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Contemporary Mathematics FOR BUSINESS AND CONSUMERS Brechner
Percents and Their
Applications in Business
PowerPoint Presentation by Domenic Tavella, MBA
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
1
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PERFORMANCE OBJECTIVES
Section I
Understanding and Converting Percents
6-1:
Converting percents to decimals and decimals to percents
6-2:
Converting percents to fractions and fractions to percents
Section II
Using the Percentage Formula to Solve Business
Problems
6-3:
Solving for the portion
6-4:
Solving for the rate
6-5:
Solving for the base
Section III Solving Other Business Problems Involving Percents
6-6:
Determining rate of increase or decrease
6-7:
Determining amounts in increase or decrease situations
6-8:
Understanding and solving problems involving percentage
points
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
2
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Understanding and Converting
Percents
percent
• A way of representing the part of a whole. Percent
means “per hundred” or “parts per hundred.”
percent sign
• The symbol, %, used to represent percents.
• For example, 1 percent would be written 1%.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
3
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STEPS
FOR CONVERTING A PERCENT TO A DECIMAL
STEP 1 Remove the percentage sign.
STEP 2 Divide by 100.
Note: If the percent is a fraction, such as 3/8% or a mixed
number such as 4 ¾ %, change the fraction to a decimal;
then follow Steps 1 and 2 above.
3/8% = .375% = .00375
4 ¾% = 4.75% = .0475
Note: If the percent is a fraction such as 2/3%, which converts to
a repeating decimal, .66666, round the decimal to
hundredths, .67; then follow Steps 1 and 2 above.
2/3% = .67% = .0067
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a publicly accessible website, in whole or in part.
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Converting Percents to Decimals
Example
37%
.37
12.5%
.125
7 ¼ % = 7.25%
.0725
.04%
.0004
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a publicly accessible website, in whole or in part.
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STEPS
FOR CONVERTING A DECIMAL OR WHOLE
NUMBER TO A PERCENT
STEP 1 Multiply by 100.
STEP 2 Write a percent sign after the number.
STEP 3 If there are fractions involved, such as ¾, convert
them to decimals first; then proceed with Steps 1
and 2 above.
¾ = .75 = 75%
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
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Converting Decimals to Percents
Example
2.9
290%
.83½ = .835
83.5%
.00827
.827%
6.24
624%
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a publicly accessible website, in whole or in part.
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STEPS
FOR CONVERTING PERCENTS TO FRACTIONS
STEP 1
Remove the percent sign.
STEP 2
(If the percent is a whole number) Write a fraction
with the percent as the numerator and 100 as the
denominator. If that fraction is improper, change it to
a mixed number. Reduce the fraction to lowest terms.
or
STEP 2
(If the percent is a fraction) Multiply the number by
1/100 and reduce to lowest terms.
or
STEP 2
(If the percent is a decimal) Convert it to a fraction
and multiply by 1/100. Reduce to lowest terms.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
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Converting Percents to Fractions
Example
5
1


5%
100
20
1
75 1
75
3

37





37.5%
100 2 100 200 8
1
2
62 1 %  62 1  1  125  1  125  5
2
100
2 100 200 8
2
.8%
8
1
8
 

 1
10 100 1000 125
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a publicly accessible website, in whole or in part.
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Converting Percents to Fractions
Example
continued
230
30
 2 100
 2 103
230% 
100
450
50
 4 100

