Calculate Percentages Without Common Mistakes

Percentage questions often look similar while asking for different calculations. “What is 15% of 240?” asks for a portion of a base value. “240 increased by 15%” asks for the original amount plus that portion. “240 decreased by 15%” subtracts it. A percentage change question compares an old value with a new value and uses the old value as the reference. Before entering numbers, rewrite the question in plain language and identify which value is the starting point. This small step prevents a correct calculation from answering the wrong question.

For a percentage of a number, convert the percentage to a decimal by dividing it by 100, then multiply by the base. For example, 15% of 240 is 0.15 × 240, which equals 36. To increase 240 by 15%, add 36 to the starting value, giving 276. To decrease it by 15%, subtract 36, giving 204. If the task asks for the percentage change from 240 to 276, compare the difference of 36 with the original 240; the increase is 15%. The reference value matters, so changing the base can change the answer.

Sequential percentages need special care. A 10% discount followed by another 10% discount is not the same as a single 20% discount, because the second discount is calculated from the already reduced price. On a starting price of 100, the first discount leaves 90; ten percent of 90 is 9, so the final amount is 81. This is a total reduction of 19%, not 20%. The same principle applies to repeated price increases, tax added after a discount, and percentage changes applied in stages. Enter each stage in order when the sequence matters.

For money, retain enough decimal places during the calculation and round only at the point required by the invoice, shop, or accounting rule. For marks, grades, and statistics, check whether the question expects a whole percentage, one decimal place, or an exact fraction. A calculator gives the arithmetic result, but it cannot decide the convention used by a form or teacher. Read the wording, identify the base, and check whether the answer is a portion, a new total, or a change between two values.