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Getting Real With ProportionS

Learn about proportions, which are statements of equality between two or more ratios. Discover real-life examples and how to solve proportion word problems step-by-step.

robertobradshaw
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Getting Real With ProportionS

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  1. Getting Real WithProportionS

  2. What are Proportions? A proportion is a statement of equality of two or more ratios Remember: A ratio is a comparison of two numbers by division

  3. Where do you see Proportions in Real Life? • Cartoons • Food and Nutrition • Fashion Design • Maps • Artists • Metric System

  4. http://www.brainpop.com/math/ratioproportionandpercent/proportions/http://www.brainpop.com/math/ratioproportionandpercent/proportions/

  5. How do you make Proportions? Find the two things you are comparing!! First Step:

  6. What are the two things we are comparing in this word problem? Suppose it takes 48 chicken fingers to feed Mr. Young’s 4th grade class of 20 students. How many chicken fingers would be needed for 30 students?

  7. Suppose it takes 48 chicken fingers to feed Mr. Young’s 4th grade class of 20 students. How many chicken fingers would be needed for 30 students? And the answer is……. Chicken Fingers and Students As a Ratio this looks like….. Chicken Fingers Students ---------------------- OR ------------- Students Chicken Fingers

  8. What are the two things we are comparing in this word problem? Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter?

  9. Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter? And the Answer is…. Meters and Seconds As a Ratio this looks like….. Meters Seconds ---------- OR ------------ Seconds Meters

  10. What are the two things we are comparing in this word problem? A car travels 125 miles in 3 hours. How far would it travel in 5 hours?

  11. A car travels 125 miles in 3 hours. How far would it travel in 5 hours? And the answer is…. Miles and Hours As a Ratio this looks like….. Miles Hours --------- OR -------- Hours Miles

  12. What is the second step? Make the two ratios (fractions) that you know Second Step:

  13. What are the two ratios (fractions) you can make out of this word problem? Suppose it takes 48 chicken fingers to feed Mr. Young’s 4th grade class of 20 students. How many chicken fingers would be needed for 30 students? First Step: Chicken Fingers Students ---------------------- OR -------------- Students Chicken Fingers

  14. Suppose it takes 48 chicken fingers to feed Mr. Young’s 4th grade class of 20 students. How manychicken fingers would be needed for 30 students? And the answer is…. Chicken Fingers 48 X -------------------- ------ AND ----- Students 20 30

  15. FYI Can you flip the ratio so that students were on top and chicken fingers were on bottom? YES! If you flip the ratios so that students are on top and chicken fingers were on bottom you must just be careful to do this for all your ratios. Therefore then 48/20 would change to 20/48 and x/30 would become 30/x.

  16. Lets see the difference…… Chicken Fingers 48 X -------------------- ---- AND ---- Students 20 30 OR Students 20 30 ----------- ------ AND ------- Chicken Fingers 48 X

  17. What are the two ratios (fractions) you can make out of this word problem? Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter? First Step: Meters Seconds ---------- OR ------------ Seconds Meters

  18. Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter? And the answer is….. Meters 100 1 --------- ------ AND ------- Seconds 15 X

  19. What are the two ratios (fractions) you can make out of this word problem? A car travels 125 miles in 3 hours. How far would it travel in 5 hours?

  20. A car travels 125 miles in 3 hours. How far would it travel in 5 hours? And the answer is….. Miles 125 X ------- ------ AND ------- Hours 3 5

  21. What is the next step? Third Step: Set the two ratios EQUAL to each other

  22. Suppose it takes 48 chicken fingers to feed Mr. Young’s 4th grade class of 20 students. How many chicken fingers would be needed for 30 students? • Chicken Fingers ---------------------- Students • 48 X ---- AND ---- 20 30 3. 48 X ----- = --- 20 30

  23. Now show me the three steps for this problem Jane ran 100 meters in 15 seconds. How long did she take to run 1 meter?

  24. And the answer is…… • Meters • ---------- • Seconds 2. Meters 100 1 --------- ------ AND ------- Seconds 15 X 3. 100 1 ------ = ------- 15 X

  25. Now show me the three steps for this problem A car travels 125 miles in 3 hours. How far would it travel in 5 hours?

  26. 1. Miles ------- Hours And the answer is….. 2. Miles 125 X ------- ------ AND ------- Hours 3 52 3. 125 X ------ = ------- 3 5

  27. What is the fourth step? Fourth Step: Cross Multiply

  28. Cross Multiply means that you MULTIPLY DIAGONALLY across….. …….Like crisscross apple sauce when you are sitting And then….. Set the two products (ANSWERS) EQUAL to each other 4X = 63

  29. What is the last step? Fifth Step: Solve for X!!!

  30. Solve the Proportion 48 X ----- = --- 20 30

  31. And the answer is…. 30 students would eat 72 chicken fingers

  32. Solve the Proportion 100 1 ------ = ------- 15 X

  33. 100 1 ------ = ------- 15 X And the answer is… (100)(X)= (15)(1) 100X= 15 X= 15/100 X= .15 It took Jane .15 seconds to run a meter

  34. Solve this proportion 125 X ------ = ------- 3 5

  35. 125 X ------ = ------- 3 5 (125)(5) = (3)(X) 625 = 3X 625/3=X X= 208.3 In 5 hours the car would have traveled 208.3 miles.

  36. Make this proportion on your own using the steps you have learned. Mix 3 liters of water with 4 lemons to make lemonade. How many liters of water are mixed with 8 lemons.

  37. Mix 3 liters of water with 4 lemons to make lemonade. How many liters of water are mixed with 8 lemons. • What are you comparing? Liters and Lemons Liters Lemons ------- OR ------- Lemons Liters

  38. Mix 3 liters of water with 4 lemons to make lemonade. How many liters of water are mixed with 8 lemons. 2. What are your two ratios? Liters 3 X --------- ------ AND ------ Lemons 4 8 • Set the two ratios equal to each other 3 X ---- = ----- 4 8

  39. Mix 3 liters of water with 4 lemons to make lemonade. How many liters of water are mixed with 8 lemons. 4. Cross Multiply 3 X ---- = ----- (4)(X) = (3)(8) 4 8 5. Solve 4X= 24 X= 24/4 X= 6 You will need 6 liters of water for 8 lemons.

  40. Solve this Problem 3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

  41. The answer is 1 gallon of paint for 300 square feet.

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