chapter six percents and their applications copyright © 2014 by the mcgraw-hill companies, inc. all...

Chapter SixPERCENTS AND THEIR APPLICATIONS

Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

6-2

LU 6-1: Conversions

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

2. Convert percents to fractions.LU 6-2: Application of Percents—Portion Formula

3. List and defi ne the key elements of the portion formula.

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

5. Calculate the rate of percent decreases and increases.

LEARNING UNIT OBJECTIVES

6-3

TABLE 6.1 - BAG OF M&M’S

Decimal PercentColor Fraction (hundredth)

(hundredth)

Yellow 18 .33 32.73% 55

Red 10 .18 18.18% 55

Blue 9 .16 16.36% 55Orange 7 .13 12.73%

55Brown 6 .11 10.91%

55Green 5 .09 9.09% 55Total 55 1.00 100.00% 55 = 1

6-4

CONVERTING DECIMALS TO PERCENTS

.66 66 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.

Step 1 Step 2 Step 1 Step 2

% %

6-5

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.

Step 3. Delete digits to the right of the identified digit.

1

%17

.0588235

6-6

ROUNDING PERCENTS

18 55 .3272727

32.73%

32.73727%

55 18.000000 =

Step 1

Step 2

Step

3

6-7

CONVERTING PERCENTS TO DECIMALS

66%

8.244824.4%

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.

66 .66

824.4

6-8

CONVERTING FRACTIONAL PERCENTS TO DECIMALS

.0775

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).

7 %3 4.0025

1

%4

1 / 4 = 31 / 4 = .25

07.75

6-9

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%153 / 4 = 1 / 5 =

.75 .20

6-10

CONVERTING A WHOLE PERCENT (OR A FRACTIONAL PERCENT) TO A

FRACTION

156%

1

Step 1. Drop the percent symbol.

Step 2. Multiply the number by 1/100.

Step 3. Reduce to lowest terms.

1800

1425

156 156 X 1 /100 =156 100

= 1 56 100

181%

8 1 X8

1 /100 =

6-11

CONVERTING PERCENTS TO DECIMALS

12.5%18

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

25 2

X 1

100=1

2

12 %

= 25200

=

= 12

12 %

=25 2

X 1

100

= 25200

=

6-12

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)

6-13

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

6-14

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®?

Portion Rate

$320,000 .80

B = $400,000

Base =

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

Base =

6-15

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 =

6-16

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.

6-17

RATE OF PERCENT INCREASE

Rate = Portion Base

2.40 oz 16.00 oz

Rate = .15 or 15% increase

Sheila Leary went to her local supermarket and bought a bag ofM&M’s®. 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.

Rate =

Difference between old and new amountOld amount

6-18

RATE OF PERCENT DECREASE

Rate = Portion Base

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?

4 oz 16.00 ozRate =

Difference between old and new amountOld amount