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Splash Screen. Five-Minute Check (over Lesson 0-5) Then/Now New Vocabulary Example 1: Determine Whether Ratios Are Equivalent Key Concept: Means-Extremes Property of Proportion Example 2: means extremes Example 3: Solve a Proportion Example 4: Real-World Example: Rate of Growth

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 0-5) Then/Now New Vocabulary Example 1: Determine Whether Ratios Are Equivalent Key Concept: Means-Extremes Property of Proportion Example 2: means extremes Example 3: Solve a Proportion Example 4: Real-World Example: Rate of Growth Example 5: Real-World Example: Scale and Scale Models Lesson Menu

  3. A. yes B. no • A • B 5-Minute Check 1

  4. A. 38 B. 40 C. 42 D. 50 • A • B • C • D 5-Minute Check 2

  5. A. 4 B. 2 C. 1.5 D. 1.2 • A • B • C • D 5-Minute Check 3

  6. A bottling machine can fill 210 bottles every 5 minutes. How many bottles can it fill in 1 hour? A. 12,600 B. 6300 C. 3425 D. 2520 • A • B • C • D 5-Minute Check 5

  7. You evaluated percents by using a proportion. (Lesson 0–5) • Compare ratios. • Solve proportions. Then/Now

  8. ratio • proportion • means • extremes • rate • unit rate • scale • scale model Vocabulary

  9. ÷1 ÷7 ÷1 ÷7 Determine Whether Ratios Are Equivalent Answer: When expressed in simplest form, the ratios are equivalent. Example 1

  10. A B C A. They are not equivalent ratios. B. They are equivalent ratios. C. cannot be determined Example 1

  11. a is to b as c is to d Means extremes Concept

  12. ? ? Means Extremes Property A. Use means extremes to determine whether the pair of ratios below forms a proportion. Write the equation. Find the means extremes Simplify. Answer: The means extremes are not equal, so the ratios do not form a proportion. Example 2

  13. ? ? Means Extremes B. Use Means-Extremes to determine whether the pair of ratios below forms a proportion. Write the equation. Find the Means extremes. Write the equation. Answer: The means-extremes are equal, so the ratios form a proportion. Example 2

  14. A B C A. Use the means-extremes to determine whether the pair of ratios below forms a proportion. A. The ratios do form a proportion. B. The ratios do not form a proportion. C. cannot be determined Example 2A

  15. A B C B. Use means extremes to determine whether the pair of ratios below forms a proportion. A. The ratios do form a proportion. B. The ratios do not form a proportion. C. cannot be determined Example 2B

  16. Answer: Simplify. Solve a Proportion A. Original proportion Find the means extremess. Simplify. Divide each side by 8. Example 3

  17. Solve a Proportion B. Original proportion Find the means extremess. (x+4)4=12·3 Simplify. (distributive ppty.) Subtract 16 from each side. Answer: x = 5 Divide each side by 4. Example 3

  18. A B C D A. A. 10 B. 63 C. 6.3 D. 70 Example 3A

  19. A B C D B. A. 6 B. 10 C. –10 D. 16 Example 3B

  20. pedal turns pedal turns wheel turns wheel turns Rate of Growth BICYCLINGThe ratio of a gear on a bicycle is 8:5. This means that for every eight turns of the pedals, the wheel turns five times. Suppose the bicycle wheel turns about 2435 times during a trip. How many times would you have to crank the pedals during the trip? UnderstandLet p represent the number pedal turns. PlanWrite a proportion for the problem and solve. Example 4

  21. Solve Original proportion Rate of Growth Find the means extremess. Simplify. Divide each side by 5. 3896 = p Simplify. Example 4

  22. Rate of Growth Answer: You will need to crank the pedals 3896 times. CheckCompare the ratios. 8 ÷ 5 = 1.6 3896 ÷ 2435 = 1.6 The answer is correct. Example 4

  23. A B C D BICYCLING Trent goes on 30-mile bike ride every Saturday. He rides the distance in 4 hours. At this rate, how far can he ride in 6 hours? A. 7.5 mi B. 20 mi C. 40 mi D. 45 mi Example 4

  24. MAPSIn a road atlas, the scale for the map of Connecticut is 5 inches =41 miles. What is the distance in miles represented by 2 inches on the map? Connecticut: scale scale actual actual Scale and Scale Models Let d represent the actual distance. Example 5

  25. Scale and Scale Models Find the means extremess. Simplify. Divide each side by 5. Simplify. Example 5

  26. Scale and Scale Models Answer: The actual distance is 20.5 miles. Example 5

  27. A B C D A. about 750 miles B. about 1500 miles C. about 2000 miles D. about 2114 miles Example 5

  28. End of the Lesson

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