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

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

Explanation

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.

Write as a unit rate: revolutions in minutes

revolutions per minute

Explanation

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.

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

Explanation

First, find the cost per marker.

$45\div15=3$

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

$25\times3=75$

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?

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 .

The two cities are miles apart.

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

$57\textup { mph}$

$47\textup { mph}$

$67\textup { mph}$

$62\textup { mph}$

$52\textup { mph}$

Explanation

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

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

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

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?

Explanation

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.

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

Explanation

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.

$3\times2=6$

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

Explanation

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 .

A janitor can clean $\frac{1}{7}$ of a stadium in $\frac{1}{3}$ of an hour. If he continues this rate, how much of the stadium can he clean per hour?

$\frac{3}{7}\textup{ of the stadium}$

$\frac{2}{7}\textup{ of the stadium}$

$\frac{1}{7}\textup{ of the stadium}$

$\frac{4}{7}\textup{ of the stadium}$

$\frac{5}{7}\textup{ of the stadium}$

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, $\frac{1}{7}$ , divided by hours, $\frac{1}{3}$ :

$\frac{\ \frac{1}{7}\ \textup{ of the stadium}}{\ \frac{1}{3}\ \textup{hours}}$

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:

$\frac{1}{7}\times\frac{3}{1}=\frac{3}{7}$

The janitor can clean $\frac{3}{7}$ of the stadium per hour.

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 $(\textup{mph})?$

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

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

$2\textup{ mph}$

$3\textup{ mph}$

$1\textup{ mph}$

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