7-2 Ratios, Rates, and Unit Rates Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Warm Up Divide. Round answers to the nearest tenth Course Ratios, Rates, and Unit Rates

Problem of the Day There are 3 bags of flour for every 2 bags of sugar in a freight truck. A bag of flour weighs 60 pounds, and a bag of sugar weighs 80 pounds. Which part of the truck’s cargo is heavier, the flour or the sugar? flour Course Ratios, Rates, and Unit Rates

Learn to work with rates and ratios. Course Ratios, Rates, and Unit Rates

Vocabulary rate unit rate unit price Insert Lesson Title Here Course Ratios, Rates, and Unit Rates

Course Ratios, Rates, and Unit Rates An aspect ratio describes a screen by comparing its width to its height. Movie and television screens range in shape from almost perfect squares to wide rectangles. Common aspect ratios are 4:3, 37:20, 16:9, and 47:20.

Additional Example 1A: Ordering Ratios A. Order the ratios 4:3, 23:10, 13:9, and 47:20 from the least to greatest. Insert Lesson Title Here Course Ratios, Rates, and Unit Rates 4:3 = 23:10 = 13:9 = 47:20 = Divide. = = = 1.4 = 2.3 = 2.35 The ratios in order from least to greatest are 4:3, 13:9, 23:10, and 47:20. The decimals in order are 1.3, 1.4, 2.3, and 2.35.

B. A television has screen width 20 in. and height 15 in. What is the aspect ratio of this screen? Insert Lesson Title Here Course Ratios, Rates, and Unit Rates Additional Example 1B: Ordering Ratios The ratio of the width to the height is 20:15. The screen has the aspect ratio 4:3. The ratio can be simplified: (4) 5(3) = =.

A. Order the ratios 2:3, 35:14, 5:3, and 49:20 from the least to greatest. Insert Lesson Title Here Try This: Example 1A Course Ratios, Rates, and Unit Rates 2:3 = 35:14 = 5:3 = 49:20 = Divide. = = = 1.6 = 2.5 = 2.45 The ratios in order from least to greatest are 2:3, 5:3, 49:20, 35:14. The decimals in order are 0.6, 1.6, 2.45, and 2.5.

B. A movie theater has a screen width 36 ft. and height 20 ft. What is the aspect ratio of this screen? Insert Lesson Title Here Try This: Example 1B Course Ratios, Rates, and Unit Rates The ratio of the width to the height is 36:20. The screen has the aspect ratio 9:5. The ratio can be simplified: (9) 4(5) = =.

Course Ratios, Rates, and Unit Rates Ratio: 90 3 Rate: 90 miles 3 hours Read as “90 miles per 3 hours.” A rate is a comparison of two quantities that have different units. A ratio is a comparison of two quantities.

Course Ratios, Rates, and Unit Rates Unit rates are rates in which the second quantity is 1. unit rate: 30 miles, 1 hour or 30 mi/h The ratio 90 3 can be simplified by dividing: 90 3 = 30 1

Insert Lesson Title Here Additional Example 2: Using a Bar Graph to Determine Rates Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week. Nevada =  12,308 acres 1 week Course Ratios, Rates, and Unit Rates 640,000 acres 52 weeks

Insert Lesson Title Here Additional Example 2 Continued Use the bar graph to find the number of acres, to the nearest acre, destroyed in Nevada and Alaska per week. Alaska =  14,423 acres 1 week Course Ratios, Rates, and Unit Rates 750,000 acres 52 weeks

Insert Lesson Title Here Montana =  18,269 acres 1 week Course Ratios, Rates, and Unit Rates 950,000 acres 52 weeks Try This: Example 2 Use the bar graph to find the number of acres, to the nearest acre, destroyed in Montana and Idaho per week.

Insert Lesson Title Here Idaho =  26,923 acres 1 week Course Ratios, Rates, and Unit Rates 1,400,000 acres 52 weeks Try This: Example 2 Continued Use the bar graph to find the number of acres, to the nearest acre, destroyed in Montana and Idaho per week.

Unit price is a unit rate used to compare costs per item. Course Ratios, Rates, and Unit Rates

Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which is the better buy? Additional Example 3A: Finding Unit Prices to Compare Costs Divide the price by the number of pens. price for package number of pens  $ =$0.39 price for package number of pens = $  $0.41 Course Ratios, Rates, and Unit Rates The better buy is the 5-pack for $1.95.

Jamie can buy a 15-oz jar peanut butter for $2.19 or a 20-oz jar for $2.78. Which is the better buy? Additional Example 3B: Finding Unit Prices to Compare Costs  $ = $0.15 = $  $0.14 Course Ratios, Rates, and Unit Rates The better buy is the 20-oz jar for $2.78. price for jar number of ounces price for jar number of ounces Divide the price by the number of ounces.

Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $ Which is the better buy? Try This: Example 3A Course Ratios, Rates, and Unit Rates Divide the price by the number of balls. price for package number of balls  $ =$1.65 price for package number of balls = $  $1.58 The better buy is the 12-pack for $18.95.

Try This: Example 3B John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which is the better buy? Course Ratios, Rates, and Unit Rates  $ = $0.09 = $  $0.11 The better buy is the 24-oz jar for $2.19. price for bottle number of ounces price for bottles number of ounces Divide the price by the number of ounces.

Lesson Quiz 1. At a family golf outing, a father drove the ball 285 ft. His daughter drove the ball 95 ft. Express the ratio of the father’s distance to his daughter’s in simplest terms. 2. Find the unit price of 6 stamps for $ Find the unit rate of 8 heartbeats in 6 seconds. 4. What is the better buy, a half dozen carnations for $4.75 or a dozen for $9.24? 5. Which is the better buy, four pens for $5.16 or a ten-pack for $12.90? $0.37 per stamp 3:1 Insert Lesson Title Here  1.3 beats/s a dozen Course Ratios, Rates, and Unit Rates They cost the same.