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Warm Up

Warm Up. Simplify each product. Chapter 4 Solving & Applying Proportions. Section 4 – 1 Ratio & Proportion. Objectives: To find ratios & proportions To solve proportions. Ratio :. A comparison of two numbers by division. The ratio of a to b is: a : b or , where b ≠ 0. Examples:

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Warm Up

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  1. Warm Up Simplify each product.

  2. Chapter 4Solving & Applying Proportions

  3. Section 4 – 1 Ratio & Proportion Objectives: To find ratios & proportions To solve proportions

  4. Ratio: A comparison of two numbers by division The ratio of a to b is: a : b or , where b ≠ 0 Examples: Ratio of Girls to Boys is : 10 : 9 The Ratio of the number of Miles Run in 20 Minutes is :

  5. Rate: When a and b represent quantities measured in different units Unit Rate: A rate with a denominator of 1. Example:

  6. Example 1 Using Unit Rates The table at the right gives prices for different sizes of Gatorade. A) Find the unit rate for the 12-oz size.

  7. B) Find the unit rates for the other two sizes. C) Which of the three sizes has the lowest cost per ounce? D) Why are unit rates important?

  8. Unit Analysis: The process of selecting conversion factors to produce the appropriate factors. Example: You need to convert 3 hours to minutes. Conversion factor: To change hours to minutes, multiply by the conversion factor: = 180 Minutes

  9. Example: You need to convert 9 feet to yards. Conversion factor: To change feet to yards, multiply by the conversion factor: = 3 yards

  10. Example: You need to convert 300 feet to miles. Conversion factor: To change feet to miles, multiply by the conversion factor: ≈ .06 miles

  11. Important Conversions: 16 ounces = 1 pound 100 cm= 1 meter 12 inches = 1 feet 3 feet = 1 yard 5,280 feet = 1 mile 60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day 365 days = 1 year

  12. Example 2 Converting Rates A) A cheetah ran 300 feet in 2.92 seconds. What was the cheetah’s speed in miles per hour?

  13. Homework Textbook Page 185 – 186; #1 – 13, 38 – 42 Even

  14. B) A sloth travels 0.15 miles per hour. Convert this speed to feet per minute.

  15. C) 1 qt/min = ____ gal/week

  16. Section 4 – 1 Continued Objectives: To solve proportions

  17. Proportion: An equation that states that two ratios are equal Example:

  18. Cross Products: In the proportion, : ad and bc are the cross products Cross Products of a Proportion: If , then ad = bc Example: , so 2(12) = 3(8)

  19. Example 4 Using Cross Products • Use cross products to solve the proportion • Use cross products to solve the proportion

  20. Use cross products to solve the proportion • Use cross products to solve the proportion

  21. Example 5 Solving Multi-Step Proportions A) Solve the proportion

  22. Solve • Solve

  23. D) Solve E) Solve

  24. You can use proportions to solve world problems! To write a correct proportion, form rates on each side that compare units in the same way, Example:

  25. Example 6 Real-World P.S. A) In 2001, Lance Armstrong won the Tour de France, completing the 3454 – km course in about 86.3 hours. Traveling at his average speed, how long would it take him to ride 185 km? Round your answer to the nearest tenth.

  26. Suppose you walk 2 miles in 35 minutes. How far would you walk in 60 minutes, if you were to continue at the same rate? • Suppose you walk 5 miles in 45 minutes. How far would you walk in 1 hour, if you were to continue at the same rate?

  27. Homework Page 185 – 186; #14 – 28 Even & 32 - 37

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