Lesson Topic: From Ratios to Rates & From Rates to Ratios

Lesson Objective: I can…• Recognize that they can associate a ratio of

two quantities. • Identify the associated ratios. Identify the unit

rate and the rate unit.• Given a rate, find ratios associated with the

rate.

Vocabulary

• Rate: A ratio of two quantities• Unit Rate: The numerical part of the

rate, written as the value of the ratio• Rate Unit: The description of the

rate, for example miles/hour (read as “miles per hour”)

From Ratios to Rates: Example

Diet cola was on sale last week; it cost $10 for every 4 packs of diet cola. Make a table. a. How much do 2 packs of cola cost? (Include

on table)b. How much does 1 pack of diet cola cost?

(Include on table)c. What is the rate?d. What is the unit rate?e. What is the rate unit?

From Rates to Ratios: Example 1

The ratio of miles to hours is 434 to 7.

a. What’s the associated rate?

The ratio of laps to minutes is 5 to 4.

b. What’s the unit rate?

c. What’s the associated rate?

The rate is 6 ft/sec.

d. What is the associated ratio?

e. What is the unit rate?

From Rates to Ratios: Example 2

Dave can clean pools at a constant rate of pools/hour.

a. How many pools can Dave clean in 10 hours?

b. How long does it take Dave to clean 15 pools?

Lesson Summary…

• A ratio, such as 5 miles per 2 hours, can be written as a rate.• The numerical part of the rate is called the unit rate and is

simply the value of the ratio, in this case 2.5 or 5/2. This means that in 1 hour, the car travels 2.5 miles.

• The unit for the rate is miles/hour, read “miles per hour”• The corresponding rate to the ratio would be 2.5 miles/hour

or miles/hour. This rate also corresponds to the unit rate above.

• All ratios associated to a given rate are equivalent because they have the same value.