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4-2 Rates
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-2 Rates
Warm Up
Divide.
1. 14 ÷ 1.75 2. 34 ÷ 0.17
3. 5.25 ÷ 1.5 4. 8.1 ÷ 2.7
8 200
3.5 3
4-2 Rates
Problem of the Day
A number rounded to the nearest tenth is 5.3. Round to the nearest hundredth, it is 5.28. What could the number be?
Possible answer: 5.279
4-2 Rates
Prep for MA.7.A.1.1 Distinguish between situations that are proportional or not proportional and use proportions to solve problems.Review of MA.6.A.2.2
Sunshine State Standards
4-2 Rates
Vocabulary
rateunit rate
4-2 Rates
A rate is a ratio that compares two quantities measured in different units.
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.
4-2 Rates
Find the rate.
Additional Example 1A: Finding Unit Rates
A Ferris wheel revolves 35 times in 105 minutes. How many minutes does 1 revolution take?
105 minutes35 revolutions
Write a rate that compares minutes and revolutions.
Simplify.
Divide the numerator and denominator by 35.
105 minutes ÷ 35 35 revolutions ÷ 35
3 minutes1 revolution
The Ferris wheel revolves 1 time in 3 minutes.
4-2 Rates
Find the rate.
Additional Example 1B: Finding Unit Rates
Sue walks 6 yards and passes 24 security lights set along the sidewalk. How many security lights does she pass in 1 yard?
24 lights6 yards
Write a rate that compares security lights and yards.
Simplify.
Divide the numerator and denominator by 6.
24 lights ÷ 6 6 yards ÷ 6
4 lights1 yard
Sue passes 4 security lights in 1 yard.
4-2 Rates
Find the rate.
Check It Out: Example 1A
A dog walks 696 steps in 12 minutes. How many steps does the dog take in 1 minute?
696 steps12 minutes
Write a rate that compares steps and minutes.
Simplify.
Divide the numerator and denominator by 12.
696 steps ÷ 12 12 minutes ÷ 12
58 steps1 minute
The dog walks 58 steps per minute.
4-2 Rates
Find the rate.
Check It Out: Example 1B
To make 12 smoothies, Henry needs 30 cups of ice. How many cups of ice does he need for one smoothie?
30 cups of ice12 smoothies
Write a rate that compares cups of ice and smoothies.
Simplify.
Divide the numerator and denominator by 12.
30 cups of ice ÷ 12 12 smoothies ÷ 12
2.5 cups of ice1 smoothie
Henry needs 2.5 cups of ice per smoothie.
4-2 Rates
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.
4-2 Rates
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?
Additional Example 2: Finding Average Speed
68 miles4 hours
Write the rate as a fraction.
68 miles ÷ 4 4 hours ÷ 4
= 17 miles1 hour
Divide the numerator and denominator by the denominator
Danielle’s average speed should be 17 miles per hour.
4-2 Rates
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?
Check It Out: Example 2
1191 miles3 hours
Write the rate as a fraction.
1191 miles ÷ 3 3 hours ÷ 3
= 397 miles1 hour
Divide the numerator and denominator by the denominator
Rhett’s average speed should be 397 miles per hour.
4-2 Rates
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, cartonAny item
Ounces, pounds, grams, kilogramsSolid
Ounces, quarts, gallons, litersLiquid
Example of UnitsType of Item
4-2 Rates
A 12-ounce sports drink costs $0.99, and a 16-ounce sports drink costs $1.19. Which size is the better buy?
Additional Example 3: Consumer Math Application
$1.1916 ounces
$0.9912 ounces
PriceSizeDivide the price by the number of ounces (oz) to find the unit price of each size.
$0.9912 oz
≈ $0.08oz
Since $0.07 < $0.08, the 16 ounce sports drink is the better buy.
$1.1916 oz
≈ $0.07oz
4-2 Rates
A 1.5 gallon container of fluid costs $4.02, and a 3.5 gallon container of fluid costs $8.75. Which size is the better buy?
Check It Out: Example 3
$8.753.5 gal
$4.021.5 gal
PriceSizeDivide the price by the number of gallons (g) to find the unit price of each size.
$4.021.5 gal
= $2.68gal
Since $2.50 < $2.68, the 3.5 gallon container is the better buy.
$8.753.5 gal
= $2.50gal
4-2 Rates
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
4-2 Rates
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
4-2 Rates
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 better buy?
7 lb bag
4-2 Rates
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
Lesson Quiz for Student Response Systems
4-2 Rates
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
Lesson Quiz for Student Response Systems
4-2 Rates
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
Lesson Quiz for Student Response Systems
4-2 Rates
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
Lesson Quiz for Student Response Systems
