5 -2 Rates California Standards AF 2 2

5 -2 Rates California Standards AF 2. 2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity. Also covered: NS 1. 2, AF 2. 3 Holt CA Course 1

5 -2 Rates Vocabulary rate A ratio that compares two quantities measured in different units. unit rate A rate in which the denominator is 1. Holt CA Course 1

Write the red part at the bottom of p 115. 5 -2 Rates A rate is a special type of ratio that compares two quantities measured in different units. A unit rate is a rate whose denominator is 1. To change a rate to a unit rate, divide both the numerator and denominator by the denominator. Dividing the numerator and denominator of a rate by the same number does not change the value of the rate. Holt CA Course 1

5 -2 Rates Example 1 A: 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 105 minutes ÷ 35 35 revolutions ÷ 35 3 minutes 1 revolution Write a rate that compares minutes and revolutions. Divide the numerator and denominator by 35 to get an equivalent rate. Simplify. The Ferris wheel takes 3 minutes for 1 revolution. Holt CA Course 1

5 -2 Rates Example 1 B: 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 24 lights ÷ 6 6 yards ÷ 6 4 lights 1 yard Write a rate that compares security lights and yards. Divide the numerator and denominator by 6 to get an equivalent rate. Simplify. Sue walks past 4 security lights in 1 yard. Holt CA Course 1

5 -2 Rates An average rate of speed is the ratio of distance traveled to time. The ratio is a rate because the units in the numerator and denominator are different. Speed is usually expressed as a unit rate. Holt CA Course 1

5 -2 Rates Example 2: 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 68 miles ÷ 4 = 17 miles 4 hours ÷ 4 1 hour Write the rate as a fraction. Divide the numerator and denominator by the denominator (4) to get an equivalent rate. Her average speed should be 17 miles per hour. Holt CA Course 1

5 -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. Type of Item Example of Units Liquid Ounces, quarts, gallons, liters Solid Ounces, pounds, grams, kilograms Any item Bottle, container, carton Holt CA Course 1

5 -2 Rates Example 3: 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? Divide the price by the number of ounces (oz) to find the unit price of each size. $0. 99 ≈ $0. 08 12 oz oz Size 12 ounces 16 ounces Price $0. 99 $1. 19 ≈ $0. 07 16 oz oz Since $0. 07 < $0. 08, the 16 -ounce sports drink is the best buy. Holt CA Course 1

5 -2 Rates Check It Out! Example 1 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 696 steps ÷ 12 12 minutes ÷ 12 58 steps 1 minute Write a rate that compares steps and minutes. Divide the numerator and denominator by 12 to get an equivalent rate. Simplify. The dog walks 58 steps per minute. Holt CA Course 1

5 -2 Rates Check It Out! Example 2 Rhett is a pilot and needs to fly 1, 191 miles to the next city. He wants to complete his flight in 3 hours. What should be his average speed in miles per hour? 1, 191 miles 3 hours Write the rate. Divide the numerator 1, 191 miles ÷ 3 = 397 miles and denominator by 3 to get an 3 hours ÷ 3 1 hour equivalent rate. Rhett’s average speed should be 397 miles per hour. Holt CA Course 1

5 -2 Rates Check It Out! Example 3 A 1. 5 gallon container costs $4. 02, and a 3. 5 gallon container costs $8. 75. Which size is the best buy? Divide the price by the number of gallons to find the unit price of each size. $4. 02 = $2. 68 1. 5 gal Size 1. 5 gal 3. 5 gal Price $4. 02 $8. 75 = $2. 50 3. 5 gal Since $2. 50 < $2. 68, the 3. 5 gallon container is the best buy. Holt CA Course 1