Lesson 4: Rates and Unit Rates

Property

A rate compares two quantities of different units. A rate is usually written as a fraction. When writing a fraction as a rate, we put the first given amount with its units in the numerator and the second amount with its units in the denominator. When rates are simplified, the units remain.

Examples

• If Bob drove his car 525 miles in 9 hours, the rate is written as $\frac{525 \text{ miles}}{9 \text{ hours}}$, which simplifies to $\frac{175 \text{ miles}}{3 \text{ hours}}$.

• A price of 595 dollars for 40 hours of work is the rate $\frac{595 \text{ dollars}}{40 \text{ hours}}$.

Property

A unit rate is a rate with a denominator of 1 unit.
To convert a rate to a unit rate, we divide the numerator by the denominator.
This gives us a denominator of 1.

Examples

• If Anita was paid 384 dollars for 32 hours, her hourly (unit) pay rate is $\frac{384 \text{ dollars}}{32 \text{ hours}} = 384 \div 32 = 12$ dollars per hour.

• If a car travels 455 miles using 14 gallons of gasoline, its unit rate is $\frac{455 \text{ miles}}{14 \text{ gallons}} = 455 \div 14 = 32.5$ miles per gallon (mpg).