Core Focus on Proportions & Probability

1. Lesson 1.4 Core Focus on Proportions & Probability Unit Rates

2. Warm-Up 1. Simplify the ratio 12 : 18 and write the ratio in all three forms. 2. The ratio of dogs to cats in a shelter was 4 : 3. a) Explain the meaning of this ratio. For every 4 dogs in the shelter, there are 3 cats. b) Write the ratio of dogs to total dogs and cats in the shelter. 3. Convert to a decimal. 0.6

3. Lesson 1.4 Unit Rates Calculate unit rates.

4. Vocabulary Rate A ratio of two numbers that have different units. Unit Rate A rate with a denominator of 1. Good to Know!  Unit rates typically involve the word “per” like miles per hour or text messages per dollar.  When written as a fraction, the unit before the word “per” is the numerator and the unit after the word “per” is the denominator.

5. Example 1 Find each unit rate. a. b. Rewrite the rate so its denominator is 1. or $4.32 per sandwich Rewrite the rate so its denominator is 1. or 20 miles per hour

6. Extra Example 1 Find each unit rate. a. b. 30 miles per hour $1.20 per baseball card

7. Example 2 An airplane flew 720 miles in 1.5 hours. How fast was it flying in miles per hour? Write the rate as miles to hours. Rewrite the rate so its denominator is 1. The airplane was flying at a rate of 480 miles per hour (480 mph).

8. Extra Example 2 An airplane flew 950 miles in 2.5 hours. How fast was it flying in miles per hour? 380 miles per hour

9. Example 3 A grocery store has a special on jumbo cookies. They are selling 16 jumbo cookies for $5.92. Find the price per cookie. Write the rate as the price compared to the number of cookies. Find the unit rate. Each cookie costs $0.37.

10. Extra Example 3 A clothing store has a special on socks. They are selling 5 pairs of socks for $11.25. Find the price for each pair of socks. $2.25 per pair of socks

11. Explore! Find the Best Deal June and May went to Hawaii on vacation. June rented a car from Rentals-To-Go. They charged her a rate of $30 for 300 miles. May rented a car from Ride-n-Fun. She was charged a rate of $48 for 400 miles. Step 1 Write June’s rental rate as dollars to miles. Step 2 Find the unit rate for June’s rental. ( ___ dollars per mile) Step 3 Write May’s rental rate as dollars to miles. Step 4 Find the unit rate for May’s rental. ( ___ dollars per mile) Step 5 Which person paid less per mile? Step 6 Their friend, April, rented a car in Portland that cost $20 for 250 miles. Did April pay more or less per mile than June? Did she pay more or less per mile than May? Explain your answer using unit rates. Step 7 Give an example of a real-world situation where it would be helpful to calculate a unit rate.

12. Communication Prompts Why would you want to know the miles per gallon your car uses when it is driven? Do you think the unit rate changes if you are driving on a freeway or driving on streets? Why or why not?

13. Exit Problems Find each unit rate. • Thomas spent $3.30 for 3 ice cream cones. Dan spent $2.50 for 2 ice cream cones. Who spent less per ice cream cone? Explain using unit rates. Thomas spent $1.10 per ice cream cone. Dan spent $1.25 per ice cream cone. Thomas spent less per ice cream cone.