1. Percents and Their Applications
Chapter Six
McGraw-Hill/Irwin
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.

2. Learning unit objectives
LU 6-1: Conversions
Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents.
Convert percents to fractions.
LU 6-2: 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.

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

4. 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.
800 %
.66 66 % 8
Step 2
Step 2
Step 1
Step 1

5. 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.
Step 3. Delete digits to the right of the identified digit.
1 % 17
5.88%

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

7. 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.
66% 66
.66
824.4%
824.4
8.244

8. 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).
1 % 4
7 % 3 4
1 / 4 =
.0025
31 / 4 =
.25
.0775
07.75

9. 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. 3 4 1 5
75%
3 / 4 =
1 / 5 =
20%
.75
.20

10. 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.
156%
156
156 X 1 /100 = 14 25
156
100 56
100 1
= 1 1% 8 1 8 1
800
1 X 8
1 /100 =

11. 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 1 2
% = 25 2
X 1
100 = 1 8 25
200 = 12 1 2
% =
12.5% = 25 2
X 1
100 = 1 8 25
200 =

12. Solve Percents with the Portion Formula
When solving problems involving portion, base, or rate, you must give two of these elements.
Portion (P) = Base (B) x Rate (R)

13. 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

14. 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 ( )
Portion
Rate
$320,000
.80
B = $400,000
Base =
Base =

15. 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?
Portion
Base
$320, 000
$400,000
R = 80%
Rate =
Rate =

16. 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.

17. Rate of Percent Increase
Sheila Leary went to her local supermarket and bought a bag of
M&M’s®. The bag gave its weight as ounces, which was 15% more than a regular 1-pound bag of M&M’s®. Sheila, who is a careful shopper, wanted to check and see if she was actually getting a 15% increase.
Rate = Portion
Base
Difference between old and new amount
Old amount
2.40 oz
16.00 oz
Rate =
Rate = .15 or 15% increase

18. Rate of Percent Decrease
The increase in the price of sugar caused the M&M/Mars company to decrease the weight of each 1-pound bag of M&M’s® to 12 ounces. What is the rate of percent decrease?
Rate = Portion
Base
Difference between old and new amount
Old amount
4 oz
16.00 oz
Rate =
Rate = .25 or 25% decrease