Chapter 06

Percents and Their Percents and Their ApplicationsApplications

McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

6-2

1. Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents

2. Convert percents to fractions

Percent and Their Applications#6#6Learning Unit ObjectivesConversionsLU6.1LU6.1

6-3

1. List and define the key elements of the portion formula

2. Solve for one unknown of the portion formula when the other two key elements are given

3. Calculate the rate of percent decreases and increases

Percent and Their Applications#6#6Learning Unit ObjectivesApplication of Percents -- Portion FormulaLU6.2LU6.2

6-4

Table 6.1 - Bag of M&M’s

Decimal PercentColor Fraction (hundredth) (hundredth)

YellowYellow 18 .33 32.73% 55

RedRed 10 .18 18.18% 55

BlueBlue 9 .16 16.36% 55OrangeOrange 7 .13 12.73%

55BrownBrown 6 .11 10.91%

55GreenGreen 5 .09 9.09% 55TotalTotal 55 1.00 100.00% 55 = 1

6-5

Converting Decimals to Percents

.6666%

8 800%

Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros.

Step 2. Add a percent symbol at the end of the number

6-6

Converting Decimals to Percents

.425

.42.5

42.5%

Step 1. Move decimal point 2 places to the right. You are multiplying by 100. If necessary add zeros.

6-7

Rounding Percents

.0588235

5.88%

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

.0588235

6-8

Rounding Percents

18 55

.3272727

32.73%

32.73727%

55 18.000000

=

Step 1 Step 2

Step 3

6-9

Converting Percents to Decimals

66%.66 8.244

824.4%

Step 1. Drop the percent symbol.

Step 2. Move decimal point 2 places to the left, You are dividing by 100. If necessary add zeros.

6-10

Converting Percents to Decimals

.4%

.4

.00.4

.004

Drop the percent symbol and move the decimal point 2 places to the left.

6-11

Converting Fractional Percents to Decimals

.0025.0775

7 %

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

3 4

6-12

Converting Fractional Percents to Decimals

1 %5

.20%

.00.20

.0020

5 1.00 =

Step 1

Step 2

Step 3

6-13

Converting Fractions to Percents

34 75%

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.

20%15

6-14

Converting Fractions to Percents

120

.05

.05.

5%

20 1.00 =Step 1

Step 2

Step 3

6-15

Converting a Whole Percent (or a Fractional Percent) to a Fraction

156%1

1%8

Step 1. Drop the percent symbol.

Step 2. Multiply the number by 1/100.

Step 3. Reduce to lowest terms

1800

1415

6-16

Converting a Whole Percent (or a Fractional Percent) to a Fraction

76%

76 x 1 100

76100

19 25

Reduce

to lowest

term

s

Step 1

Step 2

Step 3

6-17

Converting Percents to Decimals

12.5%

18

12 1/2%

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.

18

6-18

Converting a Mixed or Decimal Percent to a Fraction

22.5% 45 x 1 = 45 2 100 200

1 2

9 40

Reduce to lowest term

s

22

Step 1 Step 2

Step 3

6-19

Application of Percents - Portion Formula

Portion (P) = Base (B) x Rate (R)

Portion “is”

Base “of” Rate “%”

Base: 100% - whole. Usually given after theword of – but not always $100 – Bonus check

Rate: Usually expressed as a percent but couldalso be a decimal or fraction. 20% taxes

Portion: A number – not a percent and not thewhole $20 taxes

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.

6-20

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

6-21

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%

6-22

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®?

Base = Portion Rate

B = $320,000 .80

B = $400,000

320,000 is 80% of base (1.00 - .20)

6-23

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.

6-24

Rate of Percent Increase

Rate = Portion Diff . between old and new TV price

Base Old TV amount

Rate = 2.40 oz 16.00 oz

Rate = .15 or 15% Increase

Sheila Leary went to her local supermarket and bought the bag ofM&M’s® shown in Figure 6.1. The bag gave its weight as 18.40 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.

6-25

Rate of Percent Decrease

Rate = Portion Diff . between old and new TV price

Base Old TV amount

Rate = 4 oz. 16.00 oz

Rate = .25 or 25% 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?

6-26

Problem 6-59:

Solution:

$30.50 $4.50

= 677.78%

6-27

Problem 6-61:

Solution:

540= .06 = 6%

9000

6-28

Problem 6-67:

Solution:

2,500 x .36 = 900 people from out of state