Ratios and proportions

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Ratios and proportions

  1. 1. Ratio Proportion Proportion - Solve for variables Rate Unit Rate Scenario Application Real World Application Quick Recap Quiz
  2. 2. What is a ratio? Ratios are expressions that compare two or more quantities. Represents quantity of one entity for every amount of another entity. wikihow.com
  3. 3. Ratio – Expression Representation Example Ratio of length of tennis court to its width can be expressed in 3 ways as: Fraction 24/12 www.clipartsfree.net Width=12m Two quantities separated by colon Two quantities separated by “to” 24:12 24 to 12
  4. 4. Ratio – How to Simplify? Find highest common factor for all the entities. Example Ratio for previous example was written as 24:12 How to further simplify? 1 2 Width=12m www.clipartsfree.net 3 H.C.F for 24 and 12 = 12 Divide both numbers by 12 24/12: 12/12 = 2:1
  5. 5. Quick Question Note : Click on the checkbox Find the ratio of width of tennis court to its length in its simplest form? 24:12 1:2 Width=12m www.clipartsfree.net 2:1 12:24
  6. 6. Solution Find the ratio of width of tennis court to its length in its simplest form? Width=12m www.clipartsfree.net     24:12 Notice that the order of the entities listed has changed. 1:2 2:1 12:24 Notice that the order of the entities listed has changed. Ratio must be simplified
  7. 7. Proportion Two equal ratios form a proportion. 20 en.wikipedia.org 10 Width of swimming pool(plan) = Width of swimming pool(actual) Length of swimming pool(plan) 10 *2 20 *2 = Length of swimming pool(actual) 20 40 en.wikipedia.org
  8. 8. Proportion - How to check if ratios are proportional? 1 Reduce to lowest terms (Taking the previous example.) 20 10 en.wikipedia.org en.wikipedia.org Width of swimming pool(plan) Length of swimming pool(plan) 10 20 1 2 = = 20 40 1 2 = Width of swimming pool(actual) Length of swimming pool(actual) Reducing to lowest terms on both sides Hence ratios are proportional.
  9. 9. Proportion - How to check if ratios are proportional?(Continued) 2 Find Cross Products Extreme = = = Means Hence ratios are proportional.
  10. 10. Proportion – Quick Quiz 8 15 = 4 8 Proportional Not Proportional
  11. 11. Proportion – Quick Quiz 8 15   = 4 8 Proportional Not Proportional
  12. 12. Proportion – Quick Quiz(Continued) 5 4 = 25 20 Proportional Not Proportional
  13. 13. Proportion – Quick Quiz(Solution) 5 4   = 25 20 Proportional Not Proportional
  14. 14. Proportion – Solve for variables
  15. 15. Proportion – Work out Now watch the following video carefully and answer questions 1 and 2.
  16. 16. Proportion - Application Choose the correct formula to solve this problem: Height of fence/Length of fence shadow = Height of tree/Length of tree shadow Height of fence/Length of fence shadow = Length of tree shadow/Height of tree Height of fence*Length of fence shadow = Height of tree *Length of tree shadow Height of tree= Height of fence *Length of fence shadow
  17. 17. Proportion - Application Choose the correct formula to solve this problem:   Height of fence/Length of fence shadow = Height of tree/Length of tree shadow   Height of fence*Length of fence shadow = Height of tree *Length of tree shadow Height of fence/Length of fence shadow = Length of tree shadow/Height of tree Height of tree= Height of fence *Length of fence shadow
  18. 18. Proportion - Application The height of the tree in Keona’s garden is : 12 ft. 24 ft. 44 ft. 6 ft.
  19. 19. Proportion - Application The height of the tree in Keona’s garden is :     12 ft. 24 ft. 44 ft. 6 ft.
  20. 20. Ratios and Proportions – Word Problem Game Solve ratio word problems with Thinking Block game. http://www.thinkingblocks.com/thinkingblocks_r atios/tb_ratio_main.html en.wikipedia.org
  21. 21. Rate Compare quantities of different units. If 2 kg apples cost 7$. commons.wikimedia.org Cost to Weight rate is written as : 7$/2kg.
  22. 22. Unit Rate Unit Rates have a denominator of 1. www.flickr.com land8.com
  23. 23. Unit Rates - Example Paul takes 3 hours to cover 270km. Unit rate is written as : 1 Set up a rate 270km 3 hours 2 Divide by denominator 3 en.wikipedia.org 90km per hour 270km/3 3 hours/3 = 90km 1 hour
  24. 24. Unit Rates – Work out Test your knowledge on unit rates. Solve questions on unit rate with Braining Camp http://www.brainingcamp.com/content/rates/questions.php www.forbes.com
  25. 25. Ratios and Proportions – Scenario application
  26. 26. Ratios and Proportions – Real world application
  27. 27. Quick Recap Recall and memorize various terms used, with StudyStack http://www.studystack.com/flashcard-201074 caseywhite.hubpages.com
  28. 28. Are you prepared to take a Quiz? www.flickr.com
  29. 29. Here you go! Test your knowledge with Quia. http://www.quia.com/cb/407619.html en.wikipedia.org

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