Percentage Change

Percentage change questions are among the most frequently tested in QR. They ask you to calculate how much a value has increased or decreased as a proportion of the original value. This lesson covers calculating percentage increases and decreases, comparing percentage changes, and avoiding the common traps.

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The Formula

Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100

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

Simplified:

Percentage Change = (Change ÷ Original) × 100

Critical Rule: Always divide by the original value (the "before" value, the starting point). This is the single most important thing to remember about percentage change.

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Calculating Percentage Increase

Worked Example

Data: A town's population grew from 25,000 to 28,500.

Question: What is the percentage increase?

• Change: 28,500 − 25,000 = 3,500
• Percentage increase: (3,500 ÷ 25,000) × 100
• 3,500 ÷ 25,000 = 0.14
• 0.14 × 100 = 14%

Simplification Shortcut

When possible, simplify the fraction before dividing:

• 3,500/25,000 = 35/250 = 7/50 = 14/100 = 14%

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Calculating Percentage Decrease

Worked Example