In mathematics, percentages are a way to express a number as a fraction of 100. It is a useful tool for comparing quantities and expressing proportions. In this lesson, we will learn about percentages, how to calculate them, and how to use them in real-life situations.

## What is a Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is represented by the symbol “%”. For example, if we say that 50% of the students in a class are girls, it means that 50 out of 100 students are girls.

## Calculating Percentages:

To calculate a percentage, we need to divide the part by the whole and multiply by 100. The formula is:

Percentage = (Part/Whole) x 100

For example, if there are 25 girls in a class of 50 students, we can calculate the percentage of girls as:

Percentage of girls = (25/50) x 100 = 50%

Conversely, we can also calculate the part of a whole given the percentage and the whole using the formula:

Part = (Percentage/100) x Whole

For example, if a store has a 20% discount on a $100 item, we can calculate the discount as:

Discount = (20/100) x $100 = $20

## Using Percentages:

Percentages are commonly used in real-life situations, such as calculating taxes, discounts, and tips. Here are some examples:

- Calculating Sales Tax: If the sales tax in a state is 8%, and the cost of a product is $50, we can calculate the sales tax as:

Sales Tax = (8/100) x $50 = $4

The total cost of the product including tax would be $54.

- Calculating Tips: If you go to a restaurant and want to leave a 15% tip on a $40 bill, we can calculate the tip as:

Tip = (15/100) x $40 = $6

The total amount you would pay including the tip would be $46.

- Calculating Percent Change: If the price of a product has increased from $50 to $60, we can calculate the percent change as:

Percent Change = [(New Value – Old Value)/Old Value] x 100 = [(60 – 50)/50] x 100 = 20%

## Conclusion:

In conclusion, percentages are a useful tool in mathematics and everyday life. We can calculate percentages using the formulas and use them in various situations such as calculating taxes, discounts, tips, and percent change. Understanding percentages is essential for making informed decisions and managing finances.