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Understanding Fractions, Decimals, and Percents

Learn how to determine and construct fractions, decimals, and percents, and solve problems involving their relationships, unknowns, increase and decrease, sales tax, total cost, and simple interest.

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Understanding Fractions, Decimals, and Percents

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  1. Pre-Algebra Homework Page 402-403 #1-16 & Spiral Review

  2. Our Learning Goal Students will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest.

  3. Our Learning Goal Assignments • Learn to relate decimals, fractions, & percents (8-1) • Learn to find percents (8-2) • Learn to find a number when the percent is known (8-3) • Learn to find percent increase and decrease (8-4) • Learn to estimate with percents (8-5) • Learn to find commission, sales tax, and withholding tax (8-6) • Learn to compute simple interest (8-7)

  4. Learning Goal ScaleStudents are able to determine & construct fractions, decimals, & percents:

  5. Student Learning Goal Chart

  6. Relating Decimals, Fractions, and Percents 8-1 Warm Up Problem of the Day Lesson Presentation Pre-Algebra

  7. Relating Decimals, Fractions, and Percents 8-1 3 7 7 4 2 1 3 1 4 14 1 1 12 5 15 15 12 2 4 5 5 2 3 3 2 3 or Pre-Algebra Warm Up Evaluate. 1. 2. 3. 4. – + 14 

  8. Problem of the Day A fast-growing flower grows to a height of 12 inches in 12 weeks by doubling its height every week. If you want your flower to be only 6 inches tall, after how many weeks should you pick it? 11 weeks

  9. Today’s Learning Goal Assignment Learn to relate decimals, fractions, and percents.

  10. Vocabulary percent

  11. 3 30 50 75 10 100 100 100 1 2 3 4 Percents are ratios that compare a number to 100. 30% 50% 75%

  12. Reading Math Think of the % symbol as meaning /100. 0.75 = 75% = 75/100

  13. 1 = 1 ÷ 8 = 0.125 8 To convert a fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percent, multiply by 100 and insert the percent symbol. 0.125 100 12.5%

  14. 1 10 10 = 100 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. a: 10% =

  15. 1 = 4 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. b: 0.25 = 25%

  16. 2 4 5 10 = 40 = 100 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. c: 40% =

  17. 3 = 5 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. d: 0.60 = 60%

  18. 2 66 0.666 = 2 % = 3 3 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. e:

  19. 1 87 7 % = 875 2 8 = 1000 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 0.875 = f:

  20. 5 1 4 4 1 = 125 = 100 Additional Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. g: 125% =

  21. 1 2 5 8 3 8 1 12 1 % = 125 2 8 = 1000 Try This: Example 1 Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f 0.125 = a:

  22. 1 4 5 8 1 2 3 8 25 = 100 Try This: Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f b: 25% =

  23. 1 2 5 8 1 2 3 8 3 = 8 Try This: Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f c: 0.375 = 37 %

  24. 1 2 5 8 1 2 3 8 50 = 100 Try This: Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f d: 50% =

  25. 1 2 5 8 1 2 3 8 5 = 8 Try This: Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f e: 0.625 = 62 %

  26. 3 4 5 8 1 2 3 8 75 = 100 Try This: Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f f: 75% =

  27. 5 8 1 2 3 8 100 100 Try This: Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e c 12 % 25% 50% 75% g 1 a b d f 100% = g: 1 =

  28. 3 7 19 3 19 7 = 0.12 = 0.38 38 15 35 = 0.35 25 20 20 20 50 50 100 100 100 = = = 3 25 Additional Example 2: Finding Equivalent Fractions, Decimals, and Percents Find the equivalent fraction, decimal, or percent for each value given on the circle graph. 0.15(100) = 15% 0.12(100) = 12%

  29. Additional Example 2 Continued You can use information in each column to make three equivalent circle graphs. One shows the breakdown by fractions, one shows the breakdown by decimals, and one shows the breakdown by percents. The sum of the fractions should be 1. The sum of the decimals should be 1. The sum of the percents should be 100%.

  30. 1 9 1 5 10 20 45 25 45 100 100 100 1 1 = 4 5 Try This: Example 2 Fill in the missing pieces on the chart below. 0.1(100) = 10% =0.45 =0.25 0.25(100) = 25% = 0.2 0.2(100) = 20%

  31. parts pure gold = total parts 0.583 = 58.3% = 1 7 7 14 So 14-karat gold is 58.3%, or 58 % pure gold. 3 12 12 24 Additional Example 3: Physical Science Application Gold that is 24 karat is 100% pure gold. Gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper, zinc, silver, or nickel. What percent of 14 karat gold is pure gold? Set up a ratio and reduce. 7  12 = Find the percent.

  32. items eaten total items = 1 1 13 13 Try This: Example 3 A baker’s dozen is 13. When a shopper purchases a dozen items at the bakery they get 12. It is said that the baker eats 1 item from every batch. So, what percentage of the food the baker cooks is eaten without being sold? Set up a ratio and reduce. 0.077 = 1  13 = 7.7% Find the percent. So the baker, eats 7.7% of the items they bake.

  33. 3 5 8 8 1 5 14 25 Lesson Quiz Find each equivalent value. 1. as a percent 2. 20% as a fraction 3. as a decimal 4. as a percent 5. About 342,000 km2 of Greenland’s total area (2,175,000 km2) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice? 37.5% 0.625 56% 16%

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