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

2. Course 3 6-1 Relating Decimals, Fractions, and Percents Warm Up Evaluate. 1.2. 3.4. 1 3 1 3 + 14 2 15 3 – 7 12 3 4 5 7 2 1 2 3 1 4  4 5 2 14 5 or

3. Course 3 6-1 Relating Decimals, Fractions, and Percents 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. Course 3 6-1 Relating Decimals, Fractions, and Percents Learn to compare and order decimals, fractions, and percents.

5. Course 3 6-1 Relating Decimals, Fractions, and Percents Vocabulary percent

6. Course 3 6-1 Relating Decimals, Fractions, and Percents Percents are ratios that compare a number to 100. Ratio Equivalent Ratio with Denominator of 100Percent 3 10 1 2 3 4 30 100 50 100 75 100 30% 50% 75%

7. Course 3 6-1 Relating Decimals, Fractions, and Percents Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75 Reading Math

8. Course 3 6-1 Relating Decimals, Fractions, and Percents 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%

9. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1: Finding Equivalent Ratios and Percents 1 10 a:a:10% = 10 100 =

10. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1 Continued b:b:0.25 = 1 4 = 25%

11. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1 Continued c:c:40% = 40 100 = 2 5 4 10 =

12. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1 Continued d:d:0.60 = 3 5 = 60%

13. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1 Continued e:e: 2 3 % = 66 0.666 = 2 3

14. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1 Continued f:f: 1 2 % = 87 0.875 = 7 8 875 1000 =

15. Course 3 6-1 Relating Decimals, Fractions, and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. Additional Example 1 Continued g:g:125% = 125 100 = 5 4 = 1 4 1

16. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Find the missing ratio or percent equivalent for each letter a–g on the number line. a:a: 1 2 % = 12 0.125 = 1 8 125 1000 = c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

17. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Continued b:b:25% = 25 100 = 1 4 Find the missing ratio or percent equivalent for each letter a–g on the number line. c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

18. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Continued c:0.375 = 3 8 = 37 % 1 2 Find the missing ratio or percent equivalent for each letter a–g on the number line. c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

19. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Continued d:d:50% = 50 100 = 1 2 Find the missing ratio or percent equivalent for each letter a–g on the number line. c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

20. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Continued e:e:0.625 = 5 8 = 62 % 1 2 Find the missing ratio or percent equivalent for each letter a–g on the number line. c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

21. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Continued f:f:75% = 75 100 = 3 4 Find the missing ratio or percent equivalent for each letter a–g on the number line. c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

22. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 1 Continued g:g:1 = 100 = 100% Find the missing ratio or percent equivalent for each letter a–g on the number line. c ab e d 50%12 % f g 3838 25% 1212 5858 75% 1

23. Course 3 6-1 Relating Decimals, Fractions, and Percents Additional Example 2A: Comparing Fractions, Decimals, and Percents Compare. Write, or =. 40% 1414 1414 = 0.25 = 25% 25% < 40% Write as a percent. Compare. 1414 < 40% When multiplying a decimal by 100, simply move the decimal point two spaces to the right. Remember!

24. Course 3 6-1 Relating Decimals, Fractions, and Percents Additional Example 2B: Comparing Fractions, Decimals, and Percents Compare. Write, or =. 0.893 50% 0.893 = 89.3% 89.3% > 50% Write as a percent. Compare. 0.893 > 50%

25. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 2A Compare. Write, or =. 65% 3434 3434 = 0.75 = 75% 75% > 65% Write as a percent. Compare. 3434 > 65%

26. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 2B Compare. Write, or =. 0.136 20% 0.136 = 13.6% 13.6% < 20% Write as a percent. Compare. 0.136 < 20%

27. Course 3 6-1 Relating Decimals, Fractions, and Percents Additional Example 3: Ordering Fractions, Decimals, and Percents Write 0.075%,, 0.41, and 100% in order from least to greatest. 3434 3434 = 0.75 = 75% 0.41 = 41% Write as percents. Compare. 3434 0.075% < 41% < 75% < 100% 0.075%, 0.41,, 100%

28. Course 3 6-1 Relating Decimals, Fractions, and Percents Check It Out: Example 3 Write 35%, 0.25,, and 200% in order from least to greatest. 1212 1212 = 0.50 = 50% 0.25 = 25% Write as percents. Compare. 1212 25% < 35% < 50% < 200% 0.25, 35%,, 200%

29. Course 3 6-1 Relating Decimals, Fractions, and Percents 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? Additional Example 4: Physical Science Application Set up a ratio and reduce. parts pure gold total parts 14 24 7 12 = 7 = 7  12 = Find the percent. 0.583 = 58.3% 1 3 So 14-karat gold is 58.3%, or 58 % pure gold.

30. Course 3 6-1 Relating Decimals, Fractions, and Percents 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? Check It Out: Example 4 Set up a ratio and reduce. items eaten total items 1 13 1 = 1  13 = Find the percent. 0.077 = 7.7% The baker eats 7.7% of the items they bake.

31. Course 3 6-1 Relating Decimals, Fractions, and Percents 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 > 3 8 7 11 1 5 5 8

32. Course 3 6-1 Relating Decimals, Fractions, and Percents Lesson Quiz: Part 2 6. Write 245%,, 0.133, and 66.6% in order from least to greatest. 5. About 342,000 km 2 of Greenland’s total area (2,175,000 km 2 ) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice? 16% 0.133,, 66.6%, 245% 1 5 1 5