1. Do Now
Divide.
1. 14 ÷ ÷ 0.17
÷ ÷ 2.7 8
200
3.5 3

2. Learn to find and compare unit rates, such as average speed and unit price.

3. Vocabulary
rate
unit rate

4. Pre-Algebra
4-1
Rates
A rate is a comparison of two quantities that have different units.
For Example:
Read as
“90 miles per 3 hours.”
90 miles
3 hours
Rate: 4

5. A unit rate is a rate whose denominator is 1 when it is written as a fraction.
To change a rate to a unit rate, first write the rate as a fraction and then divide both the numerator and denominator by the denominator.

6. 4-1 Rates 90 miles 3 hours The rate can be made into a unit rate
Pre-Algebra
4-1
Rates
90 miles
3 hours
The rate
can be made into a unit rate
by dividing:
90 ÷ 3 = 30
30 miles,
1 hour
Unit rate:
or 30 mi/h
When dividing, the unit you want your answer to be in, should come first and unit you are making 1 should come second. 6

7. Example 1: 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.
3 minutes per revolution.

8. Example 2: Finding Unit Rates
Find the rate.
Sue 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.
4 lights per yard.

9. An average rate of speed is the ratio of distance traveled to time
An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units being compared are different.

10. Example 3: Finding Average Speed
Danielle is cycling 68 miles as a fundraising commitment. She wants to complete her ride in 4 hours. What should be her average speed in miles per hour?
68 miles
4 hours
Write the rate as a fraction.
68 miles ÷ 4
4 hours ÷ 4
17 miles
1 hour
Divide the numerator and denominator by the denominator =
Danielle’s average speed should be 17 miles per hour.

11. Example 4
Rhett is a pilot and needs to fly 1191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour?
1191 miles
3 hours
Write the rate as a fraction.
1191 miles ÷ 3
3 hours ÷ 3
397 miles
1 hour
Divide the numerator and denominator by the denominator =
Rhett’s average speed should be 397 miles per hour.

12. 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.
Bottle, container, carton
Any item
Ounces, pounds, grams, kilograms
Solid
Ounces, quarts, gallons, liters
Liquid
Example of Units
Type of Item

13. Example 5: Consumer Math Application
A 12-ounce sports drink costs $0.99, and a 16- ounce sports drink costs $1.19. Which size is the best buy?
$1.19
16 ounces
$0.99
12 ounces
Price
Size
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.

14. Example 6
A 1.5 gallon container of milk costs $4.02, and a 3.5 gallon container of milk costs $ Which size is the best buy?
$8.75
3.5 gal
$4.02
1.5 gal
Price
Size
Divide the price by the number of gallons (g) to find the unit price of each size.
$4.02
1.5 gal
$2.68
gal
$8.75
3.5 gal
$2.50
gal = =
Since $2.50 < $2.68, the 3.5 gallon container is the best buy.

15. 4-1 Rates 1. Find the unit price of 6 stamps for $2.22.
Pre-Algebra
4-1
Rates
1. Find the unit price of 6 stamps for $2.22.
2. Find two unit rates for 8 heartbeats in 6 seconds.
3. What is the better buy, a half dozen carnations for $4.75 or a dozen for $9.24?
4. Which is the better buy, four pens for $5.16 or a ten-pack for $12.90?
$0.37 per stamp
1.3 beats/s OR
.75 sec/beat
a dozen
They cost the same. 15

16. Lesson Quiz: Part I
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? $8
3.5 minutes 55

17. Lesson Quiz: Part II
4. Abby can buy a 7-pound bag of dry cat food for $7.40, or she can purchase a 3-pound bag for $5.38. Which size is the best buy?
7 lb bag

18. Homework p.152 5) $7.75 per hour 6) 18 minutes per pound
7) About mph
8) The 64 ounce container

19. Lesson Quiz for Student Response Systems
1. Kay earned $126 for 18 hours in a part-time job. How much did she earn each hour?
A. $6
B. $7
C. $8
D. $9

20. Lesson Quiz for Student Response Systems
2. It takes John 54 minutes to paint a fence with a length of 12 meters. On average, how long did he take to paint 1 meter of the fence?
A. 3.5 minutes
B. 4.5 minutes
C. 4.8 minutes
D. 5.4 minutes

21. Lesson Quiz for Student Response Systems
3. Helen plans to drive 130 miles to a relative’s house. She would like to complete the drive in 2 hours. What should be her average speed in miles per hour?
A. 55 miles per hour
B. 60 miles per hour
C. 65 miles per hour
D. 70 miles per hour

22. Lesson Quiz for Student Response Systems
4. Frank can purchase bags of apples in four sizes. Which size is the best buy?
A. 2-lb bag for $3.33
B. 3-lb bag for $4.70
C. 4-lb bag for $5.14
D. 5-lb bag for $6.20

23. Check It Out:
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.

24. At which table would you choose to sit at and why?
Pre-Algebra
4-1
Rates
At which table would you choose to sit at and why? 24

25. Check It Out:
Find the rate.
To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie?
30 cups of ice
12 smoothies
Write a rate that compares cups of ice and smoothies.
30 cups of ice ÷ 12
12 smoothies ÷ 12
Divide the numerator and denominator by 12.
2.5 cups of ice
1 smoothie
Simplify.
Henry needs 2.5 cups of ice per smoothie.