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Warm Up Do each of these pairs make a proportion? Solve. 5x = 85 Solve. 2x = 16 Solve 9x = 15

Warm Up Do each of these pairs make a proportion? Solve. 5x = 85 Solve. 2x = 16 Solve 9x = 15. 1. 3 5. 9 15. 10 12. 15 18. 2. Yes Yes No No 17 8 15/9 = 1 6/9 = 1 2/3. 3. 45 30. 15 5. 4. 8 9. 12 13. Review Homework

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Warm Up Do each of these pairs make a proportion? Solve. 5x = 85 Solve. 2x = 16 Solve 9x = 15

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  1. Warm Up Do each of these pairs make a proportion? Solve. 5x = 85 Solve. 2x = 16 Solve 9x = 15 1. 3 5 9 15 10 12 15 18 2. Yes Yes No No 17 8 15/9 = 1 6/9 = 1 2/3 3. 45 30 15 5 4. 8 9 12 13

  2. Review Homework Tonights HW: pg 48

  3. 48 42 16 14 40 15 3 4 ? ? = = Lesson Quiz Tell whether the ratios are proportional. yes no 1. 2.

  4. Review Explain It! Hats T-Shirts Shorts

  5. Learn to solve proportions.

  6. 10 x 5 4 = Using Properties of Equality to Solve Proportions

  7. girls boys 5 4 = 5 4 x 52 = 5 4 x 52 (52) (52)‏ = Using Properties of Equality to Solve Proportions The ratio of girls to boys in a soccer league is 5:4. If there are 52 boys in the league, how many girls are there? Write a ratio comparing girls to boys. Set Up the proportion. Let x represent the number of girls. Since x is divided by 52, multiply both sides of the equation by 56. 65 = x There are 65 girls in the league.

  8. Cats Dogs 3 2 = 3 2 x 48 = 3 2 x 48 (48) (48)‏ = Example 2 The ratio of cats to dogs at a kennel is 3:2. If there are 48 dogs at the kennel, how many cats are there? Write a ratio comparing cats to dogs. Set Up the proportion. Let x represent the number of cats. Since x is divided by 48, multiply both sides of the equation by 48. 72 = x There are 72 cats at the kennel.

  9. 6 15 x 10 = Using Cross Products to Solve Proportions Find cross products. Solve for x. 15x = 60 X = 60/15 X = 4

  10. 5 10 ? x 4 = Solve this Proportion. 10x = 20 X = 20/10 X = 2 Find cross products.

  11. 30 45 x 225 = 6750 45 45x 45 = Example 4: Business Application Nate has 225 envelopes to prepare for mailing. He takes 30 minutes to prepare 45 envelopes. If he continues at the same rate, how many more minutes until he has completed the job? Let x represent the number of minutes it takes to complete the job. Set up the proportion. 30 ∙ 225 = 45x Find the cross products. Divide both sides by 45. 150 = x Simplify. It will take 150 minutes to complete the job. Nate has already spent 30 minutes, so it will take him 150 – 30 = 120 more minutes to finish the job.

  12. 21 24 m 160 = 3360 24 24m 24 = Check It Out: Example 4 Nemo has to make 160 muffins for the bake sale. He takes 21 minutes to make 24 muffins. If he continues at the same rate, how many more minutes until he has completed the job? Let m represent the number of minutes it takes to complete the job. Set up the proportion. 21 ∙ 160 = 24m Find the cross products. Divide both sides by 24. 140 = m Simplify. It will take 140 minutes to complete the job. Nemo has already spent 21 minutes, so it will take him 140 – 21 = 119 more minutes to finish the job.

  13. More Practice 2. Solve the given proportion. A. p = 8 B. p = 9 C.p = 10 D. p = 11

  14. More Practice 3. A 225 kg weight is positioned 5 m from a fulcrum. If a 300 kg weight is placed at the opposite end of the balance, how far from the fulcrum should it be positioned? A. 5.75 m B. 4.5 m C.4.25 m D. 3.75 m

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