Editing Percentage (section)

== Calculations ==
The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1,250 apples, one first computes the ratio {{sfrac|50|1250}} = 0.04, and then multiplies by 100 to obtain 4%. The percent value can also be found by multiplying first instead of later, so in this example, the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1,250 to give 4%.

To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:
:{{math|1= {{sfrac|50|100}} × {{sfrac|40|100}} = 0.50 × 0.40 = 0.20 = {{sfrac|20|100}} = 20%.}}
It is not correct to divide by 100 and use the percent sign at the same time; it would literally imply division by 10,000. For example, {{nowrap|1= 25% = {{sfrac|25|100}} = 0.25}}, not {{sfrac|25%|100}}, which actually is {{nowrap|1= {{sfrac|{{frac|25|100}}|100}} = 0.0025}}. A term such as {{nowrap|{{sfrac|100|100}}%}} would also be incorrect, since it would be read as 1 percent, even if the intent was to say 100%.

Whenever communicating about a percentage, it is important to specify what it is relative to (i.e., what is the total that corresponds to 100%). The following problem illustrates this point.

{{blockquote|In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?}}

We are asked to compute the [[ratio]] of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that {{sfrac|60|100}} × {{sfrac|5|100}} = {{sfrac|3|100}} or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer: {{sfrac|3%|10%}} = {{sfrac|30|100}} or 30% of all computer science majors are female.

This example is closely related to the concept of [[conditional probability]].

Because of the [[commutative property]] of multiplication, reversing expressions does not change the result; for example, 50% of 20 is 10, and 20% of 50 is 10.