Chapter 6 Percent

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Chapter 6Percent
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Chapter Outline

• Introduction to Percent
• Percents and Fractions
• Solving Percent Problems Using Equations
• Solving Percent Problems Using Proportions
• Applications of Percent
• Percent and Problem Solving Sales Tax,
  Commission, and Discount
• Percent and Problem Solving Interest

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6.1

• Introduction to Decimals

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Section Objectives

• Understanding Percent
• Writing Percents as Decimals
• Writing Decimals as Percents

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Understanding Percent
48 of 100 squares are shaded or
48 is shaded.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 5
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Writing Percent as Decimals
EXAMPLE
67 of American men are happy with their current
weight. Convert this percentage into a decimal.
(Source Gallup for Wheat Foods Council)
SOLUTION
Replace the symbol with its decimal
equivalent.
.67 of American men are happy with their current
weight.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 6
7
Writing Decimals as Percents
EXAMPLE
The Munoz family saves 0.10 of their take-home
pay. Convert this decimal to a percent.
SOLUTION
Multiply the decimal by 1 in the form of 100.
The Munoz family saves 10 of their take-home pay.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 7
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6.2

• Percents and Fractions

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Section Objectives

• Writing Percents as Fractions
• Writing Fractions as Percents
• Converting Percents, Decimals, and Fractions

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Writing Percents as Fractions
EXAMPLE
Write 4.5 as a fraction or mixed number in
simplest form.
SOLUTION
Replace the percent symbol with its fraction
equivalent.
Multiply by 1 in the form of to remove the
decimal in the numerator.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 10
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Writing Fractions as Percents
EXAMPLE
Write as a percent.
SOLUTION
Multiply the fraction by 1 in the form of 100
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 11
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Converting Percents, Decimals, and Fractions
EXAMPLE
Complete the following table.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 12
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6.3
Solving Percent Problems Using Equations
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Section Objectives

• Writing Percent Problems as Equations
• Solving Percent Problems

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Writing Percent Problems as Equations
EXAMPLE
72 of 63 is what number?
SOLUTION
of means multiplication ( )
is means equals ()

what (or some equivalent) means the unknown
number
72 of 63 is what number?
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 15
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Solving Percent Problems
percent
base
amount
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 16
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6.4
Solving Percent Problems Using Proportions
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Section Objectives

• Writing Percent Problems as Proportions
• Solving Percent Problems

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Writing Percent Problems as Proportions
percent
base
amount
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 19
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Solving Percent Problems
EXAMPLE
25 of 84 is what number?
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 20
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6.5
Applications of Percent
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Section Objectives

• Solving Applications Involving Percent
• Finding Percent Increase and Percent Decrease

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Solving Applications Involving Percent
EXAMPLE
18 of Franks wages are withheld for income tax.
Find the
amount withheld from Franks wages of 3680 per
month.
SOLUTION
Amount n Base 3680 Percent 18
662.40 is the amount withheld from Franks wages.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 23
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Finding Percent Increase and Percent Decrease
EXAMPLE
The average soft-drink size has increased from
13.1 oz to 19.9 oz over the past two decades.
Find the percent increase. (Source University
of North Carolina at Chapel Hill, Journal for
American Medicine)
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 24
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Finding Percent Increase and Percent Decrease
EXAMPLE
John Smith decided to decrease the number of
calories in his diet from 3250 to 2100. Find the
percent decrease.
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 25
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6.6
Percent and Problem Solving Sales Tax,
Commission, and Discount
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Section Objectives

• Calculating Sales Tax and Total Price
• Calculating Commissions
• Calculating Discount and Sale Price

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Calculating Sales Tax and Total Price
EXAMPLE
A gold and diamond bracelet sells for 1800.
Find the total price if the sales tax rate is
6.5.
SOLUTION
The total price of the gold and diamond bracelet
is 1917.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 28
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Calculating Commissions
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 29
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Calculating Discount and Sale Price
EXAMPLE
A 2000 designer dress is on sale for 30 off.
Find the discount and the sale price.
SOLUTION
The price of the designer dress after a 600
rebate is 1400.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 30
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6.7
Percent and Problem Solving Interest
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Section Objectives

• Calculating Simple Interest
• Calculating Compound Interest
• Calculating a Monthly Payment

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Calculating Simple Interest
SOLUTION
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 33
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Calculating Compound Interest
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 34
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Calculating Compound Interest
EXAMPLE
2000 is compounded annually at a rate of 8 for
5 years.
Find the total amount of compound interest
earned. (A compound interest table can be found
in Appendix A7.)
SOLUTION
Amount at End of Year
Interest
Time
.
Rate
.
Amount at Beginning of Year
Principal
2160
160
1
.
0.08
.
2000
2000
1st year
2332.80
172.80
1
.
0.08
.
2160
2160
2nd year
2519.42
186.62
1
.
0.08
.
2332.80
2332.80
3rd year
2720.98
201.56
1
.
0.08
.
2519.42
2519.42
5th year
2938.66
217.68
1
.
0.08
.
2720.98
2720.98
6th year
The total amount of compound interest can be
found by subtracting the final amount, by the
beginning principal. 2938.66 - 2000 938.66.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 35
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Calculating a Monthly Payment
EXAMPLE
Jim Tillman borrows 1800 for 9 months. If the
interest is 148.90, find his monthly payment.
SOLUTION
Jim Tillmans monthly payment is 216.54.
Elayn Martin-Gay, PEARSON PRENTICE HALL, BASIC
COLLEGE MATHEMATICS, 3e Slide 36