1. Math 8 Unit 5: Percent, Ratio, and Rate

2. What you’ll learn: Understand percents greater than or equal to 0% Solve problems that involve percents Understand ratios Understand rates Solve problems that involve ratios and rates

3. Unit 5: Percent, Ratio, and Rate Why it’s important: Used when shopping to compare prices Used when determining prices Used in science (chemistry and physics)

4. 5.1 RELATING FRACTIONS, DECIMALS, AND PERCENTS Unit 5: Percent, Ratio, and Rate

5. 5.1 Relating Fractions, Decimals, and Percents Focus: Given a fraction, decimal or percent calculate the other two forms

6. Fraction – a ratio of one number to another – Very useful for showing parts of a whole – Unless the denominators are the same it is difficult to compare fractions – Must be reduced to lowest numbers Three out of a total of four squares are coloured in One out of a total of four squares are NOT coloured in

7. Decimal – number that shows a ratio based on fractions out of tenths, hundredths, thousandths, etc... – Very easy to compare 75 out of one hundred squares are coloured 25 out of one hundred squares are NOT coloured

8. Percent – a fraction out of 100 – 100% is one whole Seventy five percent of the squares are coloured Twenty five percent of the squares are NOT coloured

9. Ex. Convert the fractions to decimals a. b. c. d.

10. Ex. Convert the decimals to percent a. 0.23 b. 0.5 c. 0.03 d. 1.23

11. Ex. Convert decimal to fraction a.0.57 b.0.4 c.0.01 d.1.25

12. Homework

14. 5.2 CALCULATING PERCENTS Unit 5: Percent, Ratio, and Rate

15. 5.2 Calculating Percents Focus: Calculate percents from 0% to greater than 100%

16. 5.2 Calculating Percents Percent – a ratio out of one hundred 50% is the same as 50 out of 100 or

17. 5.2 Calculating Percents 10% is the same as 10 out of one hundred is the same as

18. 5.2 Calculating Percents Percent 0 < X < 100% less than one, smaller than original

19. 5.2 Calculating Percents Percent X = 100% same as original

20. 5.2 Calculating Percents Percent X > 100% more than one, greater than original 160% is one a six tenths

21. 5.2 Calculating Percents For calculations with percent use cross multiplication Ex. What is 60% of 50? X is to 60 as 50 is to 100 Cross multiply Divide by 100 to isolate X Answer

22. What is 15% of 60?

23. What is 115% of 60?

24. Percents are used for sales and taxes. A Blu-Ray costs $25. What is the tax (5%)? How much will you pay in total?

25. The tax is $1.25

26. The total cost is the original cost plus the tax.

27. 2 nd method Determine the total without calculating the tax first.

28. Ex. A sale says 20% off of a $25 Blu-ray The sale discount is $5 off the price. Sale Price = Original – Sale Discount = $25 - $5 = $20 The sale price is $20.

29. Sale Price = Original – Sale Discount = 100% - 20% = 80% The sale price is $20.

30. Homework

32. 5.3 SOLVING PERCENT PROBLEMS Unit 5: Percent, Ratio, and Rate

33. 5.3 Solving Percent Problems Focus: Find the whole, when given a percent, and find the percent increase and decrease

34. Remember All percents are fractions out of 100

35. 50% of a class is girls. There are 14 girls in the class. How many students are in the class. ????? There are 28 students in the class.

36. Double check There are 14 girls out of a class of 28 students. Is this 50%?

37. An item on sale costs $40. The sale is 20% off. What is the pre-sale cost? The pre-sale cost is $50.

39. 5.4 SALES TAX AND DISCOUNT Unit 5: Percent, Ratio, and Rate

40. 5.4 Sales Tax and Discount Focus: Investigate the use of percent in consumer math

41. 5.4 Sales Tax and Discount Use page 256 in your textbook. A student buys an iPod in Alberta for $199. How much does is it cost after tax? http://store.storeimages.cdn-apple.com/2773/as- images.apple.com/is/image/AppleInc/step0-touch-gallery- image1?wid=500&hei=440&fmt=png-alpha&qlt=95

42. 5.4 Sales Tax and Discount In Alberta PST is 6%. Method 1Method 2 The tax is $11.94. The total cost is $ 210.94.

43. 5.4 Sales Tax and Discount In BC the PST is 7% and GST is 6%. Each is independent. Calculate PST 7% The PST is $13.93. GST is $11.94 The total cost is $222.87.

44. 5.4 Sales Tax and Discount In Quebec the GST 6% and the is PST is 7% on top of GST. Calculate cost plus GST 6% The original plus GST is $210.94. The total cost is $225.71.

45. 5.4 Sales Tax and Discount Notice: The cost in BC is $222.87 The cost in Quebec is $225.71 Quebec costs more because the PST is charged on the original price plus the GST. Everywhere the rules for taxes are different.

47. 5.5 EXPLORING RATIOS Unit 5: Percent, Ratio, and Rate

48. 5.5 Exploring Ratios Focus: Used models and diagrams to investigate ratios

49. 5.5 Exploring Ratios What is a better deal? Option 1 – A $1275 dress at 75% off Option 2 – A $400 dress at 25% off

50. 5.5 Exploring Ratios Option 1 – A $1275 dress at 75% off The first dress costs $318.75.

51. 5.5 Exploring Ratios Option 2 – A $400 dress at 25% off The second dress costs $300.

