1. Ratios and Rates

2. Unit 4 – Rates & Unit Rates

3. Vocabulary
Rate – A ratio that compares two quantities measured in different units.
Unit Rate – a rate which is being compared to 1.

4. Rate vs. Unit Rate Example
Decide if each situation is a rate or unit rate.
Lucas drinks 8 glasses of water a day.
Unit Rate
2. Peter bought 3 oranges for $5.
Rate
3. Jenny can type 280 words in 4 minutes.
4. Mrs. Robinson checks 6 essays in one hour.
5. Lara plays 16 tournaments a year.

5. Calculating Unit Rates Using Fractions Example
Jim walks 900 meters in 5 minutes. At what rate does he walk?
Step 1: Write a word ratio. Which ever word will eventually become a should be the denominator.
𝐦𝐞𝐭𝐞𝐫𝐬 𝐦𝐢𝐧𝐮𝐭𝐞𝐬
Step 2: Use the word ratio to write a rate.
𝐦𝐞𝐭𝐞𝐫𝐬 𝐦𝐢𝐧𝐮𝐭𝐞𝐬 → = 𝟗𝟎𝟎 𝟓
Step 3: Divide the numerator and denominator by the denominator so that you end up with a denominator of 1.
𝐦𝐞𝐭𝐞𝐫𝐬 𝐦𝐢𝐧𝐮𝐭𝐞𝐬 → = 𝟗𝟎𝟎 𝟓 ÷ 𝟓 𝟓 = 𝟏𝟖𝟎 𝟏
Step 4: Use the unit rate to write an answer.
Jim walks 180 meters per minute

6. Calculating Unit Rates Using Bar Models Example
Jim walks 900 meters in 5 minutes. At what rate does he walk?
Step 1: Draw a bar model to represent the story in the question.
Step 2: Write the equation from the information given in the bar models.
Step 3: Solve for the value of a single box
Jim walks 180 meters per minute

7. The plumber earns $45 per hour
Calculating Unit Rates Using Fractions Example
A plumber earns $180 for 4 hours of work. How much does the plumber earn per hour?
Step 1: Write a word ratio. Which ever word will eventually become a should be the denominator.
𝐝𝐨𝐥𝐥𝐚𝐫𝐬 𝐡𝐨𝐮𝐬
Step 2: Use the word ratio to write a rate.
𝐝𝐨𝐥𝐥𝐚𝐫𝐬 𝐡𝐨𝐮𝐫𝐬 → = 𝟏𝟖𝟎 𝟒
Step 3: Divide the numerator and denominator by the denominator so that you end up with a denominator of 1.
𝐝𝐨𝐥𝐥𝐚𝐫𝐬 𝐡𝐨𝐮𝐫𝐬 → = 𝟏𝟖𝟎 𝟒 ÷ 𝟒 𝟒 = 𝟒𝟓 𝟏
Step 4: Use the unit rate to write an answer.
The plumber earns $45 per hour

8. A plumber makes $45 per hour
Calculating Unit Rates Using Bar Models Example
A plumber earns $180 for 4 hours of work. How much does the plumber earn per hour?
Step 1: Draw a bar model to represent the story in the question.
Step 2: Write the equation from the information given in the bar models.
Step 3: Solve for the value of a single box
A plumber makes $45 per hour