Ratios & Proportional Relationships - Common Core: 7th Grade Math
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A car travels 
miles in 
hours. At what rate does the car travel?
A car travels
Divide the number of miles by the number of hours to get the number of miles per hour.
Divide the number of miles by the number of hours to get the number of miles per hour.
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Write as a unit rate: 
revolutions in 
minutes
Write as a unit rate:
Divide the number of revolutions by the number of minutes to get revolutions per minute:
,
making 
revolutions per minute the correct choice.
Divide the number of revolutions by the number of minutes to get revolutions per minute:
making
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On a map, 
. If two cities are 
apart on the map, how many miles apart are they in reality?
On a map,
Set up the following proportion:
,
where 
is the number of miles the cities are apart.
Now, solve for 
.
The two cities are 
miles apart.
Set up the following proportion:
where
Now, solve for
The two cities are
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A factory can make 
tents in 
minutes. At this rate, how long, in minutes, would it take the factory to make 
tents?
A factory can make
First, find out how long it takes the factory to produce 
tent.
Since it takes the factory 
minutes to make 
tent, multiply this number by 
to find how long it takes to make 
tents.
It will take the factory 
minutes to make 
tents.
First, find out how long it takes the factory to produce
Since it takes the factory
It will take the factory
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If Billy can drink 
cans of soda in 
days, how many cans of soda can he drink in 
days?
If Billy can drink
First, find how many cans of soda Billy can drink in 1 day.
Since, he can drink 
cans in 
day, then the following equation will tell us how many cans he drinks in 
days.
First, find how many cans of soda Billy can drink in 1 day.
Since, he can drink
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It costs 
to buy 
markers. How much would it cost to buy 
markers?
It costs
First, find the cost per marker.
Now, multiply this cost per marker by 
, the number of markers we want.
First, find the cost per marker.
Now, multiply this cost per marker by
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A 
gallon tank of water is leaking 
gallons every 
minutes. After how many hours will the tank be empty?
A
Set up the following proportion:
,
where 
is the number of hours it'll take to empty 
gallons.
Now solve for 
.
Set up the following proportion:
where
Now solve for
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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?
Chuck is building a driveway that measures
First, find the area of the driveway.
Since it takes 
pounds of cement per square feet,
pounds will be needed to complete the driveway.
First, find the area of the driveway.
Since it takes
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Julie can read 
pages in 
minutes. How long, in minutes, would it take Julie to read a book that had 
pages?
Julie can read
First, figure out how long it takes Julie to read 1 page.
It takes Julie 
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.
It will take Julie 
minutes to read 
pages.
First, figure out how long it takes Julie to read 1 page.
It takes Julie
It will take Julie
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If it takes Dennis 
minutes to paint 
walls, how many minutes does it take him to paint 
wall?
If it takes Dennis
Divide the time it take Dennis to paint 
walls by the number of walls he painted to find how long it will take him to paint one wall.
It will take Dennis 
minutes to paint one wall.
Divide the time it take Dennis to paint
It will take Dennis
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An arcade charges players 
to play on the machine for 
minutes. How much money would it cost a player if she wanted to play for an hour?
An arcade charges players
First, find out how much money it costs to play for one minute.
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.
It will cost her 
to play for one hour.
First, find out how much money it costs to play for one minute.
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.
It will cost her
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Joanna can finish 
math problems in 
minutes. How many minutes would it take her to finish 
math problems?
Joanna can finish
First, find out how long it will take her to finish 
math problem.
Since it takes Joanna 
minutes to finish one problem, multiply this number by the amount of questions she needs to do.
It will take her 
minutes to finish 
questions.
First, find out how long it will take her to finish
Since it takes Joanna
It will take her
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If a doctor charges 
per hour for her services, how much would it cost to hire this doctor for 
minutes?
If a doctor charges
First, convert the minutes to hours.
Since 
minutes is 
hours, multiply this by the doctor's hourly rate to find how much it will cost to hire this doctor for 
minutes.
First, convert the minutes to hours.
Since
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A dentist charges 
per hour for the first three hours of an appointment. Any amount of time greater than three hours is charged at 
per hour. If a patient had a 
hour long appointment, how much would this appointment cost?
A dentist charges
Use the dentist's rate to find how much the first three hours of the appointment will cost.
Next, use the dentist's second rate to find out how much the last five hours of the appointment will cost.
Now, add these values together to get the cost of the entire appointment.
Use the dentist's rate to find how much the first three hours of the appointment will cost.
Next, use the dentist's second rate to find out how much the last five hours of the appointment will cost.
Now, add these values together to get the cost of the entire appointment.
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Drew walks 
of a mile in 
of an hour. If he continues at this rate, what is Drew's speed in miles per hour 
Drew walks
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, 
, divided by hours, 
:
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Drew can walk at a speed of:
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,
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Drew can walk at a speed of:
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Sarah drinks 
of a liter of water in 
of an hour. If she continues at this rate, how many liters per hour does Sarah drink?
Sarah drinks
The phrase "liters 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 liters, 
, divided by hours, :
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Sarah drinks 
The phrase "liters 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 liters,
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Sarah drinks
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Kalea eats 
of a bag of chips in 
of an hour. If she continues at this rate, how much of the bag can she eat per hour?
Kalea eats
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 chips, 
, divided by hours, 
:
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Kalea can eat 
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 chips,
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Kalea can eat
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Joe used 
of a bag of oranges to squeeze 
of a gallon of juice. At this rate, how many bags of oranges does he use per gallon of juice?
Joe used
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, 
, divided by gallons, 
:
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Joe will use 
bags of oranges to fill a gallon of juice.
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,
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Joe will use
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Megan can clean 
of a house in 
of an hour. If she continues at this rate, how much of the house can Megan clean per hour?
Megan can clean
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, 
, divided by hours, 
:
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Megan can clean 
of the house per hour.
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,
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Megan can clean
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Armen can complete 
of his homework in 
of an hour. If he continues at this rate, how much of his homework can Armen complete per hour?
Armen can complete
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, 
, divided by hours, 
:
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Armen can complete 
of his homework per hour.
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,
Remember that when we divide fractions, we can simply multiply by the reciprocal of the denominator to solve.
Therefore:
Armen can complete
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