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Math 8

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

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Math 8

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

  2. Unit 5: Percent, Ratio, and Rate 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. Unit 5: Percent, Ratio, and Rate 5.1 Relating Fractions, Decimals, and Percents

  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 • 0.57 • 0.4 • 0.01 • 1.25

  12. Homework

  13. Unit 5: Percent, Ratio, and Rate 5.2 Calculating Percents

  14. 5.2 Calculating Percents • Focus: Calculate percents from 0% to greater than 100%

  15. 5.2 Calculating Percents • Percent – a ratio out of one hundred 50% is the same as 50 out of 100 or

  16. 5.2 Calculating Percents • 10% is the same as 10 out of one hundred is the same as

  17. 5.2 Calculating Percents Percent • 0 < X < 100% less than one, smaller than original

  18. 5.2 Calculating Percents Percent • X = 100% same as original

  19. 5.2 Calculating Percents Percent • X > 100% more than one, greater than original • 160% is one a six tenths

  20. 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

  21. What is 15% of 60?

  22. What is 115% of 60?

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

  24. The tax is $1.25

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

  26. 2nd method • Determine the total without calculating the tax first.

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

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

  29. Homework

  30. Unit 5: Percent, Ratio, and Rate 5.3 Solving Percent Problems

  31. 5.3 Solving Percent Problems • Focus: Find the whole, when given a percent, and find the percent increase and decrease

  32. Remember • All percents are fractions out of 100

  33. 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.

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

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

  36. Unit 5: Percent, Ratio, and Rate 5.4 Sales Tax and Discount

  37. 5.4 Sales Tax and Discount • Focus: Investigate the use of percent in consumer math

  38. 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

  39. 5.4 Sales Tax and Discount • In Alberta PST is 6%. • Method 1 Method 2 The tax is $11.94. The total cost is $ 210.94. The total cost is $ 210.94.

  40. 5.4 Sales Tax and Discount • In BC the PST is 7% and GST is 6%. Each is independent. Calculate PST 7% The total cost is $222.87. The PST is $13.93. GST is $11.94

  41. 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 total cost is $225.71. The original plus GST is $210.94.

  42. 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.

  43. Unit 5: Percent, Ratio, and Rate 5.5 Exploring Ratios

  44. 5.5 Exploring Ratios • Focus: Used models and diagrams to investigate ratios

  45. 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

  46. 5.5 Exploring Ratios • Option 1 – A $1275 dress at 75% off The first dress costs $318.75.

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