450% 
100
4 12
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a publicly accessible website, in whole or in part.
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STEPS
FOR CONVERTING FRACTIONS TO PERCENTS
STEP 1 Change the fraction to a decimal by dividing the
numerator by the denominator.
STEP 2 Multiply by 100. (Move the decimal point two
places to the right. Add zeros as needed.)
STEP 3 Write a percent sign after the number.
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
11
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Converting Fractions to Percents
Example
3
 .75  75%
4
12
 2 52  2.4 
5
240%
125
 1 14  1.25 
100
125%
78
 3 14  3.25  325%
24
4 15  4.2  420%
©2014 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to
a publicly accessible website, in whole or in part.
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Using the Percentage Formula to
Solve Business Problems
base
• The variable of the percentage formula that
represents 100%, or the whole thing.
portion
• The variable of the percentage formula that
represents a part of the base.
rate
• The variable of the percentage formula that
defines how much or what part the portion is of the
base. The rate is the variable with the percent
sign.
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a publicly accessible website, in whole or in part.
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STEPS
FOR SOLVING PERCENTAGE PROBLEMS
STEP 1 Identify the two knowns and the unknown.
STEP 2 Choose the formula that solves for the unknown.
STEP 3 Solve the equation by substituting the known values
for the letters in the formula.
Hint:
By remembering one basic formula, P = R × B, you
can derive the other two by using your knowledge
of solving equations from Chapter 5. Because
multiplication is indicated, we isolate the unknown
by performing the inverse, or opposite, operation,
division.
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a publicly accessible website, in whole or in part.
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STEPS
FOR SOLVING PERCENTAGE PROBLEMS
continued
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a publicly accessible website, in whole or in part.
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Percentage Problem Example
Maritza Torres owns 37% of the family
restaurant.
If the total worth of the business is
$160,000.00. How much is Maritza’s share?
P  R  B  .37  160,000  $59,200.00
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a publicly accessible website, in whole or in part.
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Percentage Problem Example
continued
What is the sales tax in a state where the tax
on a purchase of $464 is $25.52?
P 25.52
R 
 .055  5.5%
B
464
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a publicly accessible website, in whole or in part.
17
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Percentage Problem Example
continued
The Daily Times reports that 28% of its advertising is
for mobile telephone services.
If the mobile telephone advertising amounts to
$46,200, what is the total advertising revenue of the
newspaper?
P 46,220
B 
 $165,071.43
R
0.28
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a publicly accessible website, in whole or in part.
18
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Percentage Problem Example
continued
Geri Carroll, a sales associate for a large company,
successfully makes the sale on 40% of her sales
presentations.
If she made 25 presentations last week, how many
sales did she make?
P  R  B  .4  25  10
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a publicly accessible website, in whole or in part.
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Percentage Problem Example
continued
A quality control process finds 17.2 defects
for every 8,600 units of production.
What percent of the production is defective?
P 17.2
R 
 .002  0.2%
B 8,600
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a publicly accessible website, in whole or in part.
20
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Percentage Problem Example
continued
The Torryville Tigers have won 80% of their
basketball games. If they lost 4 games, how
many games have been played?
Won = 80%
Lost = 20%
P
4
B 
 20
.2
R
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a publicly accessible website, in whole or in part.
21
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STEPS
FOR DETERMINING THE RATE OF INCREASE OR
DECREASE
STEP 1 Identify the original and the new amounts and find
the difference between them.
STEP 2 Using the rate formula R = P ÷ B, substitute the
difference from Step 1 for the portion and the
original amount for the base.
STEP 3 Solve the equation for R. Remember, your answer
will be in decimal form, which must be converted
to a percent.
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a publicly accessible website, in whole or in part.
22
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Rate of Increase or Decrease
Example
Allied Plumbing sold 2,390 feet of 5/8-inch galvanized
pipe in July. If 2,558 feet were sold in August, what is
the percent increase in pipe footage sales?
P  Increase  2,558  2,390  168
B  Original Amount  2,390
P
168
R 
 .07  7%
B 2,390
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a publicly accessible website, in whole or in part.
23
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Rate of Increase or Decrease
Example
continued
The supermarket price of yellow onions dropped from
$.59 per pound to $.45 per pound. What is the percent
decrease in the price of onions?
P  Decrease  $0.59  $0.45  $0.14
B  Original Amount  $0.59
P .14
R 
 .2372  23.72%
B .59
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a publicly accessible website, in whole or in part.
24
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STEPS
FOR DETERMINING THE NEW AMOUNT AFTER A
PERCENT CHANGE
STEP 1 In the formula Portion = Rate × Base, substitute the
original amount, or starting point, for the base.
STEP 2 If the rate change is an increase, add that rate to
100% to get the rate.
or
STEP 2 If the rate change is a decrease, subtract that rate
from 100% to get the rate.
STEP 3 Solve the equation for the portion.
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a publicly accessible website, in whole or in part.
25
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Determining the New Amount
After a Percent Change Example
Economists predict that next year housing
prices will drop by 4%. This year’s price for
an average house is $110,000. What will the
average price of a house be next year?
Rate  100%  4%  96%
Base  Original Amount  110,000
P  R  B  .96  110,000  $105,600.00
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a publicly accessible website, in whole or in part.
26
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STEPS
FOR DETERMINING THE ORIGINAL AMOUNT
BEFORE A PERCENT CHANGE
STEP 1 In the formula Base = Portion ÷ Rate, substitute the
new amount for the portion.
STEP 2 If the rate change is an increase, add that rate to
100% to get the rate.
or
STEP 2 If the rate change is a decrease, subtract that rate
from 100% to get the rate.
STEP 3 Solve the equation for the base.
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a publicly accessible website, in whole or in part.
27
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Determining the Original Amount
Before a Percent Change Example
City Auto sold 112 cars this month. If this is
40% better than last month, how many cars
were sold last month?
Portion  112
Rate  100%  40%  140%  1.4
P
112
B 

