Percentage definition
A percentage is a way of writing a number as parts out of 100. The word percent means per hundred. For example, 25% means 25 out of 100. This is the same as the fraction 25 over 100, which simplifies to 1 over 4, and it is also the same as the decimal 0.25. Percentages are useful because they make comparisons easier when totals are different.
Percentages are used in number, fractions, decimals, ratio, proportion, statistics, probability, finance, discounts, tax, interest, exam results and real-life decision making. At GCSE level, students calculate percentages of amounts, convert between fractions, decimals and percentages, compare percentage changes and solve reverse percentage problems. Percentages are one of the most practical areas of maths.
To convert a percentage to a decimal, divide by 100. For example, 36% becomes 0.36. To convert a decimal to a percentage, multiply by 100. For example, 0.72 becomes 72%. To convert a fraction to a percentage, find an equivalent fraction out of 100 or convert the fraction to a decimal and then multiply by 100.
Finding a percentage of an amount means finding a fraction of that amount. For example, 10% of 80 is 8 because 10% means one tenth. Then 20% of 80 is 16 because it is double 10%. Another method is to write the percentage as a decimal and multiply. For example, 35% of 200 is 0.35 times 200, which equals 70.
Percentage increase means increasing an amount by a percentage of the original amount. For example, if a price of 50 pounds increases by 20%, the increase is 10 pounds, so the new price is 60 pounds. Percentage decrease works in a similar way. If 80 pounds is reduced by 25%, the decrease is 20 pounds, so the new price is 60 pounds.
Multipliers are a powerful way to calculate percentage change. To increase by 15%, multiply by 1.15. To decrease by 15%, multiply by 0.85. This method is especially useful for compound interest, repeated percentage changes and calculator questions. It also helps students avoid confusing the original value with the final value in reverse percentage problems.
Percentages are common in real life. Shops use percentages for discounts, banks use percentages for interest rates, schools use percentages for test scores, and surveys use percentages to summarise responses. In statistics, percentages help compare groups of different sizes. For example, 30 out of 50 is 60%, and 18 out of 30 is also 60%, so the proportions are the same even though the totals differ.
Related ideas include fractions, decimals, ratio, proportion, percentage increase, percentage decrease, multipliers, interest, discounts and probability. A clear definition of percentage helps students understand that percentages are not separate from fractions and decimals. In exams, identify the original amount, convert carefully, and check whether the question asks for the percentage, the change or the final value.