Chapter 6
Percents and their Applications
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%
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.
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
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
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%=
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
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
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.
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
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.
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.
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.
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
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.
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
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
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)
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)?
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.