PERCENTAGE BASICS
Per cent means out of 100, so 10% means "10 out of 100".
To work out the percentage OF something, replace the word OF with multiplication (×).

Percentages are an essential topic in GCSE mathematics, and they are used to express a fraction or a proportion of a whole as a percentage. Data in the form of percentages can be used to compare quantities and calculate discounts or taxes.

Percentages are just one way of expressing numbers that are part of a whole. These numbers can also be written as fractions or decimals. 50% can also be written as a fraction, 1221, or a decimal, 0.5. They are all exactly the same amount.

So, a percentage is a number expressed as a fraction of 100, represented by the symbol ‘%’. For example, 25% is equivalent to $$\frac{25}{100}$$ or 0.25. Similarly, 75% is equal to $$\frac{75}{100}$$ or 0.75.

## Calculating Percentages

To calculate a percentage, we can use the following formula:

Percentage $$=\frac{\text { Value }}{\text { Total Value }} \times 100$$

For example, if there are 20 students in a class and 10 of them are boys, we can calculate the Percentage of boys in the class as follows:

Percentage of boys = $$\frac{10}{20} × 100 = 50%$$%

Another example is if a shirt originally costs £50 but is discounted by 20%, we can calculate the discounted price as follows:

Discounted price = £50 - (20% × £50) = £40

## Percentage Change

Percentage change is used to calculate the difference between two quantities in percentage terms. The formula for percentage change is:

Percentage Change $$=\frac{\text { (New Value - Old Value) }}{\text { Old Value }} \times 100$$

For example, if the price of a product increases from £10 to £15, we can calculate the percentage increase as follows:

Percentage Increase = $$\frac{(15 - 10)}{10} × 100$$ = 50%

Alternatively, if the price of the same product decreases from £15 to £10, we can calculate the percentage decrease as follows:

Percentage Decrease = $$\frac{(15 - 10)}{15} × 100$$ = 33.33%

## Percentage of a Quantity

To calculate the Percentage of a quantity, we can use the following formula:

Percentage of Quantity = $$\frac{Percentage}{100} × Quantity$$

For example, if we want to find 20% of 500, we can use the formula as follows: 20% of 500 = (20 ÷ 100) × 500 = 100

## Percentage Increase/Decrease by a Percentage

To calculate the percentage increase or decrease by a percentage, we can use the following formula:

Final Value = Initial Value × (1 ± Percentage ÷ 100)

If the Percentage is positive, it represents an increase; if it is negative, it means a decrease.

For example, if the price of a product increases by 10%, and the original price was £100, we can calculate the new price as follows:

New price = £100 ×$$\frac{(1 + 10)}{100}$$ = £110

Similarly, if the price of the product decreases by 20%, we can calculate the new price as follows:

New price = £100 ×$$\frac{(1 - 20)}{100}$$ = £80

Percentages are a fundamental topic in GCSE mathematics and are widely used in everyday life. For example, they are used to compare quantities, calculate discounts or taxes, and understand data in percentages. Therefore, understanding the concepts of percentage change, Percentage of a quantity, and percentage increase/decrease by a percentage is crucial for success in GCSE mathematics.

## Revision Quiz

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