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

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 percentages Copyright © 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) = ( )%  labeled price = 106%  $21 = 1.06  $21 = $ 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