Percentage, percent

Percent, decimal number and fraction conversions
Percent - base, rate and portion (part or amount)
Basic percent formulas

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.
 Examples:
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 ±   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