Rates and Unit Rates

What Is a Rate?

A rate is a ratio that compares two quantities with different units.

Examples: miles per hour, dollars per pound, words per minute

Unit Rate

A unit rate is a rate with a denominator of 1.

Finding a unit rate: Divide the first quantity by the second.

Example: A car travels 240 miles in 4 hours. $\text{Unit rate} = \frac{240 \text{ miles}}{4 \text{ hours}} = 60 \text{ miles per hour}$

Comparing Unit Rates

Store A: 5 apples for $3.00. Store B: 8 apples for $4.40.

Store A: \frac{\3.00}{5} = $0.60$per apple Store B:$\frac{$4.40}{8} = $0.55$ per apple

Store B is the better deal! (lower cost per apple)

Unit Price

The unit price tells the cost per single item: $\text{Unit price} = \frac{\text{Total cost}}{\text{Number of items}}$

Speed, Distance, and Time

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

$\text{Distance} = \text{Speed} \times \text{Time}$

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

Example: How far does a car going 55 mph travel in 3 hours? $55 \times 3 = 165 \text{ miles}$

Percent as a Rate

A percent is a rate per 100:

• 75% = $\frac{75}{100}$ = 0.75

Consumer tip: Always compare unit prices when shopping! The biggest package isn't always the best deal.