1. Unit Rates
October 4, 2012

2. Warm Up 10/4 Page 4
Write 2 equivalent ratios for each of the following ratios:
5 to 4
6:2
18 to 43
9: 2

3. Vocabulary
A rate is a ratio that compares two quantities measured in different units.

4. Vocabulary
The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1

5. Finding unit rate. Find the rate.
A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute?
696 steps
12 minutes
Write a rate that compares steps and minutes.
696 steps ÷ 12
12 minutes ÷ 12
Divide the numerator and denominator by 12.
58 steps
1 minute
Simplify.
The dog walks 58 steps per minute.

6. There were 15 cake orders at a bakery in 3 days
There were 15 cake orders at a bakery in 3 days. How many orders would that be in one day?

7. There were 150 sheets of paper in 5 notebooks
There were 150 sheets of paper in 5 notebooks. How many sheets of paper are in one notebook?

8. What is the unit rate?
driving 120 miles in 3 hours

9. What is the unit rate?
54 hot dogs for 18 people

10. What is the unit rate?
160 words typed in 4 minutes

11. What is the unit rate?
$284 for a 4 day car rental

12. Which is the better deal?
$4.25 for 2 gallons of milk or
$2.55 for 1 gallon of milk

13. Which is the better deal?
inline skate rentals at:
$30.00 for 4 hours or
$54.00 for 7 hours

14. Which is the better deal?
$380 for a bus for 32 people or
$420 for a bus for 38 people

15. Finding Unit Rates
Find the rate.
A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take?
105 minutes
35 revolutions
Write a rate that compares minutes and revolutions.
105 minutes ÷ 35
35 revolutions ÷ 35
Divide the numerator and denominator by 35.
3 minutes
1 revolution
Simplify.
The Ferris wheel revolves 1 time in 3 minutes.

16. Finding Unit Rates
Find the rate.
Naja walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard?
24 lights
6 yards
Write a rate that compares security lights and yards.
24 lights ÷ 6
6 yards ÷ 6
Divide the numerator and denominator by 6.
4 lights
1 yard
Simplify.
Naja passes 4 security lights in 1 yard.

17. Examples Rate: 150 heartbeats 2 minutes
How can we get the denominator to be 1?
This is how we find a unit rate.

18. Find the Unit Rate
Amy can read 88 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?)

19. A unit price is the price of one unit of an item
A unit price is the price of one unit of an item. The unit used depends on how the item is sold. The table shows some examples.
Type of Item
Example of Units
Liquid
Ounces, quarts, gallons, liters
Solid
Ounces, pounds, grams, kilograms
Any item
Bottle, container, carton

20. Additional Example
A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the best buy?
Size
Price
12 ounces
$0.99
16 ounces
$1.19
Divide the price by the number of ounces (oz) to find the unit price of each size.
$0.99
12 oz
$0.08 oz
$1.19
16 oz
$0.07 oz ≈ ≈
Since $0.07 < $0.08, the 16 oz sports drink is the best buy.

21. Check It Out:
A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $8.75. Which size is the best buy?
Size
Price
1.5 gal
$4.02
3.5 gal
$8.75
Divide the price by the number of grams (g) to find the unit price of each size.
$4.02
1.5 gal
$2.68
gal
$8.75
3.5 gal
$2.50 g = =
Since $2.50 < $2.68, the 3.5 gallon container is the best buy.

22. Example
Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline?
25 miles =
Unit Rate
1 gallon
8 gallons

23. Example
Juice is sold in two different sizes. A 48-fluid ounce bottle costs $ A 32-fluid ounce bottle costs $ Which is the better buy?

24. Insert Lesson Title Here
Ticket out the door
1. Ian earned $96 babysitting for 12 hours. How much did he earn each hour?
2. It takes Mia 49 minutes to complete 14 homework problems. On average, how long did it take to solve each problem?
3. Seth’s family plans to drive 220 miles to their vacation spot. They would like to complete the drive in 4 hours. What should their average speed be in miles per hour?