Percentages
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 doublecheck calculations for accuracy, especially when dealing with financial matters.