Percentage · lesson 12 of 20 · free

Percentage change: up or down? — How to calculate percentage

Percentage change is one formula for both increases and decreases. Find the change, divide by the OLD value, multiply by 100, and then say whether it went up or down. The most common mistake is dividing by the new value.

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How to work it out

From the old value — “percentage change = change ÷ old value × 100, then say increase or decrease”

  1. Change = bigger − smaller; say whether it went up (increase) or down (decrease).
  2. Percentage change = change ÷ OLD value × 100.
  3. Never divide by the new value: 40 → 50 is a 25% increase, but 50 → 40 is a 20% decrease.

Use it for: News about prices and marks, comparing this year with last year, and Class 8–10 comparing-quantities problems.

🧮 Check your own sums with the free Percentage calculator — it shows the working.

Worked example: A number changes from 50 to 40. Which is the right percentage change? 20% decrease

  1. Change = 50 − 40 = 10. It went down, so it is a decrease.
  2. Percentage change = change ÷ OLD value (50, not 40) × 100 = 10 ÷ 50 × 100.
  3. 10 × 100 = 1000, and 1000 ÷ 50 = 20. So it is 20%.
  4. So the answer is “20% decrease”.

Check: 20% of 50 = 10, and 50 − 10 = 40 ✓

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🏁 Lesson 12 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Percentage Change Worksheet

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