copyright © 2011 pearson education, inc. numbers in the real world
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Copyright © 2011 Pearson Education, Inc.
Numbers in the Real World
Copyright © 2011 Pearson Education, Inc.
Slide 3-3
Unit 3A
Uses and Abusesof Percentages
Copyright © 2011 Pearson Education, Inc.
Calculating Percents
The key to calculating percents, in my opinion is to understand the words percent, is and of. Percent means for each 100. So the key is the following:
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is
of%
100
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Example 1
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29 is what % of 62?
Is = 29, of = 62, % = ?
29*10062x2900
62x
x = 46.774%
is
of%
1002962
=𝑥100
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Example 2
What is 48% of 1300?
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is
of%
100
Is = x, of = 1300, % = 48
x
130048
100
481300100x 62400
100x
x = 624
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Example 3
350 is 180% of what?
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Is = 350, of = x, % = 180
is
of%
100350
x180
100
350100180x 35000
180x
x = 194.44
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Slide 3-8
As fractions:
15% of the 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.
Three Ways of Using Percentages
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Slide 3-9
value reference
value referencevaluenew
value reference
change absolutechange relative
The absolute change describes the actual increase or decrease from a reference value (starting number) to a new value:
absolute change = new value – reference value
The relative change is a fraction that describes the size of the absolute change in comparison to the reference value:
Absolute and Relative Change
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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 = 0.5 = 50%
relative change =value reference
change absolute
Absolute vs. Relative Change
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Slide 3-11
The absolute difference is the actual difference between the compared value and the reference value:
absolute difference = compared value – reference value The relative difference describes the size of the
absolute difference as a fraction of the reference value:
value reference
difference absolutedifference relative
value reference
value referencevalue compared
Absolute and Relative Difference
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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.
Of versus More Than (or Less Than)
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Slide 3-13
Percentages of Percentages
Example: If a bank increases its interest rate from 4% to 5%, the interest rate increased by 1 percentage point.
When a change or difference is expressed in percentage points, assume it is an absolute
change or difference. with the % sign or the word percent, it is a relative
change or difference.
%2525.0%4
%4%5
change relative
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Slide 3-14
Solving Percentage Problems
value referencevalue compared )%100( P
)%100( P
value comparedvalue reference
If the compared value is P% more than the reference value, then
and
If the compared value is less than the reference value, use (100 – P) instead of (100 + P) in the above calculations.
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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)% x labeled price
= 106% x $21 = 1.06 x $21 = $22.26
Solving Percentage Problems
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Slide 3-16
Abuses of Percentages
Beware of Shifting Reference Values
A 10% pay cut is followed by a 10% pay raise. Less than Nothing
Decrease caloric intake by 150% to lose weight. Don’t Average Percentages
If 70% of the boys and 60% of the girls in a class voted to go to a water park, then 65% of the students in the class voted to go to the water park.
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In-Class Group Assignment
P. 141–143 18 – 96 multiples of 3
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