Embed Size (px)
Citation preview
Copyright © 2008 Pearson Education, Inc.
Chapter 3
Copyright © 2008 Pearson Education, Inc. Slide 3-3
Three Ways of Using Percentages
As fractions:
15% of the 850 students in a school were absent.
To describe change:
The price of a stock increased 75% from $50 per share.
For comparisons:
A Mercedes costs 25% more than a Lexus.
3-A
Copyright © 2008 Pearson Education, Inc. Slide 3-4
The relative difference describes the size of the absolute difference as a fraction of the reference value:
Absolute and Relative Difference or Change
The absolute difference is the actual difference between the compared value and the reference value:
3-A
absolute difference = compared value reference value
value reference
difference absolutevalue reference
value referencevalue compareddifference relative
Copyright © 2008 Pearson Education, Inc. Slide 3-5
Absolute Change vs. Relative Change
3-A
Example: A diversified portfolio grows from $1,500 to $2,250.
absolute change = new value – reference value
= $2,250 – $1,500 = $750
= $750 / $1,500 = 50%
relative change
Unemployment Rate in Humboldt County
The annual average unemployment rate for Humboldt County in 2008 was 7.2%. The annual average unemployment rate for Humboldt County for 2010 was 11.1%. (EDD at CA.gov)
What is the absolute change?
What is the relative change?
This was an example of percentages of percentagesCopyright © 2008 Pearson Education, Inc. Slide 3-6
Copyright © 2008 Pearson Education, Inc. Slide 3-7
Percentages of percentages
3-A
Suppose a bank increases its interest rate from 3% to 4%. The interest rate was increased by 1 percentage point (the absolute change)
The relative change
Copyright © 2008 Pearson Education, Inc. Slide 3-8
Of versus More Than (or Less Than) Summary
3-A
If the compared value is P% more than the reference value, it is (100 + P)% of the reference value.
If the compared value is P% less than the reference value, it is (100 - P)% of the reference value.
With Some Numbers
70% more than = (100+70)% of = 170% of
35% less than = (100 – 35)% of = 65% of
Copyright © 2008 Pearson Education, Inc. Slide 3-9
Example from the News:
Consumer Prices increase 0.5% in December, up 1.5% over last 12 months. (US Bureau of Labor and Statistics 1/14/2011)
Could be stated:
Consumer Prices in December are 100.5% of what they were in November.
Consumer Prices in December are 101.5% of what they were over the last 12 months.
Copyright © 2008 Pearson Education, Inc. Slide 3-10
Copyright © 2008 Pearson Education, Inc. Slide 3-11
Solving Percentage Problems an “Of vs. More Than” problem
You purchase a shirt with a labeled (pre-tax) price of $21. The local sales tax rate is 6%. What is your final cost (including tax)?
final cost = labeled price + (6% of labeled price)
= (100 + 6)% labeled price
= 106% $21 = 1.06 $21 = $22.26
3-A
Another “Of vs More Than”
An item originally priced at $55 is marked 25% off. What is the sale price?
Sale price = original price – (25% of original price)
= (100-25)% X original price
= 75% X $55
= .75 ($55) = $41.25
Copyright © 2008 Pearson Education, Inc. Slide 3-12
Relative Change with Percentages
Ex 11 (pg 146): The rate [of smoking] for eighth graders is up 44%, to 10.4%. What was the previous smoking rate for eighth graders?
Copyright © 2008 Pearson Education, Inc. Slide 3-13
Copyright © 2008 Pearson Education, Inc. Slide 3-14
Abuses of Percentages
Beware of Shifting Reference Values
A 10% pay cut followed by a 10% pay raise
Less than Nothing
Decrease caloric intake by 150% to lose weight
Don’t Average Percentages
70% of the boys and 60% of the girls in a class voted to go to a water park. So 65% of the students in the class voted to go to the water park.
3-A
