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Rates, Ratios, and Proportions

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1 Rates, Ratios, and Proportions
2-3 Rates, Ratios, and Proportions Holt Algebra 1 Warm Up Lesson Presentation Practice/Assessment

2 Check It Out! Example 1 The ratio of games lost to games won for a baseball team is 2:3. The team has won 18 games. How many games did the team lose? Write a ratio comparing games lost to games won. Write a proportion. Let x be the number of games lost. Since x is divided by 18, multiply both sides of the equation by 18. The team lost 12 games.

3 Objectives To Review the English measurement system and the metric system To Convert measurement units using conversion factors To Convert measurement units using dimensional analysis To Learn and use the term rate

4 Do Now: The ratio of the number of bones in a human’s ears to the number of bones in the skull is 3:11. There are 22 bones in the skull. How many bones are in the ears? Write a ratio comparing bones in ears to bones in skull. Write a proportion. Let x be the number of bones in ears. Since x is divided by 22, multiply both sides of the equation by 22. There are 6 bones in the ears.

5 Vocabulary rate unit rate conversion factor Dimensional Analysis

6 A rate is a ratio of two quantities with different units, such as Rates are usually written as unit rates. A unit rate is a rate with a second quantity of 1 unit, such as or 17 mi/gal. You can convert any rate to a unit rate.

7 Example 2: Finding Unit Rates
Raulf Laue of Germany flipped a pancake 416 times in 120 seconds to set the world record. Find the unit rate. Round your answer to the nearest hundredth. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is about 3.47 flips/s.

8 Check It Out! Example 2 Cory earns $52.50 in 7 hours. Find the unit rate. Write a proportion to find an equivalent ratio with a second quantity of 1. Divide on the left side to find x. The unit rate is $7.50.

9 A rate such as in which the two quantities are equal but use different units, is called a conversion factor.

10 Example A Jonas drove his car from Montana to Canada on vacation. While there, he needed to buy gasoline and noticed that it was sold by the liter rather than by the gallon. Use the conversion factor 1 gallon = 3.79 liters to determine how many liters will fill his 12.5-gallon gas tank.

11 Some conversions require dimensional analysis.
To convert a rate from one set of units to another, we multiply by a conversion factor.

12 Example 3A: Converting Rates
Serena ran a race at a rate of 10 kilometers per hour. What was her speed in kilometers per minute? Round your answer to the nearest hundredth. To convert the second quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The rate is about 0.17 kilometer per minute.

13 Example B A radio-controlled car traveled 30 feet across the classroom in 1.6 seconds. How fast was it traveling in miles per hour?

14

15 Example 3B: Converting Rates
A cheetah can run at a rate of 60 miles per hour in short bursts. What is this speed in feet per minute? Step 1 Convert the speed to feet per hour. Step 2 Convert the speed to feet per minute. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the second quantity. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The speed is 316,800 feet per hour. The speed is 5280 feet per minute.

16 Example 3B: Converting Rates
The speed is 5280 feet per minute. Check that the answer is reasonable. There are 60 min in 1 h, so 5280 ft/min is 60(5280) = 316,800 ft/h. There are 5280 ft in 1 mi, so 316,800 ft/h is This is the given rate in the problem.

17 Check It Out! Example 3 A cyclist travels 56 miles in 4 hours. What is the cyclist’s speed in feet per second? Round your answer to the nearest tenth, and show that your answer is reasonable. Step 1 Convert the speed to feet per hour. Change to miles in 1 hour. To convert the first quantity in a rate, multiply by a conversion factor with that unit in the second quantity. The speed is 73,920 feet per hour.

18 Check It Out! Example 3 Step 2 Convert the speed to feet per minute. To convert the second quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The speed is 1232 feet per minute. Step 3 Convert the speed to feet per second. To convert the second quantity in a rate, multiply by a conversion factor with that unit in the first quantity. The speed is approximately 20.5 feet per second.

19 Practice Textbook p. 111/ 2-5

20 A scale is a ratio between two sets of measurements, such as 1 in:5 mi
A scale is a ratio between two sets of measurements, such as 1 in:5 mi. A scale drawing or scale model uses a scale to represent an object as smaller or larger than the actual object. A map is an example of a scale drawing.

21 Example 5A: Scale Drawings and Scale Models
A contractor has a blueprint for a house drawn to the scale 1 in: 3 ft. A wall on the blueprint is 6.5 inches long. How long is the actual wall? blueprint in. actual ft. Write the scale as a fraction. Let x be the actual length. x • 1 = 3(6.5) Use the cross products to solve. x = 19.5 The actual length of the wall is 19.5 feet.

22 Example 5B: Scale Drawings and Scale Models
A contractor has a blueprint for a house drawn to the scale 1 in: 3 ft. One wall of the house will be 12 feet long when it is built. How long is the wall on the blueprint? blueprint in. actual ft. Write the scale as a fraction. Let x be the actual length. 12 = 3x Use the cross products to solve. 4 = x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. The wall on the blueprint is 4 inches long.

23 Check It Out! Example 5 A scale model of a human heart is 16 ft. long. The scale is 32:1. How many inches long is the actual heart it represents? model in. actual in. Write the scale as a fraction. Let x be the actual length. Convert 16 ft to inches. Use the cross products to solve. 32x = 192 Since x is multiplied by 32, divide both sides by 32 to undo the multiplication. x = 6 The actual heart is 6 inches long.

24 Lesson Quiz: Part 1 1. In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there? 162 Find each unit rate. Round to the nearest hundredth if necessary. 2. Nuts cost $10.75 for 3 pounds. $3.58/lb 3. Sue washes 25 cars in 5 hours. 5 cars/h 4. A car travels 180 miles in 4 hours. What is the car’s speed in feet per minute? 3960 ft/min


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