Percentage

What is a percentage?

Percentage is a way of expressing a number as a fraction of 100. It is commonly used to represent a portion of a whole or to compare two numbers. Percentages are often denoted with the symbol "%". For example, if there are 100 cars in a garage and 25 of them are white, we could say that 25% of the cars in the garage are white.

Calculating Percentage

Calculating percentage means finding the share out of the whole, in terms of 100. There are two ways to calculate percentage:

  • By changing the denominator of the fraction to 100: In this method, we just find the equivalent fraction of a given fraction such that the resultant denominator is 100. Then the numerator itself is the percentage. For example:
    4/25 = 4/25 × 4/4 = 16/100 = 16%
  • By using the unitary method: In this method, we just multiply the fraction by 100 to get the percentage. For example, the percentage that corresponds to the fraction 4/25 is:
    4/25 × 100 = 400/25 = 16%

Percentage Formula

The percentage formula is used to find the share of a whole in terms of 100. Using this formula, you can represent a number as a fraction of 100. 

Percentage = (Value/Total Value)×100

How to calculate the percentage of a number?

To calculate the percentage of a number, we need to use a different formula such as:

P% of Number = X

where X is the required percentage.

If we remove the % sign, then we need to express the above formulas as;

P/100 * Number = X

Percentage Increase

Percentage increase refers to the percentage change in the value when it is increased over a period of time. For example, population increase, increase in the number of bacteria on a surface, etc. Percentage increase can be calculated by using the following formula:

Percentage Increase = (Increased Value-Original value)/Original value × 100

Percentage Decrease

Percentage decrease refers to the percentage change in the value when it is decreased over a period of time. For example, decrease in the level of rainfall, decrease in the number of Covid patients, etc. Percentage decrease can be calculated by using the following formula:

Percentage Decrease= (Original value-Decreased Value)/Original Value × 100

Percentage Difference Formula

If we are given with two values and we need to find the percentage difference between these two values, then it can be done using the formula:

Percentage Difference = |N1-N2|[(N1+N2)2]×100

Converting Percentage to Fraction

In some cases, we are provided with the percentage and need to convert it to a fraction number. For converting percentages to fractions, some calculations are required. We can use the formula,

Fraction = Percentage/100

Converting Fractions to Percentage

A fraction can be represented by a/b.

Multiplying and dividing the fraction by 100, we have

ab×100100=(ab×100)1100.......(i)

From the definition of percentage, we have;

(1/100) = 1%

Thus, equation (i) can be written as:

(a/b) × 100%

Therefore, a fraction can be converted to a percentage simply by multiplying the given fraction by 100.

Difference between Percentage and Percent

The words percentage and percent are related to each other, but there is a difference between both them. Percent is always accompanied by a number, for example, 35%. While percentage does not need a number to be accompanied by the term. For example, the percentage of people who participated in the voting in 2023 is more than the percentage of people who participated in 2022.

Percentage Tricks

There are percentage tricks that can be used while calculating the percentage of numbers. Below given trick is the most used,

% x of y = % y of x

What is percentage change?

Percentage change of a number is the change in percentage from the old value to the new value. It is calculated using the formula,

Percentage Change = {(Difference between old value and new value) / Old value} × 100.