Percentages are a fundamental concept in mathematics and are used extensively in everyday life. A percentage is simply a particular type of fraction, meaning 'out of 100', and is denoted by the symbol %. Therefore, if we say that 50% of a group of people prefer coffee, it means that 50 out of every 100 people like coffee.

To calculate a percentage, we need to know both the part and the whole. For example, if we are given that 25 out of 100 students in a class are boys, 25% of the class are boys. Similarly, if we know that a group of 50 people includes 20 women, we can say that the percentage of women in the group is:

$$\frac{20}{50}$$ × 100% = 40%

Notice that to find the percentage, we multiplied the fraction by 100 to convert it to a percentage.

## Percentage of a quantity

A common type of percentage calculation is to find the percentage of a quantity. For example, if we know that a shirt originally costs £30 and is now on sale for 20% off, we can find the sale price by multiplying the original price by the percentage reduction:

20% of £30 = 0.2 x £30 = £6

Therefore, the sale price of the shirt is £30 - £6 = £24.

## Percentage change

Another percentage calculation type is percentage change, which occurs when something increases or decreases in value. To calculate the percentage change, we need to know both the original and the new values.

The percentage change is then given by:

Percentage change $$=\frac{(\text { New } \text { value }- \text { original value })}{\text { Original value }} \times 100$$

For example, if a share in a company was originally worth £10 and is now worth £12, we can calculate the percentage increase as follows:

Percentage increase $$=\frac{(12-10)}{10} \times 100 %=20 %$$ = 20%

As a result, the share's value is a 20% increase.

In conclusion, percentages are a vital part of mathematics and everyday life. Understanding how to calculate percentages and use them in real-life situations is essential for success in many areas. Knowing how to calculate percentages of a quantity, percentage change, and mental percentage calculations can help you in your daily life and GCSE Mathematics exams.