What is a percentage?

Understanding Percentages

A percentage is a common way of expressing a proportion or a part of a whole.
It represents a number as a fraction of 100.

The Concept of Percentages

The term ‘percent’ comes from the Latin ‘per centum’, which means ‘per hundred’.
When a value is expressed as a percentage, it means that value per hundred units of the whole.
For example, 25% means 25 out of 100.

Calculating Percentages

To calculate a percentage, convert the fraction or decimal into a number over 100.
For instance, to calculate 15% of 60: first convert 15% into decimal, i.e. 15 ÷ 100 = 0.15. Then, multiply 0.15 by 60 = 9. So, 15% of 60 is 9.

Common Uses of Percentages

Percentages are used in various contexts, such as calculating discounts, grades, interest rates and growth or decrease rates.
For instance, if a shop offers a 20% discount on a £50 shirt, it means you will pay £50 less 20% (£10), totalling £40.

Converting Between Fractions, Decimals, and Percentages

You can convert fractions to percentages by dividing the numerator by the denominator and multiplying by 100.
Convert decimals to percentages by multiplying by 100 and adding the ‘%’ symbol.
For instance, 0.20 as a percentage is 20%, while the fraction 1/5 is equivalent to 20% when expressed as a percentage.

Problem Solving with Percentages

Solving problems involving percentages requires multiplication, division, addition and subtraction, and sometimes involves fractions and decimals.
You may need to calculate percentage changes, increases or decreases or find the original quantity given the changed amount and the percentage change.
It’s crucial to ensure you are comfortable with these types of problem-solving tasks involving percentages. Practise a variety of problems to improve your skill set.