The document provides examples and explanations for converting between fractions, decimals, and percentages. It includes steps for converting a fraction to a decimal by dividing the numerator by the denominator, and converting a decimal to a percentage by multiplying by 100. Examples are provided for finding equivalent fractions and percentages on a number line, comparing fractions, decimals and percentages, and ordering fractions, decimals and percentages from least to greatest.

1. Warm Up California Standards Lesson Presentation Preview

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

3. NS1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications . California Standards

4. Vocabulary percent

5. Percents are ratios that compare a number to 100. 30% 50% 75% 0.30 0.50 0.75 Percent Decimal Ratio 3 10 30 100 = 1 2 50 100 = 3 4 75 100 =

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

7. 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 % 1 8 = 1 ÷ 8 = 0.125

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

23. 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%

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

25. 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%

26. Additional Example 3: Ordering Fractions, Decimals, and Percents Write 0.075%, , 0.41, and 100% in order from least to greatest. 3 4 3 4 = 0.75 = 75% 0.41 = 41% Write the numbers in the same form. Compare. 3 4 0.075% < 41% < 75% < 100% 0.075%, 0.41, , 100%

27. Check It Out! Example 3 Write 35%, 0.25, , and 200% in order from least to greatest. 1 2 1 2 = 0.50 = 50% 0.25 = 25% Write the numbers in the same form. Compare. 1 2 25% < 35% < 50% < 200% 0.25, 35%, , 200%

28. 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. 7  12 = Find the percent. parts pure gold total parts 14 24 7 12 = 7 12 = 0.583 = 58.3% 1 3 So 14-karat gold is 58.3%, or 58 % pure gold.

29. 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. 1  13  Find the percent. 0.077  7.7% The baker eats about 7.7% of the items they bake. items eaten total items 1 13 1 13 =

30. 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

31. 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