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Relating Decimals, Fractions, and Percents 8.1 Pre-Algebra Warm Up Evaluate. 1. 2 + 3 1 2. 7 – 3 1 15 15 3 12 12 3 3. 4 7 14 or 2 4 4. 1 1 14 3 5 2 5 5 2 4 Learn to relate decimals, fractions, and percents. Vocabulary percent Percents are ratios that compare a number to 100. Equivalent Ratio with Ratio Percent Denominator of 100 3 30 10 100 30% 1 50 100 50% 2 3 75 100 75% 4 Reading Math Think of the % symbol as meaning /100. 0.75 = 75% = 75/100 To convert a fraction to a decimal, divide the numerator by the denominator. 1 = 1 ÷ 8 = 0.125 8 To convert a decimal to a percent, multiply by 100 and insert the percent symbol. 0.125 100 12.5% Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 10 1 a: 10% = = 100 10 Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 b: = 0.25 = 25% 4 Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 40 4 2 c: 40% = = = 100 10 5 Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 3 d: = 0.60 = 60% 5 Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 2 2 e: 66 %= 0.666 = 3 3 Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 875 f: 87 %= 0.875 = = 7 2 1000 8 Example: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 125 5 1 g: 125% = = = 1 100 4 4 Try This Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 125 a: 12 1 % = 0.125 = = 1 2 1000 8 Try This Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 25 1 b: 25% = = 100 4 Try This Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 3 1 c: = 0.375 = 37 % 8 2 Try This Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 50 1 d: 50% = = 100 2 Try This Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 5 1 e: = 0.625 = 62 % 8 2 Try This Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 75 3 f: 75% = = 100 4 Try This Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 c e 12 % 25% 50% 75% g 2 5 1 a b 3 d f 8 8 100 100% g: 1 = = 100 Example: Finding Equivalent Fractions, Decimals, and Percents Find the equivalent fraction, decimal, or percent for each value given on the circle graph. Fraction Decimal Percent 15 = 3 0.15 0.15(100) = 15% 100 20 35 = 7 7 = 0.35 100 20 35% 20 38 19 19 = 0.38 = 38% 100 50 50 3 3 = 0.12 25 0.12(100) = 12% 25 Example 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 The sum of the The sum of the fractions should decimals should percents should be 1. be 1. be 100%. Try This Fill in the missing pieces on the chart below. Fraction Decimal Percent 1 0.1(100) = 10% 10 0.1 45 = 9 45 =0.45 45% 100 20 100 1 25 =0.25 0.25(100) = 25% 4 100 1 1 = 0.2 5 0.2(100) = 20% 5 Example: 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? parts pure gold 14 = 7 Set up a ratio and total parts 24 12 reduce. 7 = 7 12 = 0.583 = 58.3% Find the percent. 12 1 So 14-karat gold is 58.3%, or 58 3 % pure gold. Try This 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? items eaten 1 Set up a ratio and total items 13 reduce. 1 = 1 13 = 0.077 = 7.7% Find the percent. 13 So the baker, eats 7.7% of the items they bake. Lesson Quiz Find each equivalent value. 1. 3 as a percent 37.5% 8 1 2. 20% as a fraction 5 5 3. as a decimal 0.625 8 4. 14 as a percent 56% 25 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? 16%