Percentages – iGCSE Mathematics OxfordAQA Revision

Percentages are a way of expressing a proportion or fraction as parts out of a hundred. The symbol “%” is used to indicate a percentage.
The term “percent” comes from the Latin ‘per centum’, meaning ‘for each hundred’.
100% represents a whole or everything of something. Any number can be expressed as a percentage of itself by stating it as 100%.
A percentage less than 100% represents a portion less than the whole, and a percentage greater than 100% represents an amount greater than the whole.
Percentages are often used in real-life situations, such as sales discounts, tax calculations, and data representation.

To calculate a percentage of a given amount, multiply the number by the percentage, then divide by 100. For example, to find 20% of 50, multiply 50 by 20 and then divide by 100 to get the answer 10.
The formula to calculate the original amount given the final amount and the percentage increase or decrease is Original Amount = Final Amount / (1 + Percentage Increase / 100) or Original Amount = Final Amount / (1 - Percentage Decrease / 100)

A percentage increase refers to the proportion by which an amount has been increased with reference to its original size.
A percentage decrease refers to the proportion by which an amount has been reduced with reference to its original size.
To calculate the percentage increase or decrease between two numbers, subtract the original number from the new number, divide by the original number, and then multiply by 100.

Understanding percentages is key to many areas of maths, from everyday applications, such as shopping sales, to more complex areas like statistical analysis.
Working fluently with percentages requires practice and familiarity. Regularly work through a variety of problem types.
Remember to check any calculations carefully to avoid common errors, such as forgetting to divide by 100 when converting a percentage to a decimal.