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Formula Fun: Converting Fractions, Decimals, and Percentages

Learn how to convert fractions into decimals, decimals into percentages, and fractions into percentages with Formula Fun! Also, discover how to calculate percent change and use scales in the real world.

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Formula Fun: Converting Fractions, Decimals, and Percentages

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  1. Formula Fun! The Same What?! Weigh it on your . . . Percent Challenge Teacher’s Choice 1 pts 1 pts 1 pts 1 pts 1 pts 2 pts 2 pts 2 pts 2 pts 2 pts 3 pts 3 pts 3 pts 3 pts 3 pts 4 pts 4 pts 4 pts 4 pts 4 pts 5 pts 5 pts 5 pts 5 pts 5 pts

  2. Formula Fun! How do you convert a fraction into a decimal? • AnswerBack to Board

  3. How do you convert a fraction into a decimal? Divide the numerator by the denominator. • Back to Board

  4. Formula Fun! How do you convert from a decimal to a percent? • AnswerBack to Board

  5. How do you convert from a decimal to a percent? Multiply the decimal by 100 (move the decimal point two “spaces” to the right). • Back to Board

  6. Formula Fun! How do you convert from a fraction to a percent? (provide at least 1 example) • AnswerBack to Board

  7. How do you convert from a fraction to a percent? (provide at least 1 example) Divide the numerator by the denominator and then multiply by 100. Set up a proportion - set your fraction equal to x over 100 and solve for x. (Examples may vary) • Back to Board

  8. Formula Fun! How do you calculate percent change? • Answer Back to Board

  9. How do you calculate percent change? Use the following formula: %∆ = new - original * 100 original • Back to Board

  10. Formula Fun! What pieces of information do you need to know in order to calculate your grade? • Answer Back to Board

  11. What pieces of information do you need to know in order to calculate your grade? • The grading scale • Your average in each category Or • The total possible points • The points earned • Back to Board

  12. The Same What?! List 3 equivalent fractions to the following decimal: 0.5 • AnswerBack to Board

  13. List 3 equivalent fractions to the following decimal: 0.5 Answers may vary • Back to Board

  14. The Same What?! Convert 100% into 4 different fractions. • AnswerBack to Board

  15. Convert 100% into 4 different fractions. Answers may vary • Back to Board

  16. The Same What?! Solve for x in the following equation: 50 . x . 100 = 25 • AnswerBack to Board

  17. Solve for x in the following equation: x = 12.5 • Back to Board

  18. The Same What?! While shopping, I bought a dress that was 15% off, what part of the dress did I actually pay for? • AnswerBack to Board

  19. While shopping, I bought a dress that was 15% off, what part of the dress did I actually pay for? You paid for 85% of the dress. • Back to Board

  20. The Same What?! How can you prove that the NYC Subway Map is not drawn to scale? • AnswerBack to Board

  21. How can you prove that the NYC Subway Map is not drawn to scale? Measure the distance between two stops on the map and compare it to the distance between those two stops in the real world. Measure the distance between two different stops on the map and compare it to the distance between those two stops in the real world. Compare these proportions, they are most likely not equivalent. If they are, repeat process until you find a discrepancy. It should not take long! • Back to Board

  22. Weigh it on your . . . Give an example of where we see scales in the real world. • AnswerBack to Board

  23. Give an example of where we see scales in the real world. • Maps • Blueprints • Instruction manuals • Crime shows • Math Class . . . (not really the real world!) • Back to Board

  24. Weigh it on your . . . Translate the following into a flowing sentence: 1cm : 5 miles • AnswerBack to Board

  25. Translate the following into a flowing sentence:1cm : 5 miles 1 centimeter on the map is equivalent to 5 miles in the real world. • Back to Board

  26. Weigh it on your . . . State the scale given the following information: “5 centimeters on my map is equivalent to 25 kilometers in the real world.” • AnswerBack to Board

  27. State the scale given the following information:“5 centimeters on my map is equivalent to 25 kilometers in the real world.” • 5 cm : 25 km or • 1 cm : 5 km • Back to Board

  28. Weigh it on your . . . I need to make a scaled drawing of the NYC subway map for math class . . . I’ve decided that 1 cm : 1 block. How many centimeters should I put between 42nd Street and 50th Street? • AnswerBack to Board

  29. I need to make a scaled drawing of the NYC subway map for math class . . . I’ve decided that 1 cm : 1 block. How many centimeters should I put between 42nd Street and 50th Street? 8 centimeters • Back to Board

