6-1

1. Relating Decimals, Fractions, and Percents 6-1 Course 3 Warm Up Problem of the Day Lesson Presentation

2. 7 1 7 4 3 3 2 1 4 1 14 1 15 4 12 12 15 2 5 3 5 3 2 5 2 3 or Warm Up Evaluate. 1. 2. 3. 4. – + 14 

3. 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

4. Learn to compare and order decimals, fractions, and percents.

5. Vocabulary percent

6. 3 30 50 75 10 100 100 100 1 2 3 4 Percents are ratios that compare a number to 100. 30% 50% 75%

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

8. 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%

9. 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% =

10. 1 = 4 Additional Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. b: 0.25 = 25%

11. 2 4 5 10 = 40 = 100 Additional Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c: 40% =

12. 3 = 5 Additional Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. d: 0.60 = 60%

13. 2 66 0.666 = 2 % = 3 3 Additional Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. e:

14. 1 87 7 % = 875 2 8 = 1000 Additional Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 0.875 = f:

15. 5 1 4 4 1 = 125 = 100 Additional Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. g: 125% =

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

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

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

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

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

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

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

23. Remember! When multiplying a decimal by 100, simply move the decimal point two spaces to the right. Additional Example 2A: Comparing Fractions, Decimals, and Percents Compare. Write <, >, or =. 40% 1 4 1 4 = 0.25 = 25% Write as a percent. 25% < 40% Compare. 1 4 < 40%

24. Additional Example 2B: Comparing Fractions, Decimals, and Percents Compare. Write <, >, or =. 0.893 50% 0.893 = 89.3% Write as a percent. 89.3% > 50% Compare. 0.893 > 50%

25. Check It Out: Example 2A Compare. Write <, >, or =. 65% 3 4 3 4 = 0.75 = 75% Write as a percent. 75% > 65% Compare. 3 4 > 65%

26. Check It Out: Example 2B Compare. Write <, >, or =. 0.136 20% 0.136 = 13.6% Write as a percent. 13.6% < 20% Compare. 0.136 < 20%

27. Additional Example 3: Ordering Fractions, Decimals, and Percents 3 4 Write 0.075%, , 0.41, and 100% in order from least to greatest. 3 4 = 0.75 = 75% Write as percents. 0.41 = 41% 0.075% < 41% < 75% < 100% Compare. 3 4 0.075%, 0.41, , 100%

28. Check It Out: Example 3 1 2 Write 35%, 0.25, , and 200% in order from least to greatest. 1 2 = 0.50 = 50% Write as percents. 0.25 = 25% 25% < 35% < 50% < 200% Compare. 1 2 0.25, 35%, , 200%

29. 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 4: 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.

30. items eaten total items = 1 1 13 13 Check It Out: Example 4 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? Set up a ratio and reduce. 0.077 = 1  13 = 7.7% Find the percent. The baker eats 7.7% of the items they bake.

31. 3 5 8 8 1 5 7 11 Lesson Quiz: Part 1 Find each equivalent value. 1. as a percent 2. 20% as a fraction 3. as a decimal Compare. Write <, >, or =. 4. 30% 5. 0.650 97% 37.5% 0.625 > <

32. 1 5 1 5 Lesson Quiz: Part 2 6. Write 245%, , 0.133, and 66.6% in order from least to greatest. 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? 0.133, , 66.6%, 245% 16%