Increasing / decreasing a quantity by a percentage

Understanding Increase/Decrease by a Percentage

A percentage increase represents a growth in quantity by a certain fraction out of 100. If a quantity increases by 20%, it increases by 20 out of 100 (or 1/5) of its original value.
Similarly, a percentage decrease represents a reduction in quantity by a certain fraction out of 100. If a quantity decreases by 25%, it decreases by 25 out of 100 (or 1/4) of its original value.

Calculating Percentage Increase

To calculate a percentage increase, find the difference between the new value and the original value. Divide this by the original value, multiply by 100 to convert it to a percentage.
For example, if an item originally costs £10 and has increased to £12, the percentage increase is (12-10) ÷10 *100 = 20%.

Calculating Percentage Decrease

To calculate a percentage decrease, find the difference between the original value and the new (reduced) value, divide this by the original value, then multiply by 100 to convert it to a percentage.
For instance, if an item originally cost £10 and has decreased to £7, the percentage decrease is (10-7) ÷ 10 * 100 = 30%.

Effects of Percentage Increase and Decrease

While calculating percentage increase or decrease, it’s crucial to remember that these changes are not symmetric. A 50% decrease doesn’t get balanced out by a 50% increase. For example, if the price of an item decreases by 50% from £100 to £50 and then increases by 50%, it becomes £75, not the original £100.
A more significant percentage decrease is needed to return to the original quantity after a percentage increase and vice versa, due to the effects of compounding.

Practical Application of Percentage Increase/Decrease

Understanding percentage increase and decrease is important for various practical applications, such as calculating discounts while shopping, changes in stock market prices, variations in salary or rent, or determining the rate of inflation.

Solving Problems Involving Percentage Increase/Decrease

To solve problems related to percentage increase or percentage decrease, you need to be comfortable working with fractions and percentages. And remember to double-check your answers, as answers that lead to a negative amount or more than 100% can indicate a miscalculation or misunderstanding of the problem.