# Percentages

## Basic Concepts of Percentages

• A percentage is a way of expressing a number as a fraction of 100.

• It is denoted by the % symbol. For example, 50% means 50 out of 100.

• Percentages are used to compare proportions in different sizes of collections or quantities.

## Calculating Percentages

• To calculate a percentage of a quantity, multiply the quantity by the percentage and then divide by 100.

• Example: To find 30% of 200, calculate (30/100) * 200.

## Converting between Percentages, Fractions and Decimals

• To convert a fraction to a percentage, divide the numerator by the denominator, multiply by 100, then add the % symbol.

• To convert a decimal to a percentage, multiply the decimal by 100, then add the % symbol.

• To convert a percentage to a fraction, write the percentage as a fraction of 100 and simplify if possible.

• To convert a percentage to a decimal, divide the percentage by 100.

## Percentage Increase and Decrease

• A percentage increase occurs when you add a certain percentage to an original quantity.

• To calculate this, find the percentage of the original quantity and then add it to the original quantity.

• A percentage decrease occurs when you subtract a certain percentage from an original quantity.

• To calculate this, find the percentage of the original quantity and then subtract it from the original quantity.

## Calculating Percentage Change

• Percentage change is a way to express a change in value as a percentage of the original value.

• It is calculated as follows: Divide the change by the original value, then multiply by 100 to get the percentage.

• Example: If a price goes from £50 to £75, the change is £25. So, the percentage change is (25/50) * 100 = 50%.

## Reverse Percentages

• Working out the original value after a percentage change (increase or decrease) is known as a reverse percentage calculation.

• To do this, you need to work backwards using the final amount and the percentage change.

• For an increase, divide the final amount by 1 plus the percentage increase (in decimal form).

• For a decrease, divide the final amount by 1 minus the percentage decrease (in decimal form).

## Using Percentages in Real Life Contexts

• Percentages are widely used in everyday life, including in situations involving discounts, sales, interest rates, tax, and more.

• Always double-check calculations for accuracy, especially when dealing with financial matters.