Lecture Practical business math procedures (11/e) - Chapter 6: Percents and their applications

After completing this chapter, students will be able to: Convert decimals to percents (including rounding percents), percents to decimals, and fractions to percents; convert percents to fractions; 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.

Chapter Six Percents and Their

Applications

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 define 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

Table 6.1 - Bag of M&M’s

Decimal Percent

Yellow 18 .33 32.73%

55

55

55

Orange 7 .13 12.73%

55

Brown 6 .11 10.91%

55

Green 5 .09 9.09%

55

Converting Decimals to Percents

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

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

Rounding Percents

18

32.73%

32.73727%

55 1 8.0 000

00 =

Ste p 1

Ste

p 2

St ep 3

Converting Percents to Decimals

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

824.4

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

.25

07.75

Converting Fractions to Percents

3

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%

1 5

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

1 800

14 25

156 156 X 1 /100 =

156

100 = 1 56 100

1 8

8 1 /100 =

Converting Percents

to Decimals

12.5%

1 8

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.

1 8

25

2 X 1

100 =

=

25

200 =

= 12 12 %

= 25 2 X

1

= 25

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)

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)

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 =

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 Rate =

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.

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 of

M&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 amount

Old amount

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 oz Rate =

Difference between old and new amount Old amount