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All courses Math Foundations · MF.PR.2 16 of 60
Compute and interpret unit rates, including rates with fractional or decimal quantities.

Find a unit rate from whole numbers

Problem
A car travels \(180~\text{miles}\) in \(3~\text{hours}\). What is the unit rate in miles per hour?
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Hint

Set up the rate as miles divided by hours: 180 miles ÷ 3 hours, since the question asks for miles per 1 hour.

A unit rate tells how much goes with exactly 1 of the second quantity. For miles per hour, divide miles by hours and keep the units in that order.

Solution walkthrough

01

Set up miles per hour

\[\text{unit}~\text{rate}~=~180~\text{miles}~/~3~\text{hours}\]

Miles per hour requires miles in the numerator and hours in the denominator.

02

Scale to one hour

\[180~/~3~=~60;~3~/~3~=~1\]

Dividing both quantities by 3 gives the distance traveled in exactly 1 hour.

03

Check the original trip

\[60~\text{miles}/\text{hour}~\times~3~\text{hours}~=~180~\text{miles}\]

The unit rate reproduces the given 180-mile distance over 3 hours.

04

State the unit rate

\[60~\text{miles}~\text{per}~\text{hour}\]

The car travels 60 miles for each hour.

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Another way

  1. Use an equivalent-rate table and divide both 180 miles and 3 hours by 3.

!

Common mistake

Do not reverse the division. Hours divided by miles would produce hours per mile, not the requested miles per hour.

Solution walkthrough video