1. 6-1 Relating Fractions, Decimals, and Percents NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications. California Standards

2. 6-1 Relating Fractions, Decimals, and Percents Percents are ratios that compare a number to 100. RatioDecimalPercent 30% 50% 75% 3 10 30 100 = 1 2 50 100 = 3 4 75 100 = 0.30 0.50 0.75

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

4. 6-1 Relating Fractions, Decimals, 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%

5. 6-1 Relating Fractions, Decimals, and Percents Find the missing fraction or percent equivalent for each letter a–g on the number line. Additional Example 1: Finding Equivalent Fractions and Percents 1 10 a:a:10% = 10 100 =

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

7. 6-1 Relating Fractions, Decimals, and Percents Additional Example 1 Continued c:c:40% = 40 100 = 2 5 4 10 = Find the missing fraction or percent equivalent for each letter a–g on the number line.

8. 6-1 Relating Fractions, Decimals, and Percents Additional Example 1 Continued d:d:0.60 = 3 5 = 60% Find the missing fraction or percent equivalent for each letter a–g on the number line.

9. 6-1 Relating Fractions, Decimals, and Percents Additional Example 1 Continued e:e: 2 3 % = 66 0.666 = 2 3 Find the missing fraction or percent equivalent for each letter a–g on the number line.

10. 6-1 Relating Fractions, Decimals, and Percents Additional Example 1 Continued f:f: 1 2 % = 87 0.875 = 7 8 875 1000 = Find the missing fraction or percent equivalent for each letter a–g on the number line.

11. 6-1 Relating Fractions, Decimals, and Percents Additional Example 1 Continued g:g:125% = 125 100 = 5 4 = 1 4 1 Find the missing fraction or percent equivalent for each letter a–g on the number line.

12. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 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 Find the missing fraction or percent equivalent for each letter a–g on the number line.

13. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 Continued b:b:25% = 25 100 = 1 4 Find the missing fraction 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

14. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 Continued c:0.375 = 3 8 = 37 % 1 2 Find the missing fraction 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

15. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 Continued d:d:50% = 50 100 = 1 2 Find the missing fraction 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

16. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 Continued e:e:0.625 = 5 8 = 62 % 1 2 Find the missing fraction 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

17. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 Continued f:f:75% = 75 100 = 3 4 Find the missing fraction 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. 6-1 Relating Fractions, Decimals, and Percents Check It Out! Example 1 Continued g:g:1 = 100 = 100% Find the missing fraction 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. 6-1 Relating Fractions, Decimals, 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!

20. 6-1 Relating Fractions, Decimals, 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%

21. 6-1 Relating Fractions, Decimals, 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%

22. 6-1 Relating Fractions, Decimals, 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%

23. 6-1 Relating Fractions, Decimals, 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 the numbers in the same form. Compare. 3434 0.075% < 41% < 75% < 100% 0.075%, 0.41,, 100%

24. 6-1 Relating Fractions, Decimals, 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 the numbers in the same form. Compare. 1212 25% < 35% < 50% < 200% 0.25, 35%,, 200%

25. 6-1 Relating Fractions, Decimals, 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. What percent of 14 karat gold is pure gold? Additional Example 4: Physical Science Application Set up a ratio and simplify. 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.

26. 6-1 Relating Fractions, Decimals, 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 simplify. 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.