Percentages

Percentage is a term used in arithmetic to denote that a whole quantity divided into 100 equal parts is taken as the standard of measure. Percentage is indicated by the percent sign (%). Thus percent, or %, means a number of parts of one hundred (100). For example, 4% may be written as 4/100 or .04. Notice that 4/100 reduces to 1/25.


Percents may be added, subtracted, multiplied or divided, just as other specific denominations are treated.

  6% + 12% = 18%
8% - 3% = 5%
20% / 5% = 4%
6% x 7% = 42%

 

To change a percent to a fraction...
     ...divide the percent quantity by 100 and reduct to lowest terms.
8% = 8/100 = 2/25
75% = 75/100 = 3/4
80% = 80/100 = 4/5
Fractional Equivalents of Percents

10% = 1/10     12 1/2% = 1/8     8 1/3% = 1/12
20% = 1/5    25% = 1/4    16 2/3% = 1/6
40% = 2/5    37 1/2% = 3/8    33 1/3% = 1/3
50% = 1/2    62 1/2% = 5/8    66 2/3% = 2/3
60% = 3/5    87 1/2% = 7/8    83 1/3% = 5/6
To change a percent to a decimal...
     ...remove the percent sign and move the decimal point two places to the left.
Example: Change 25% to a decimal.
  • 25% = .25     Moving decimal point two places to the left.
Example: Change 1.5% to a decimal.
  • 1.5% = .015     To move the decimal point two places to the left, one zero had to be prefixed.
To change a decimal to a percent...
     ...move the decimal point two places to the right and add a percent sign.
Example: Change .24 to a percent.
  • .24 = 24%     Moving decimal point two places to the right and adding the % sign.
Example: Change .0043 to a percent.
  • .0043 = .43%     Note that this is less than 1%.
Example: Change 2.45 to a percent.
  • 2.45 = 245%     Note that any whole number greater than 1 which designates a percent is more than 100%.

 


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Definitions

 

The terms commonly used in percentage are:
  • (R) rate
  • (B) base
  • (P) percentage
  • (A) amount
  • (D) difference

Rate (R) or rate percent is the fractional part in hundredths that is to be found.

Example:
  • 4% of 50 = 2
  • 4%, 1/25 or .04 is the rate.
The base (B) is the whole quantity of which some percent is to be found.

Example:
  • In 4% of 50 = 2, 50 is the base or whole quantity.
The percentage (P) is the result obrained by taking a given hundredth part of the base.

Example:
  • In 4% of 50 = 2, 2 is the percentage or the part taken.
The amount (A) is the sum of the base and the percentage.

Example:
  • In 4% of 50 = 2, 2 the amount is 50 + 2, or 52.
The difference (D) is the remainder of the base left when the percentage is subtracted.

Example:
  • In 4% of 50 = 2, 50 - 2 or 48 is the difference.

 

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The Three Types of Percentage Problems

 

1
Finding a percent
of a number:

given the base and the rate
to find the percentage.
Example 1: Find 14% of $300.

$300base
x .14rate
______
1200
300
______
$42.00 percentage - Answer
EXPLANATION:
14% is equal to .14.
Multiplying $300 by .14,
the product is $42 or 14% of $300.
2
Finding what percent
one number is of another:

given the base and the percentage
to find the rate.
Example 2: 120 is what percent of 240 ?

120/240=50% - Answer
120=the percentage
240=the base
50%=the rate

Rate = Percentage / Base    or... E = P / B .
EXPLANATION:
This is another way of saying
what fractional part of 240 is 120.
Change the answer to percent.
3
Finding a number
when a percent of that number
is known:

given the rate and the percentage
to find the base.
Example 3: 225 is 25% of what amount ?

25%=1/4,   225 / 1/4 = 225 x 4/1 = 900 - Answer
225=the percentage
20%=the rate
900=the base

Base = Percentage / Rate    or... B = P / R .
EXPLANATION:
This is another way of saying
1/4 of a number equals 225,
and asking what does the
whole number equal.

The formulas given above make the solution of percentage problems easy
if you lean to identify the base, the rate, and the percentage.