1. R.1 Fractions
6.2 Rates
Objectives
Write rates as fractions.
Find unit rates.
Find the best buy based on cost per unit.

2. Write rates as fractions.
A rate is comparison of measurements with different types of units.
If you hike 18 miles in 4 hours, this can be expressed as a rate.
In a rate, you often find one of these words separating the quantities you are comparing.
in for on per from

3. Write rates as fractions.
Example
Write each rate as a fraction.
5 gallons of chemical for $60
$1500 wages in 10 weeks
2225 miles on 75 gallons of gas

4. Find unit rates.
When the denominator of a rate is 1, it is called a unit rate.
If you earn $12.75 for 1 hour of work, this can be expressed as a unit rate.
$12.75 per hour or $12.75/hour
Use per or a / mark when writing unit rates.

5. Find unit rates.
Example
Write miles on 13.5 gallons of gas as a unit rate.
The unit rate is 25 miles per gallon or 25 miles/gallon.

6. Find unit rates.
Example
Write 549 miles in 18 hours as a unit rate.
The unit rate is 30.5 miles per hour or 30.5 miles/hour.

7. Find unit rates.
Example
Write $810 in 6 days as a unit rate.
The unit rate is $135 dollars per day or $135/day.

8. Find the best buy based on cost per unit.

9. Find the best buy based on cost per unit.
Example
The local store charges the following prices for pancake syrup. Find the best buy.
The best buy is the container with lowest cost per ounce.

10. Find the best buy based on cost per unit.
Example
(continued)
The 24 ounce container is the best buy.

11. Find the best buy based on cost per unit.
Example
Which of the choices of laundry detergent shown below is the best buy?
Find cost per unit for each detergent. (Note that the same number of ounces per load are used for each type of detergent.)

12. Find the best buy based on cost per unit.
Example
(continued)
To find Sudzy’s unit cost, divide $3.99 by 64 ounces, not 50 ounces. You’re getting as many clothes washed as if you bought 64 ounces.
To find White-O’s unit cost, divide $9.89 by 256 ounces (twice 128 ounces, or 2 × 128 = 256 ounces).

13. Find the best buy based on cost per unit.
Example
Suppose you are looking at these choices for “extra-strength” pain reliever. Both brands have the same amount of pain reliever in each tablet.
Brand X is $2.29 for 50 tablets
Brand Y is $10.75 for 200 tablets
You have a 40¢ coupon for Brand X and a 75¢ coupon for Brand Y. Which is the better buy?
First subtract the coupon, then divide to find the cost per unit.

14. Find the best buy based on cost per unit.
Example
(continued)
Brand X has the lower cost per tablet.