Percentage Change

GCSE Percentages percent change
Practice this formula All formulas
\( \%\,\text{change}=\frac{\text{new}-\text{old}}{\text{old}}\times100\% \)

Statement

The percentage change formula measures how much a value increases or decreases compared to its original value. It is defined as:

\[ \% \text{ change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\% \]

If the result is positive, it represents a percentage increase. If negative, it represents a percentage decrease.

Why it’s true

  • The numerator \((\text{new} - \text{old})\) gives the absolute change.
  • Dividing by the old value compares the change relative to the original amount.
  • Multiplying by 100 converts the ratio into a percentage form.

Recipe (how to use it)

  1. Identify the original (old) and new values.
  2. Calculate the difference: new − old.
  3. Divide this difference by the old value.
  4. Multiply the result by 100 to express as a percentage.

Spotting it

Percentage change is commonly used in finance, shopping discounts, population growth, exam scores, and everyday comparisons of “before and after.”

Common pairings

  • Percentage increase and decrease problems.
  • Compound growth and depreciation.
  • Profit, loss, and discounts.

Mini examples

  1. Given: Price rises from £40 to £50. Find: percentage change. Answer: \((50-40)/40 \times 100 = 25\%\).
  2. Given: Population decreases from 200 to 160. Find: percentage change. Answer: \((160-200)/200 \times 100 = -20\%\), i.e. a 20% decrease.

Pitfalls

  • Dividing by the new value instead of the old one.
  • Forgetting to multiply by 100.
  • Not recognising that negative results mean decreases.

Exam strategy

  • Clearly identify which value is “old” and which is “new.”
  • Check the sign — positive for increase, negative for decrease.
  • Simplify fractions before multiplying by 100 when possible.

Summary

The percentage change formula compares the difference between new and old values relative to the old value, then converts this into a percentage. It is vital in handling real-world percentage problems, from shopping discounts to population growth and finance.