GCSE MATHS • HIGHER TIER

Percentage Decrease Made Simple

Calculate reductions, discounts and depreciation using percentages and multipliers.

Clear method

Exam practice

Worked proofs

Percentage Decrease in Four Moves

1 Identify

Identify the original amount and the percentage decrease.

2 Convert

Convert the decrease percentage into a decimal multiplier when appropriate .

3 Calculate

Multiply or find the decrease amount and subtract it from the original .

4 Check

Make sure the new value is smaller and your percentage is based on the original amount .

What You’ll Learn

Understand Percentage Decrease

Recognise when a value has fallen by a percentage .

Find the Percentage Decrease

Use the decrease and original amount to calculate the percentage fall .

Decrease an Amount

Calculate a percentage of an amount and subtract it .

Use Multipliers

Apply decrease multipliers such as 0.90, 0.80 and 0.65 .

Apply the Skill

Solve discounts, depreciation and real-life decrease problems .

Key Rules

Percentage Decrease = (Decrease ÷ Original Amount) × 100

This formula calculates how much a value has fallen as a percentage of its original value.

Worked Proof: Percentage Decrease

Step-by-Step Method

More Worked Examples

1

Question: Decrease £200 by 15%

Multiplier = 0.85

£200 × 0.85 = £170

Answer = £170

2

Question: Decrease £120 by 8%

Multiplier = 0.92

£120 × 0.92 = £110.40

Answer = £110.40

3

Question: Decrease £450 by 18%

Multiplier = 1 − 0.18 = 0.82

£450 × 0.82 = £369

Answer = £369

4

Question: A jacket costs £240 and is reduced by 35%. Find the sale price .

Multiplier = 1 − 0.35 = 0.65

£240 × 0.65 = £156

Answer = £156

Original amount: Do not use the new amount as the denominator.
Multiply by 100: Include × 100 when calculating a percentage decrease.
Multiplier: Use a decrease multiplier, not an increase multiplier.
Percentage amount: Calculate the percentage rather than subtracting the percentage number directly.

Identify the original amount before calculating a percentage decrease.
For a decrease of p%, use the multiplier 1 − p/100.
Check that a decrease produces a smaller final value.
Use the percentage decrease formula when both the original and new values are given.
Keep calculator working clear in depreciation and money questions.
Round money appropriately when needed.