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Numbers in the Real World
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Slide 3-3
Unit 3A
Uses and Abusesof Percentages
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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.
3-A
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In-Class Group Assignment
P. 141–143 18 – 96 multiples of 3
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