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

2. Percents: ratios that compare a number to 100.
Think of the % symbol as meaning per 100 or / % = 75/100 = 0.75
Reading Math

3. Fraction  decimal: divide the numerator by the denominator1 8
= 1 ÷ 8 = 0.125
decimal  percent: multiply by 100 (move decimal 2 places to the right) and write %
0.125  100  12.5%

4. 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% =

5. 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%

6. 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% =

7. 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%

8. 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 =

9. 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 =

10. 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% =

11. Example 2: Comparing Fractions, Decimals, and Percents
A. 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!

12. Example 2: Comparing Fractions, Decimals, and Percents
B. Compare. Write <, >, or =. %
0.893 = 89.3%
Write as a percent.
89.3% > 50%
Compare.
0.893 > 50%

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

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

15. 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%

16. 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%

17. 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.

18. 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
>
<

19. 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%