 80 cars
R
1.4
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Determining the Original Amount
Before a Percent Change Example
continued
The second shift of a factory produced 17,010
units. If this amount was 5 ½% less than the
first shift, how many units were produced on
the first shift?
Portion  17,010
Rate  100%  5 12 %  94 12 %  .945
P 17,010
B 
 18,000 units
R
.945
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a publicly accessible website, in whole or in part.
29
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Problems Involving Percentage
Points
percentage points
• A way of expressing a change from an original
amount to a new amount without using a
percentage sign.
Change in percentage points
Rate of
=
change
Original amount of percentage points
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a publicly accessible website, in whole or in part.
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Problems Involving Percentage
Points Example
After a vigorous promotion campaign, Erie
Electronics increased its market share from
5.4% to 8.1%, a rise of 2.7 percentage points.
What percent increase in market share does
this represent?
Portion  Increase  2.7%  .027
Base  5.4%  .054
P
.027
Rate of change 

 .5  50%
B
.054
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Problems Involving Percentage
Points Example
continued
The unemployment rate in Glen Haven
dropped from 8.8% to 6.8% in the past year, a
decrease of 2 percentage points. What
percent decrease does this represent?
Portion  Decrease  2.0%  .020
Base  8.8%  .088
P
.020
Rate of change 

 .2272  22.72%
B
.088
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a publicly accessible website, in whole or in part.
32
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CHAPTER REVIEW PROBLEM 1
Solve the following by converting to
decimals:
.89
89%
.26%
.0026
9 ¾% = 9.75
.0975
23
5
%
4 53 %  4.6%  .046
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a publicly accessible website, in whole or in part.
33
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CHAPTER REVIEW PROBLEM 2
An ad read, “This week only, all merchandise
35% off!” If a television set normally sells for
$349.95, what is the amount of the savings?
Rate  35%
Base  Original Amount  349.95
P  R  B  .35  349.95  122.48
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a publicly accessible website, in whole or in part.
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CHAPTER REVIEW PROBLEM 3
If 453 runners out of 620 completed a
marathon, what percent of runners finished
the race?
Portion  453
Base  Original Amount  620
P 453
R 
 .731  73.1%
B 620
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a publicly accessible website, in whole or in part.
35
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CHAPTER REVIEW PROBLEM 4
By what percent is a 100-watt light bulb
brighter than a 60-watt light bulb?
Portion  Increase  100  60 
40
Base  Original Amount  60
P 40
R 
 .667  66.7%
B 60
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a publicly accessible website, in whole or in part.
36
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CHAPTER REVIEW PROBLEM 5
A pre-election survey shows that the popularity of
a presidential candidate has increased from 26.5
percent to 31.3 percent of the electorate, an
increase of 4.8 percentage points. What percent
increase does this represent?
Portion  Increase  31.3  26.5 
4.8
Base  Original Amount  26.5
P
4.8
R 
 .181  18.1%
B 26.5
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a publicly accessible website, in whole or in part.
37