Year 10 maths lesson · Percentages

Percentage Change

Find the percentage change between two amounts by working out the multiplier, and find the overall change when an amount goes up and down several times.

  • About 4–7 minutes
  • 5 quick questions as you go
  • Then about 5 minutes of practice
Practice questions → Set for Class

Worked examples

A price rises from $40 to $50.40. What is the percentage change?

  1. Multiplier × original = final, so 40x = 50.4
  2. x = 50.4 ÷ 40 = 1.26
  3. 1.26 = 1 + 0.26, a 26% increase

A shirt costs $80 but sells for $68. What is the percentage change?

  1. 80x = 68, so x = 68 ÷ 80 = 0.85
  2. 0.85 is less than 1, so it's a decrease
  3. 1 − 0.85 = 0.15, a 15% decrease

$8000 grows by 20%, then by 20% again. What is the overall change?

  1. Each 20% increase is × 1.2
  2. 1.2 × 1.2 = 1.44, a 44% increase
  3. 1.44 × 8000 = $11,520

$30,000 gains 20%, loses 30%, then gains 25%. What is the overall change?

  1. Multipliers: 1.2, 0.7 and 1.25
  2. 1.2 × 0.7 × 1.25 = 1.05, a 5% increase
  3. 1.05 × 30,000 = $31,500

Before this lesson

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Lesson transcript

Everything the lesson says, word for word

A price of $40 rises to $50.40. What is the percentage change? Think of it like this: some multiplier times the original equals the final. So something times 40 equals 50.4. Let’s call the unknown multiplier x. In algebra we write 40x equals 50.4. To solve, we divide both sides by 40. On the left the 40s cancel, leaving just x. On the right, 50.4 divided by 40 is 1.26. Sense check — 1.26 is bigger than 1, so multiplying by it makes the value bigger. That matches: this was an increase. Now, 1.26 equals 1 plus 0.26 — so it’s a 26% increase.

A shirt costs $80 but sells for $68. What’s the percentage change? Same setup: 80x equals 68. Divide both sides by 80. x equals 68 divided by 80, which is 0.85. 0.85 is less than 1 — multiplying by it shrinks the value — so this is a decrease. To find the percentage, 1 minus 0.85 is 0.15. That’s a 15% decrease.

An $8000 investment grows by 20%, then 20% again. What is the overall percentage change? We start with 8000. To increase by 20%, we multiply by 1.2. Then we increase that by another 20%, so we multiply by 1.2 again. Let’s look at the multiplier — 1.2 times 1.2. That’s 1.44. So the multiplier is 1.44 — a 44% increase. Final value: 1.44 × 8000 = $11,520.

Priya invests $30,000 in shares. In year 1 they gain 20%, in year 2 they lose 30%, in year 3 they gain 25%. What is the overall percentage change? We start with 30,000. In year 1 they gain 20%, so we multiply by 1.2. In year 2 they lose 30%, so we multiply by 0.7. In year 3 they gain 25%, so we multiply by 1.25. Let’s look at the multiplier — 1.2 times 0.7 times 1.25 works out to 1.05. So the multiplier is 1.05 — a 5% increase. Final value: 1.05 × 30,000 = $31,500.

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