  30. Weigh it on your . . . You are making a blueprint drawing of a 6 foot by 10 foot room using a scale of .5 inches : 1 foot. What are the dimensions of your blueprint drawing? • AnswerBack to Board

  31. You are making a blueprint drawing of a 6 foot by 10 foot room using a scale of .5 inches : 1 foot. What are the dimensions of your blueprint drawing? .5inches * 6 feet = 3 inches 1 foot _______________ .5inches * 10 feet = 5 inches 1 foot ________________ 3 inches by 5 inches • Back to Board

  32. Percent Challenge I want to leave a 20% tip on a $10 bill, how much money should I leave? • AnswerBack to Board

  33. I want to leave a 20% tip on a $10 bill, how much money should I leave? $10 * .20 = $2 $2 + $10 = $12 • Back to Board

  34. Percent Challenge I saved $30 yesterday after taking advantage of a 50% off sale! What was the price of my original item? • AnswerBack to Board

  35. I saved $30 yesterday after taking advantage of a 50% off sale! What was the price of my original item? Let x be the original price of the item. .50 * x = $30 .50 * x = $30 .50 .50 x = $60 • Back to Board

  36. Percent Challenge A television is on sale for $900. If the sale price is 10 % less than the regular price, what was the regular price? Give your answer to the nearest one hundredth. • Answer Back to Board

  37. A television is on sale for $900. If the sale price is 10 % less than the regular price. What was the regular price? Give your answer to the nearest one hundredth. Let x be the regular price of the item. If you got 10% off, you paid for 90% of the item. .90 * x = $900 .90 * x = $900 .90 .90 x = $1000 • Back to Board

  38. Percent Challenge My real estate agent told me that my house had appreciated in value over the last three years. In other words, it has gone from being worth $102,500 to being worth $111,000. What is the percent increase in the value of my house? • AnswerBack to Board

  39. My real estate agent told me that my house had appreciated in value over the last three years. In other words, it has gone from being worth $102,500 to being worth $111,000. What is the percent increase in the value of my house? Original worth: $102,500 New worth: $111,000 Percent Change = new – original = 111,000 – 102,500 = 8,500 = .083 original 102,500 102,500 The value of my house has increased by 8.3%! • Back to Board

  40. Percent Challenge I’m starting a new job on Monday. In my old job, my hours were 9:00am to 5:00pm Monday through Friday. My new hours are 10:00am to 7:00pm Monday through Thursday. What is the percent change in my weekly work commitment? • Answer Back to Board

  41. I’m starting a new job on Monday. In my old job, my hours were 9:00am to 5:00pm Monday through Friday. My new hours are 10:00am to 7:00pm Monday through Thursday. What is the percent change in my weekly work commitment? Old job: 8 hours/day * 5 days/week = 40 hours/week New job: 9 hours/day * 4 days/week = 36 hours/week Percent Change = new – original = 36 – 40 = -4 = - 10% original 40 40 My new job provides me with a 10% decrease in my weekly hours! • Back to Board

  42. Teacher’s Choice Explain the logic behind grading to the following student: “How is it possible that I got A’s on all of my math tests . . . 90%’s on all of my quizzes . . . And yet I only have a C in math class?!” • AnswerBack to Board

  43. “How is it possible that I got A’s on all of my math tests . . . 90%’s on all of my quizzes . . . And yet I only have a C in math class?!” Something to the effect of: “You probably didn’t do any of your homework, were disruptive in class, and didn’t take your projects that seriously!” Lesson learned . . . • Back to Board

  44. Teacher’s Choice Under what circumstances would you expect to see a percent increaseversus a percentdecrease? • AnswerBack to Board

  45. Under what circumstances would you expect to see a percent increaseversus a percentdecrease? I would expect to see a percent increase when my new value is larger than my original. I would expect to see a percent decreasewhen my new value is smaller than my original. • Back to Board

  46. Teacher’s Choice Under what circumstances would you want a high interest rate, and under what circumstances would you want a low interest rate? • AnswerBack to Board

  47. Under what circumstances would you want a high interest rate, and under what circumstances would you want a low interest rate? You would want a high interest rate if you are the one loaning the money (to a bank, to your friend, etc). You would want a low interest rate if you are the one borrowing the money (from your credit card company, from mortgage lender, etc.) • Back to Board

  48. Teacher’s Choice If you want to write your own percent change problem, what elements do you DEFINITELY need to have? • AnswerBack to Board

  49. If you want to write your own percent change problem, what elements do you DEFINITELY need to have? Some initial value and some new value. • Back to Board

  50. Teacher’s Choice Make an argument in support or against the following: “There is no such thing as 110%!” • AnswerBack to Board

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