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

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

3. Percent: Ratio that compares a number to 100.

4. Fraction 3/4 Decimal 0.75 Percent 75% Read It (3 ÷ 4) Write It 4 3
Solve It .75
Write the percent as a fraction over Then simplify.
Move the decimal 2 times to the left.
Move the decimal 2 times to the right.

5. 0.25 0.83 5.67 3.33 87.9 34.85 Change the fraction to a decimal: 2. 1.6.
Change the fraction to a decimal: 1. 3. 5.
Continue…….

6. Change decimals to percents
Continue…….

7. Change percents to decimals.
Continue…….

8. Change percents to fractions.
Continue…….

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

24. Additional Example 2B: Comparing Fractions, Decimals, and Percents
Compare. Write <, >, or =. %
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
= = 75%
Write as a percent.
75% > 65%
Compare. 3 4
> 65%

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

27. Additional Example 3: Ordering Fractions, Decimals, and Percents4
Write 0.075%, , 0.41, and 100% in order
from least to greatest. 3 4
= = 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
= = 50%
Write as percents.
0.25 = 25%
25% < 35% < 50% < 200%
Compare. 1 2
0.25, 35%, , 200%

29. 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?
parts pure gold
total parts 14 24 7 12 =
Set up a ratio and reduce. 7 12 =
7  12 =
0.583 =
58.3%
Find the percent. 1 3
So 14-karat gold is 58.3%, or % pure gold.

30. 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?
items eaten
total items 1 13
Set up a ratio and reduce. 1 13 =
1  13 
0.077 
7.7%
Find the percent.
The baker eats about 7.7% of the items they bake.

31. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 31

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

33. Lesson Quiz: Part II
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? 1 5 1 5
0.133, , 66.6%, 245%
16%

34. Lesson Quiz for Student Response Systems5 9
1. Identify the equivalent value of as a percent.
A. 45.3%
B. 55.5%
C. 78.3%
D. 86.5% 34

35. Lesson Quiz for Student Response Systems
2. Identify the equivalent value of 45% as a fraction. A. B. C. D. 35

36. Lesson Quiz for Student Response Systems3 8
3. Identify the equivalent value of as a decimal. A B C D 36

37. Lesson Quiz for Student Response Systems
4. Identify the correct symbol to compare.
0.430___50%
A. >
B. <
C. =
D. > 37