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**Ratios, Rates, and Unit Rates**

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

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**Ratios, Rates, and Unit Rates**

Pre-Algebra 7-2 Ratios, Rates, and Unit Rates Warm Up Divide. Round answers to the nearest tenth. 420 18 73 21 23.3 3.5 380 16 430 18 23.9 23.8

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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

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**Learn to work with rates and ratios.**

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Vocabulary rate unit rate unit price

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**Movie and television screens range in shape from almost perfect squares to wide rectangles.**

An aspect ratio describes a screen by comparing its width to its height. Common aspect ratios are 4:3, 37:20, 16:9, and 47:20.

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**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 4 3 Divide. = 1.3 1 4:3 = = 1.3 23 10 23:10 = = 2.3 13 9 13:9 = = 1.4 47 20 47:20 = = 2.35 The decimals in order are 1.3, 1.4, 2.3, and 2.35. The ratios in order from least to greatest are 4:3, 13:9, 23:10, and 47:20.

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**Additional Example 1B: Ordering Ratios**

B. A television has screen width 20 in. and height 15 in. What is the aspect ratio of this screen? The ratio of the width to the height is 20:15. The ratio can be simplified: 20 15 5(4) 5(3) 4 3 = = . The screen has the aspect ratio 4:3.

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

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

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**A ratio is a comparison of two quantities.**

A rate is a comparison of two quantities that have different units. 90 3 Ratio: Read as “90 miles per 3hours.” 90 miles 3 hours Rate:

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**Unit rates are rates in which the second quantity is 1.**

The ratio 90 3 can be simplified by dividing: 90 3 30 1 = 30 miles, 1 hour unit rate: or 30 mi/h

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**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. 640,000 acres 52 weeks Nevada = 12,308 acres 1 week

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**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. 750,000 acres 52 weeks Alaska = 14,423 acres 1 week

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**950,000 acres Montana = 52 weeks 18,269 acres 1 week**

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. 950,000 acres 52 weeks Montana = 18,269 acres 1 week

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**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. 1,400,000 acres 52 weeks Idaho = 26,923 acres 1 week

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**Unit price is a unit rate used to compare costs per item.**

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**Additional Example 3A: Finding Unit Prices to Compare Costs**

Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $ Which is the better buy? Divide the price by the number of pens. price for package number of pens $1.95 5 = $0.39 price for package number of pens $6.20 15 = $0.41 The better buy is the 5-pack for $1.95.

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**Additional Example 3B: Finding Unit Prices to Compare Costs**

Jamie can buy a 15oz jar peanut butter for $2.19 or a 20 oz jar for $ Which is the better buy? Divide the price by the number of ounces. price for jar number of ounces $2.19 15 = $0.15 price for jar number of ounces $2.78 20 = $0.14 The better buy is the 20-oz jar for $2.78.

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

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

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What’s the error? A clothing store charges $30 for 12 pairs of socks. A student says that the unit price is $0.40 per pair. What is the error? What is the correct unit price?

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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 $2.22. 3. 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?

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