1. 8-1 Relating Decimals, Fractions, and Percents Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra

2. 8-1 Relating Decimals, Fractions, and Percents Warm Up 1. 2. 3. 4. 2
Pre-Algebra
8-1
Relating Decimals, Fractions, and Percents
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

3. 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. Learn to relate decimals, fractions, and percents.

5. Vocabulary
percent

6. Equivalent Ratio with Denominator of 100
Percents are ratios that compare a number to 100.
Ratio
Equivalent Ratio with Denominator of 100
Percent 3 10 30
100
30% 1 2 50
100
50% 3 4 75
100
75%

7. Think of the % symbol as meaning /100.
0.75 = 75% = 75/100
Reading Math

8. 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. 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: Finding Equivalent Ratios and Percents
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: Finding Equivalent Ratios and Percents
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: Finding Equivalent Ratios and Percents
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: Finding Equivalent Ratios and Percents
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: Finding Equivalent Ratios and Percents
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: Finding Equivalent Ratios and Percents
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. Try This: Example 1
Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 2
12 %
25% c
50% e
75% g 5 8 3 8 a b d f 1 1 2
% = 12
125
1000 = 1 8 a:
0.125 =

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

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

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

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

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

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

23. Fraction Decimal Percent
Additional Example 2: Finding Equivalent Fractions, Decimals, and Percents
Find the equivalent fraction, decimal, or percent for each value given on the circle graph.
Fraction
Decimal
Percent
 0.15
35%
38%  3 20 15
100 =
0.15(100) = 15% 7 20 35
100 = 7 20
= 0.35 19 50 38
100 = 19 50
= 0.38 3 25 3 25
= 0.12
0.12(100) = 12%

24. Additional Example 2 Continued
You can use information in each column to make three equivalent circle graphs. One shows the breakdown by fractions, one shows the breakdown by decimals, and one shows the breakdown by percents.
The sum of the fractions should be 1.
The sum of the decimals should be 1.
The sum of the percents should be 100%.

25. Try This: Example 2
Fill in the missing pieces on the chart below.
Fraction
Decimal
Percent
 0.1
45% 1 10
0.1(100) = 10% 45
100 9 20 = 45
100
=0.45 1 4 25
100
=0.25
0.25(100) = 25% 1 5 1 5
= 0.2
0.2(100) = 20%

26. Additional Example 3: 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.

27. Try This: Example 3
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. So, what percentage of the food the baker cooks is eaten without being sold?
items eaten
total items 1 13
Set up a ratio and reduce. 1 13 =
1  13 =
0.077 =
7.7%
Find the percent.
So the baker, eats 7.7% of the items they bake.

28. Lesson Quiz
Find each equivalent value.
1. as a percent
2. 20% as a fraction
as a decimal
as a percent
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? 3 8 5 8 14 25