Percentage, percent calculations

Percentage, percent

Percent, decimal number and fraction conversions

Percent problems

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 or 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 value (x).

The number of percent is the rate (p), and the portion of the base value expressed as the percent of it is the

part (y) or amount.

The formal way to solve a percent problems is by using proportion,

part : base (whole) = rate : 100

y : x = p : 100.

Basic percent formulas

Thus, from the proportion we calculate, the part or amount y, the rate p and the base value x:

the part or amount

the rate

the base 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?

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