Compute Unit Rates Associated with Ratios of Fractions: CCSS.Math.Content.7.RP.A.1 - 7th Grade Math

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Question

Kalea eats $\frac{1}{4}$ of a bag of chips in $\frac{1}{3}$ of an hour. If she continues at this rate, how much of the bag can she eat per hour?

Answer

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, $\frac{1}{4}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{4}\ \textup{bag of chips}}{\ \frac{1}{3}\ \textup{hours}}$

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:

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

Kalea can eat $\frac{3}{4}\textup{ of a bag of chips per hour}$

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Question

Jenni drinks $\frac{1}{3}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues this rate, how many liters per hour does Jenni drink?

Answer

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, $\frac{1}{3}$ , divided by hours, $\frac{1}{2}$ :

$\frac{\ \frac{1}{3}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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:

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

Jenni drinks $\frac{2}{3}\textup{ liters per hour}$

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Question

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

Answer

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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Question

Write as a unit rate: revolutions in minutes

Answer

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

$330\div 15 = 22$ ,

making revolutions per minute the correct choice.

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Question

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?

Answer

Set up the following proportion:

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

where is the number of miles the cities are apart.

Now, solve for .

The two cities are miles apart.

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Question

A factory can make tents in minutes. At this rate, how long, in minutes, would it take the factory to make tents?

Answer

First, find out how long it takes the factory to produce tent.

$\frac{15}{300}=0.05$

Since it takes the factory minutes to make tent, multiply this number by to find how long it takes to make tents.

$0.05\times9000=450$

It will take the factory minutes to make tents.

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Question

If Billy can drink cans of soda in days, how many cans of soda can he drink in days?

Answer

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

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

Since, he can drink cans in day, then the following equation will tell us how many cans he drinks in days.

$3\times2=6$

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Question

It costs to buy markers. How much would it cost to buy markers?

Answer

First, find the cost per marker.

$45\div15=3$

Now, multiply this cost per marker by , the number of markers we want.

$25\times3=75$

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Question

A gallon tank of water is leaking gallons every minutes. After how many hours will the tank be empty?

Answer

Set up the following proportion:

$\frac{2}{0.5}=\frac{200}{x}$ ,

where is the number of hours it'll take to empty gallons.

Now solve for .

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Question

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?

Answer

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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Question

Julie can read pages in minutes. How long, in minutes, would it take Julie to read a book that had pages?

Answer

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

$2\div5=0.4$

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.

$0.4\times120=48$

It will take Julie minutes to read pages.

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Question

If it takes Dennis minutes to paint walls, how many minutes does it take him to paint wall?

Answer

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.

$120\div8=15$

It will take Dennis minutes to paint one wall.

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Question

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?

Answer

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

$1.25\div3=0.41667$

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.

$0.41667\times60=25$

It will cost her to play for one hour.

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Question

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

Answer

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

$45\div10=4.5$

Since it takes Joanna 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 minutes to finish questions.

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Question

If a doctor charges per hour for her services, how much would it cost to hire this doctor for minutes?

Answer

First, convert the minutes to hours.

$45\div60=0.75$

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.

$500\times0.75=375$

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Question

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?

Answer

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

$50\times 3=150$

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

$25\times5=125$

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

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Question

Drew walks $\frac{1}{3}$ of a mile in $\frac{1}{2}$ of an hour. If he continues at this rate, what is Drew's speed in miles per hour $(\textup{mph})?$

Answer

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, $\frac{1}{3}$ , divided by hours, $\frac{1}{2}$ :

$\frac{\ \frac{1}{3}\ \textup{miles}}{\ \frac{1}{2}\ \textup{hours}}$

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:

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

Drew can walk at a speed of:

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

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Question

Sarah drinks $\frac{1}{2}$ of a liter of water in $\frac{1}{2}$ of an hour. If she continues at this rate, how many liters per hour does Sarah drink?

Answer

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

$\frac{\ \frac{1}{2}\ \textup{liters}}{\ \frac{1}{2}\ \textup{hours}}$

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:

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

Sarah drinks $1\textup{ liter per hour}$

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Question

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?

Answer

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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Question

Megan can clean $\frac{1}{7}$ of a house in $\frac{1}{4}$ of an hour. If she continues at this rate, how much of the house can Megan clean per hour?

Answer

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, $\frac{1}{7}$ , divided by hours, $\frac{1}{4}$ :

$\frac{\ \frac{1}{7}\ \textup{of a house}}{\ \frac{1}{4}\ \textup{hours}}$

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:

$\frac{1}{7}\times\frac{4}{1}=\frac{4}{7}$

Megan can clean $\frac{4}{7}$ of the house per hour.

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