment, how much would this appointment cost?

Possible Answers:

\(\displaystyle \$275\)

\(\displaystyle \$300\)

\(\displaystyle \$250\)

\(\displaystyle \$325\)

Correct answer:

\(\displaystyle \$275\)

Explanation:

Use the dentist's rate to find how much the first three hours of the appointment will cost.

\(\displaystyle 50\times 3=150\)

Next, use the dentist's second rate to find out how much the last five hours of the appointment will cost.

\(\displaystyle 25\times5=125\)

Now, add these values together to get the cost of the entire appointment.

\(\displaystyle 150+125=275\)

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