
Percentage,
percent



Percent, decimal number and
fraction conversions 
Percent  base, rate and portion (part or
amount)

Basic percent formulas 
Percent problems

Percent
increase or decrease






Percent, decimal number and
fraction conversions 
A percent (per cent) is a ratio or a fraction with 100 as the
denominator, represented by the symbol %, 

written 

Realize
that 

for
example, 




Conversions between a percent, a decimal number and a fraction
are shown below. 


Percent  base, rate and portion (part
of
amount)

We use percentage to express relationship between two quantities
or their parts taking 100 as the base of a comparison. 
While
comparing, the quantity (or the number) of which we compute the percent we consider as a whole or
100% of an amount, and call it
the base or initial value (x). 
The number of percent is the
rate (p).
The portion of the base value expressed as the percent of it is the
part (y)
of
amount. 
The formal way to solve a percentage problems is
by using proportion, 

part
: base (whole) = rate : 100 
or 
y
: x =
p
: 100. 



Percentage formulas 
Thus, from the proportion we calculate,
the part of whole (or amount) y,
the rate p
and the base value x: 
the part or amount 

the rate 

the base
(initial) value 



Example: 
What is 25% of 80? 
x =
80,
p%
= 25%,
y =
? 




The percent represents relationship between a part and the whole. 
Example: 
What percent of 80 is 20? 
y =
20,
x =
80,
p%
=
? 





The base value 

therefore 

represents
1% of the base value. 



Example: 
What is the base value if 25% of it is 20? 
p%
= p/100 = 25%,
y =
20,
x =
? 




Percent
increase or decrease
 base (x),
amount (y),
percent (p) 

from 
x
: 100
=
( x
±
y )
: ( 100
±
p) 
and 
y
: p
=
( x
±
y )
: ( 100
±
p) 


where
x
±
y denotes
original or base value x increased or decreased by amount
y 


Example: 
In the price of $33 included is tax of 10%. 
What is net price? 




Example: 
Price reduced by 20% amounts
to $320. 
How much is reduced? 











Beginning
Algebra Contents B 



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