52. 5.5 Exploring Ratios Homework

54. 5.6 EQUIVALENT RATIOS Unit 5: Percent, Ratio, and Rate

55. 5.6 Equivalent Ratios Focus: Write equivalent ratios

56. 5.6 Equivalent Ratios Equivalent Ratios – Two ratios that are the same Example: 1:3 and 2:6 are the same.

57. 5.6 Equivalent Ratios A walker travels at 1.0 m/s. The ratio of distance to time will be the same. Time (s)Distance (m) 0 1 3 7 13

58. 5.6 Equivalent Ratios A jogger travels at 2.0 m/s. The ratio of distance to time will be the same. Time (s)Distance (m) 0 1 3 7 13

59. 5.6 Equivalent Ratios A runner travels at 7.5 m/s. The ratio of distance to time will be the same. Time (s)Distance (m) 0 1 3 7 13

60. 5.6 Equivalent Ratios A student checks his piggy bank. The ratio of twoonies to loonies is 1:3. http://upload.wikimedia.org/wikipedia/en/thu mb/d/d2/Toonie_-_front.png/220px-Toonie_- _front.png http://media.mmgdailies.topscms.com/images /bd/15/19a700bc412cbc6404f223e6fa0b.jpeg How many coins could be in the piggy bank? What are the possible values of the coins in the piggy bank?

61. 5.6 Equivalent Ratios Homework

62. 5.7 COMPARING RATIOS Unit 5: Percent, Ratio, and Rate

63. 5.7 Comparing Ratios Focus: Use different strategies to compare ratios

64. 5.7 Comparing Ratios A recipe for 3 people’s pancakes requires 1.5 cups of flour. How many cups of flour are required for 12 people? How many cups of flour are required for 4 people? Which was easier? http://www.clubfrancophone.com/images/coo king_metric_measurements.gif

65. 5.7 Comparing Ratios The ratio is 3 people : 1.5 cups 12 people need 6 cups.

66. 5.7 Comparing Ratios The ratio is 3 people : 1.5 cups 4 people need 2 cups. Rounding makes this less accurate

67. 5.7 Comparing Ratios Two different pizza companies advertise the pepperoniest pizza in town. To test students order pizzas from each and count the pepperoni. A – Two large pizzas had 8 slices each and a total of 80 pepperonis. B – Three large pizzas had 10 slices each and a 135 pepperonis total. How many pepperonis are there per slice?

68. 5.7 Comparing Ratios A – Two large pizzas had 8 slices each and a total of 80 pepperonis.

69. 5.7 Comparing Ratios B – Three large pizzas had 10 slices each and a 135 pepperonis total. Company A has more pepperonis per slice. It has the pepperoniest pizza.

70. Homework

72. 5.8 SOLVING RATIO PROBLEMS Unit 5: Percent, Ratio, and Rate

73. 5.8 Solving Ratio Problems Focus: Set up a proportion to solve a problem

74. 5.8 Solving Ratio Problems There are three feet in a yard. A football player carries the ball 5 yards. How many feet is that? One yard

75. 5.8 Solving Ratio Problems Draw it out Five yards is fifteen feet. One yardTwo yardThree yardFour yard Five yard

76. 5.8 Solving Ratio Problems One inch is the same as 2.54 centimetres. Mr. Montgomery is 74 inches tall. How many cm is this?

77. 5.8 Solving Ratio Problems One inch is the same as 2.54 centimetres. Mr. Montgomery is 74 inches tall. How many cm is this? Mr. Montgomery is 187.96 cm tall.

78. 5.8 Solving Ratio Problems An Albertan drives down to the United States. The speed limit is 60 miles per hour. 1 mile is the same as 1.609 km. What is the legal speed limit in miles per hour?

79. 5.8 Solving Ratio Problems An Albertan drives down to the United States. The speed limit is 60 miles per hour. 1 mile is the same as 1.609 km. What is the legal speed limit in miles per hour? The speed limit 60 miles per hour is the same as 96.54 km/h.

80. 5.8 Solving Ratio Problems Homework

81. 5.9 EXPLORING RATES Unit 5: Percent, Ratio, and Rate

82. 5.9 Exploring Rates Focus: Use models and diagrams to investigate rates

83. 5.9 Exploring Rates Rates are ratios out of one. – They are very useful for comparisons and measurements.

85. 5.10 COMPARING RATES Unit 5: Percent, Ratio, and Rate

86. 5.10 Comparing Rates Focus: Use unit rates to compare rates

87. 5.10 Comparing Rates The fastest man in the world title is traditionally given to the fastest runner of the 100 m dash. In 1996 Donovan Bailey (Canadian) ran 100 m in 9.84 s. Michael Johnson (USA) ran 200 m in 19.32 s. Who ran the fastest?

88. 5.10 Comparing Rates Donovan Bailey Michael Johnson Michael Johnson covered more metres in one second than Donovan Bailey. Is this a fair comparison? http://www.youtube.com/watch?v=id8v-yTK5Do

89. 5.10 Comparing Rates At a store you can buy two 2 litre bottles of Pepsi (4000 ml) for $3.75 or you can by six 355 ml cans (2130 ml) for $3.00. Which is the better buy? http://www.totuckshop.ca/images/pepsi%202 L.jpg http://www.infobarrel.com/media/image/305. jpg

90. 5.10 Comparing Rates 2 L bottles Six pack The 2litre bottles are the better buy because you get more Pepsi per dollar. Method 1

91. 5.10 Comparing Rates 2 L bottles Six pack The 2litre bottles are the better buy because they cost less per millilitre. Method 2

92. 5.10 Comparing Rates Homework