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Chapter 6
Percents and their Applications
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What is a percent?
A percent is 1 one hundredth of a number.
For instance, a penny is 1/100 of a dollar.
Each one hundredth is 1%
A nickel is 5/100 of a dollar or 5%
A dime is 10/100 of a dollar or 10%
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No. of fraction % of decimal currency
pennies of dollar a dollar number (cents)
50 50/100 50% .50 $.50
25 25/100 25% .25 $.25
10 10/100 10% .10 $.10
5 5/100 5% .05 $.05
1 1/100 1% .01 $.01
Notice the difference between these two sets of numbers.
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Visualize the alphabet to determine which way to move the decimal
point when converting from decimals to percent and from percent to
decimals
a b c D e f g h i j k l m n o P q r s t u v w x y z
Left Right
Toward D Toward P
.xx xx.
Decimal to Percent (from D toward P) – move the decimal
point two places to the right
Percent to Decimal (from P toward D) – move the decimal
point two places to the left
D for
Decimal
P for
Percent
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Converting Decimals to Percents
.75 75%
5.00 500%
Move decimal point 2 places to the right, and add zeros if
necessary. Add a percent symbol at the end of the number.
.01 1%
a b c D e f g h i j k l m n o P q r s t u v w x y z
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Converting a fraction to a decimal number, to a percent,
and then rounding to the hundredth place
513
13 5.000000
.384615
=
38.4615% 38.46%=
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Converting Percents to Decimals, example 1
35% .35
2.50250%
Drop the percent symbol. Move decimal point 2
places to the left, add zeros if necessary
8% .08
a b c D e f g h i j k l m n o P q r s t u v w x y z
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Converting Percents to Decimals-- Example 2
Drop the percent symbol
Move the decimal point 2 places to left.
.8% .8 .00.8 .008
A B C D
In this case we had to add zeros to fill in the empty
places to the left of the 8.
a b c D e f g h i j k l m n o P q r s t u v w x y z
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Converting Fractional Percents to Decimals
12
1.00 2 .00.5
.005
% .5
A fractional percent is a part (fraction) of a percent.
Start by dividing the denominator into the numerator.
At this point, the number is
still a percent and has to
be converted to a decimal.
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Converting Proper Fractions to Percents
1.00 10 10%.10.1
10
Remember, converting from a decimal number to a
percent means moving the decimal point two places to
the right. (D to P) Then add the percent sign (%).
Fraction ► Decimal ► Percent
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Converting a Whole Percent to a Fraction
76% 76 x 11 100
76100
1925
Divide 4 into the numerator and the denominator
to reduce this fraction to lowest terms.
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Converting a Mixed Percent
(also called a Decimal Percent) to a Fraction
12½ %
252
25 x
1 = 252 100 200
1
8
Drop % symbol, and change the mixed
percent to an improper fraction.
Multiply improper fraction by 1/100
Reduce to lowest terms.
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Application of Percents - Portion Formula
Portion (P) = Base (B) x Rate (R)
Portion “is”
Base “of” Rate “%”
Base: 100% - whole. Usually given after the word of – but not always $100 – Bonus check
Rate: Usually expressed as a percent but could also be a decimal or fraction. 20% taxes
Portion: A number – not a percent and not the whole $20 taxes
X
Center line stands for
division.
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To find the portion, multiply the rate x base
To find the rate, divide portion by base
To find base, divide portion by rate Very
Useful
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McDonalds has two major categories of sales—
drive-through and eat-in. Both are portions of
total McDonalds sales. The following business
math problems have to do with these portions
of the total sales.
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Solving for PortionSales to McDonalds drive-thru customers are
60% of total sales. Total sales are $1,600,000.
What are the drive-thru sales?
Portion = Base x Rate
P = $1,600,000 x .60
P = $960,000
base
rate
portion
960,000
.60 1,600,000
portion
rate base
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Solving for Rate
Sales to McDonalds drive-thru customers are $960,000.
Total sales are $1,600,000. What Percent of customers
eat in the restaurant?
Rate = PortionBase
R = $640,000$1,600,000
R = 40%
$1,600,000
- 960,000
640,000
drive-thruEat in
total
rate
÷base
portion
? 1,600,000
640,000
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Solving for Base
Sales to McDonalds drive-thru customers are 60% of total sales.
Sales to eat-in customers are $640,000. What are total sales?
Base = PortionRate
B = $640,000.40
B = $1,600,000
eat in salesPercent of
customers that
eat-in (1.00 - .60)
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Rate of Decrease (rates are percent)
15 oz.
bunch
Rate = PortionBase
Rate = 1215
Amount of Decrease
(Portion)
Original Weight (Base)
.80 or 80% decrease
3 oz.
bunch
Original New
The actual decrease in size
(portion) is 15 oz. – 3 oz. = 12 oz.
What percent is 12 (the decrease)
of 15 (the original size)?
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Rate of Percent Increase
$1,000
Rate = PortionBase
Rate = $1,500$1,000 Original sales
(Base)
1.5 or 150%Increase
$2,500
Original New
Amount of
Increase (Portion)
Percent of
Increase (Rate)
The actual increase (portion) is
2,500 – 1,000 = 1,500
What percent is 1,500 (the
increase) of 1,000 (the original
size)? You are seeking the rate.