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

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

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

Learn to relate decimals, fractions, and percents.

Vocabulary percent

Equivalent Ratio with Denominator of 100 Percents are ratios that compare a number to 100. Ratio Equivalent Ratio with Denominator of 100 Percent   3 10 30 100 30% 1 2 50 100 50% 3 4 75 100 75%

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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%.

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

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? parts pure gold total parts 14 24 7 12 = Set up a ratio and reduce. 7 12 = 7  12 = 0.583 = 58.3% Find the percent. 1 3 So 14-karat gold is 58.3%, or 58 % pure gold.

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. What percent of the food does the baker eat? items eaten total items 1 13 Set up a ratio and reduce. 1 13 = 1  13 = 0.077 = 7.7% Find the percent. The baker eats 7.7% of the items they bake.

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? 3 8 37.5% 1 5 5 8 0.625 14 25 56% 16%