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

2. Relating Fractions, Decimals, and Percents 6-1 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. Relating Fractions, Decimals, and Percents 6-1 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. Relating Fractions, Decimals, and Percents 6-1 Prep for MA.8.A.6.4 Perform operations on real numbers (including…percents…)… Review MA.6.A.5.1 Review MA.6.A.5.2 Sunshine State Standards

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

6. Relating Fractions, Decimals, and Percents 6-1 Percents are ratios that compare a number to 100.

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

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

26. Relating Fractions, Decimals, and Percents 6-1 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. Relating Fractions, Decimals, and Percents 6-1 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. Relating Fractions, Decimals, and Percents 6-1 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. Relating Fractions, Decimals, and Percents 6-1 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. Relating Fractions, Decimals, and Percents 6-1 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 about 7.7% of the items they bake.

31. Relating Fractions, Decimals, and Percents 6-1 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

32. Relating Fractions, Decimals, and Percents 6-1 Lesson Quiz: Part I 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

33. Relating Fractions, Decimals, and Percents 6-1 Lesson Quiz: Part II 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

34. Relating Fractions, Decimals, and Percents 6-1 1. Identify the equivalent value of as a percent. A. 45.3% B. 55.5% C. 78.3% D. 86.5% Lesson Quiz for Student Response Systems 5 9

35. Relating Fractions, Decimals, and Percents 6-1 2. Identify the equivalent value of 45% as a fraction. A. B. C. D. Lesson Quiz for Student Response Systems

36. Relating Fractions, Decimals, and Percents 6-1 3. Identify the equivalent value of as a decimal. A. 0.252 B. 0.375 C. 0.456 D. 0.698 Lesson Quiz for Student Response Systems 3 8

37. Relating Fractions, Decimals, and Percents 6-1 4. Identify the correct symbol to compare. 0.430___50% A. > B. < C. = D. > Lesson Quiz for Student Response Systems