1. Percents and Their Applications
Chapter 6
Percents and Their Applications

2. Learning Unit Objectives#6
Percent and Their Applications
Learning Unit Objectives
LU6.1
Conversions
Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents
Convert percents to fractions

3. Learning Unit Objectives#6
Percent and Their Applications
Learning Unit Objectives
LU6.2
Application of Percents -- Portion Formula
List and define the key elements of the portion formula
Solve for one unknown of the portion formula when the other two key elements are given
Calculate the rate of percent decreases and increases

4. Table 6.1 - Bag of M&M’s Decimal Percent
Color Fraction (hundredth) (hundredth)
Yellow % 55
Red %
Blue %
Orange %
Brown %
Green %
Total %
55 = 1

5. Converting Decimals to Percents
Step 1. Move decimal point 2 places to the right. You are multiplying by If necessary add zeros.
Step 2. Add a percent symbol at the end of the number
.66
66% 8
800%

6. Converting Decimals to Percents
Step 1. Move decimal point 2 places to the right. You are multiplying by If necessary add zeros.
.42.5
.425
42.5%

7. Rounding Percents
Step 1. When you convert from a fraction or decimal, be sure your answer is in percent before rounding.
Step 2. Identify the specific digit. If the digit to the right of the identified digit is 5 or greater, round the identified digit.
Delete digits to the right of the identified digit.
1 % 17
5.88%

8. Rounding Percents .3272727 Step 1 55 18.000000 = Step 2 18 55=
Step 2 18 55 %
Step 3
32.73%

9. Converting Percents to Decimals
Step 1. Drop the percent symbol.
Step 2. Move decimal point 2 places to the left, You are dividing by If necessary add zeros.
824.4%
66%
8.244
.66

10. Converting Percents to Decimals
Drop the percent symbol and move the decimal point 2 places to the left.
.95
.00.95
.95%
.0095

11. Converting Fractional Percents to Decimals
Step 1. Convert a single fraction percent to its decimal equivalent by dividing the numerator by the denominator.
Step 2. If a fractional percent is combined with a whole number ( mixed fractional percent) convert the fractional percent first. Then combine the whole number and the fractional percent.
Step 3. Drop the percent symbol; move the decimal point two places to the left (this divides the number by 100). 3 4
7 %
1 % 4
.0775
.0025

12. Converting Fractional Percents to Decimals
Step 1
.20% =
Step 2
1 % 5
.00.20
Step 3
.0020

13. Converting Fractions to Percents
Step 1. Divide the numerator by the denominator to convert the fraction to a decimal.
Step 2. Move decimal point 2 places to the right; add the percent symbol. 1 5
20% 3 4
75%

14. Converting Fractions to Percents
.05
Step 1 =
Step 2 1 20
.05.
Step 3 5%

15. Converting a Whole Percent (or a Fractional Percent) to a Fraction
Step 1. Drop the percent symbol.
Step 2. Multiply the number by 1/100.
Step 3. Reduce to lowest terms 1% 8
156% 14 15 1
800 1

16. Converting a Whole Percent (or a Fractional Percent) to a Fraction
76 x 1
100
Step 1
Step 2
76% 76
100
Reduce to lowest terms 19 25
Step 3

17. Converting Percents to Decimals
Step 1. Drop the percent symbol.
Step 2. Change the mixed percent to an improper fraction.
Step 3. Multiply the number by 1/100
Step 4. Reduce to lowest terms
Note: If you have a mixed or decimal percent, change the decimal portion to fractional equivalent and continue with Steps 1 to 4.
12.5%
12 1/2% 1 8 1 8

18. Converting a Mixed or Decimal Percent to a Fraction1 2 22
Step 1
Step 2
45 x = 45
22.5%
Reduce to lowest terms 9 40
Step 3

19. Application of Percents - Portion Formula
Portion (P) = Base (B) x Rate (R)
Assume you received a small bonus check of $100 and your company did not withhold any taxes. Compute taxes assuming a 20% in tax rate.
Portion “is”
Base “of”
Rate “%”

20. Portion (P)= Base (B) x Rate (R)
Solving for Portion
Sales of Milk Chocolate M&M’s® are 80% of total M&M’s® sales. Total M&M’s® sales are $400,000. What are the sales of Milk Chocolate M&M’s®?
Portion (P)= Base (B) x Rate (R)
P = $400,000 x .80
P = $320,000

21. Solving for Rate
Sales of Milk Chocolate M&M’s® are 320,000. Total M&M’s® sales are $400,000. What is the percent of Milk Chocolate M&M’s® sales compared to total M&M’s® sales?
Rate = Portion
Base
R = $320, 000
$400,000
R = 80%

22. Solving for Base
Sales of Peanut and other M&M’s® chocolate candies are 20% of total M&M’s® sales. Sales of Milk Chocolate M&M’s® sales are $320,000. What are the total sales of all M&M’s®?
320,000 is 80% of base ( )
Base = Portion
Rate
B = $320,000
.80
B = $400,000

23. Calculating Percent Decreases and Increases
Step 1. Find the difference between amounts (such as advertising costs).
Step 2. Divide step 1 by the original amount (the base): R = P / B. Be sure to express your answer in percent.

24. Rate of Percent Decrease
Original Price $1,500
Rate = Portion Diff . between old and new TV price
Base Old TV amount
Rate = $600 ($1,500-$900)
$1,500
Rate = .40 or 40% Decrease
New Price $900

25. Rate of Percent Increase
Original Price $1,000
Rate = Portion Diff . between old and new TV price
Base Old TV amount
Rate = $200 ($1,200-$1,000)
$1,000
Rate = .20 or 20% Decrease
New Price $1,200

26. Problem 6-59:
Solution:
$30.50
$4.50
= %

27. Problem 6-61:
Solution:
$24,500 x 1.15 = $28,175

28. Problem 6-67:
Solution:
$19.95
$49.95
= 39.94%