In mathematics, a percentage represents a value as a fraction of 100, providing a straightforward way to express proportions. Often symbolized by the % sign, percentages are widely used in fields like finance, statistics, and everyday calculations.

For example, 35% means 35 out of every 100 units, which can also be represented as the decimal 0.35 or the fraction35/100.

Percentages are calculated by multiplying a ratio by 100. For instance, in a classroom where 25 out of 50 students are male:

• The ratio is 25/50 = 0.5.
• By multiplying by 100, we get 50%, indicating half of the students are male.

Percentage Formula

The basic formula for calculating percentages involves:

• P: The percentage
• V1: The initial value
• V2: The resulting value

Formula: P × V1 = V2

Example: To find the percentage of 30 that results in 1.5:

Percentage Difference Formula

The percentage difference between two values is calculated as:

Example: To calculate the percentage difference between 10 and 6:

• Absolute difference: |10 - 6| = 4
• Average: (10 + 6) / 2 = 8
• Percentage Difference: (4 / 8) × 100 = 50%

Percentage Change Formula

The percentage change formula calculates how much a value has increased or decreased relative to its original value:

Example: If a price of $500 increases by 10%, the new price is:

Similarly, if the price decreases by 10%, the new price is: