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Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Learn to work with rates and ratios.

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Presentation on theme: "Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Learn to work with rates and ratios."— Presentation transcript:

1 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Learn to work with rates and ratios.

2 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Vocabulary rate unit rate unit price

3 Pre-Algebra 7-2 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.

4 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Additional Example 1A: Ordering Ratios A. Order the ratios 4:3, 23:10, 13:9, and 47:20 from the least to greatest. 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.

5 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates B. A television has screen width 20 in. and height 15 in. What is the aspect ratio of this screen? 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) = =.

6 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates A. Order the ratios 2:3, 35:14, 5:3, and 49:20 from the least to greatest. Try This: Example 1A 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.

7 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates B. A movie theater has a screen width 36 ft. and height 20 ft. What is the aspect ratio of this screen? Try This: Example 1B 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) = =.

8 Pre-Algebra 7-2 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.

9 Pre-Algebra 7-2 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

10 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates 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 640,000 acres 52 weeks

11 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates 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 750,000 acres 52 weeks

12 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Montana =  18,269 acres 1 week 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.

13 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Idaho =  26,923 acres 1 week 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.

14 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Unit price is a unit rate used to compare costs per item.

15 Pre-Algebra 7-2 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 The better buy is the 5-pack for $1.95.

16 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates 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 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.

17 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates 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 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.

18 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates 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?  $ = $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.

19 Pre-Algebra 7-2 Ratios, Rates, and Unit Rates 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  1.3 beats/s a dozen They cost the same.


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