### Understanding the Percentage Formula

The percentage formula is used to determine how one number relates to another number in terms of 100. It is commonly used in various fields such as finance, statistics, and everyday calculations.

### Basic Formula

The basic formula to calculate the percentage is:

$\text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$
Here, the **part** represents the quantity you're interested in, and the **whole** is the total or complete quantity.

### Example Calculation

Suppose you scored 45 marks out of a total of 60 marks in an exam. To find the percentage:

$\text{Percentage} = \left( \frac{45}{60} \right) \times 100$
Breaking it down:

$\text{Percentage} = \left( \frac{3}{4} \right) \times 100 = 75\%$
So, your score is **75%**.

### Rearranging the Formula

You can also rearrange the formula to find either the **part** or the **whole** if you have the percentage and one of the other quantities:

#### Finding the Part

$\text{Part} = \left( \frac{\text{Percentage} \times \text{Whole}}{100} \right)$
#### Finding the Whole

$\text{Whole} = \left( \frac{\text{Part} \times 100}{\text{Percentage}} \right)$
### Application Example

If you know that 60% of a class of 50 students passed an exam, you can find out how many students passed (the Part):

$\text{Part} = \left( \frac{60 \times 50}{100} \right) = 30$
Thus, **30 students** passed the exam.

### Summary

- The percentage formula helps in comparing values relative to 100.
- Basic formula: $\left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$
- Can be rearranged to find unknown quantities (part or whole).

Understanding percentages is vital for data analysis, budgeting, and various other practical applications in daily life and professional settings.