All skills Math

Learn Index · Fractions, Decimals, and Percentages Grade 9–10

Percentage change

The change divided by the original amount, written as a percent.

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How much did it change?

Percent change describes how much something grew or shrank compared to where it started.

Percent change = (new value − original value) ÷ original value × 100%

  • Positive → percent increase
  • Negative → percent decrease

The original value is always the base (the denominator).

Examples

Increase: A bus fare rises from $3.00 to $3.30.

  • Change = 0.30
  • 0.30 ÷ 3.00 = 0.10 → 10% increase

Decrease: A town’s population falls from 25,000 to 23,500.

  • Change = −1,500
  • −1,500 ÷ 25,000 = −0.06 → 6% decrease

Why the base matters

From 50 to 100 is a 100% increase (it doubled). From 100 back to 50 is a 50% decrease. Same numbers, different base!

Finding the original value

Sometimes you know the new value and the percent change.

Example: After a 20% increase, a price is $96. Original price?

  • 1.20 × original = 96
  • Original = 96 ÷ 1.20 = $80

A common mistake is to take 20% off $96 ($76.80). That’s wrong, because the 20% was of the original, not of $96.

Percent change vs percentage points

If an interest rate goes from 4% to 5%:

  • It rose 1 percentage point (5 − 4).
  • It rose 25% (1 ÷ 4).

News reports sometimes mix these up.

Repeated changes

Two changes multiply; they don’t add.

  • +10% then +10%: 1.1 × 1.1 = 1.21 → 21% total increase.
  • +50% then −50%: 1.5 × 0.5 = 0.75 → 25% decrease overall.

Real-life uses

  • Price changes and inflation
  • Population growth
  • Test score improvements
  • Stock prices
  • Comparing sales from one year to the next

Worked examples

Example 1: A plant grows from 12 cm to 15 cm. Percent change?

3 ÷ 12 = 0.25 → 25% increase.

Example 2: A laptop drops from $1,200 to $900. Percent change?

−300 ÷ 1,200 = −25% (25% decrease).

Example 3: After a 15% discount, a coat costs $68. Original price?

68 ÷ 0.85 = $80.

Common mistakes

  • Dividing by the new value instead of the original.
  • Adding successive percent changes.
  • Confusing percentage points with percent change.

Try it yourself

  1. From 40 to 50: percent change?
  2. From 80 to 60: percent change?
  3. A salary rose 4% to $52,000. Original?
  4. A score went from 60% to 75%. Change in percentage points? Percent change?

Answers: 1) 25% increase 2) 25% decrease 3) $50,000 4) 15 points; 25% increase

Quick recap

  • Percent change = change ÷ original value × 100%.
  • The original is always the base.
  • Successive changes multiply; percentage points ≠ percent change.