Percent means out of 100
What you will learn
Know the rule, then use it
These are the short notes. Read each one, then check you can use it in the worked example below.
Method
Use a multiplier: for a 15% decrease, the multiplier is 1 − 0.15 = 0.85
Write the percentage remaining
If 15% is removed, 100% − 15% = 85% remains
Convert to a decimal multiplier
85% = 85 ÷ 100 = 0.85
Multiply the original price
£360 × 0.85 = £306
Watch out
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer
A television costs £360. It is reduced by 15% in a sale. Find the sale price.
Write the percentage remaining: If 15% is removed, 100% − 15% = 85% remains. We want to find 85% of the original price.
85. Using a multiplier combines the 'find the percentage' and 'subtract' steps into one.
Multiply the original price: £360 × 0.85 = £306.
£306
Build up to the hardest questions
Do them in order. If you miss a step, read the solution, then redo the question without looking.
WorkedreasoningA television costs £360. It is reduced by 15% in a sale. Find the sale price.
3 marks4 minspercentages-workedShow solution
A television costs £360. It is reduced by 15% in a sale. Find the sale price.
- 1.Write the percentage remaining: If 15% is removed, 100% − 15% = 85% remains. We want to find 85% of the original price.
- 2.85. Using a multiplier combines the 'find the percentage' and 'subtract' steps into one.
- 3.Multiply the original price: £360 × 0.85 = £306.
£306
- M1: write the percentage remaining
- M1: convert to a decimal multiplier
- M1: multiply the original price
- A1: £306
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
DiagnosticrecallFind 35% of 240
1 mark2 minspercentages-q1Show solution
Find 35% of 240
- 1.Spot the skill: Use a multiplier: for a 15% decrease, the multiplier is 1 − 0.15 = 0.85.
- 2.Use the write the percentage remaining stage first, then convert to a decimal multiplier.
- 3.Keep the final answer visible: 84.
84
- 85.one multiplication gives the final answer directly, which is faster and less error-prone than finding 15% and subtracting.
- A1: 84
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
EasyprocedureIncrease £480 by 12%
2 marks3 minspercentages-q2Show solution
Increase £480 by 12%
- 1.Spot the skill: Use a multiplier: for a 15% decrease, the multiplier is 1 − 0.15 = 0.85.
- 2.Use the convert to a decimal multiplier stage first, then multiply the original price.
- 3.Keep the final answer visible: £537.60.
£537.60
- 85.one multiplication gives the final answer directly, which is faster and less error-prone than finding 15% and subtracting.
- A1: £537.60
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
MediumreasoningA coat costs £126 after a 30% discount. Find the original price.
3 marks4 minspercentages-q3Show solution
A coat costs £126 after a 30% discount. Find the original price.
- 1.Spot the skill: Use a multiplier: for a 15% decrease, the multiplier is 1 − 0.15 = 0.85.
- 2.Use the multiply the original price stage first, then write the percentage remaining.
- 3.Keep the final answer visible: £180.
£180
- 85.one multiplication gives the final answer directly, which is faster and less error-prone than finding 15% and subtracting.
- A1: £180
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
Hardproblem solvingA population of 8000 increases by 5% each year. Find the population after 3 years.
3 marks5 minspercentages-q4Show solution
A population of 8000 increases by 5% each year. Find the population after 3 years.
- 1.Spot the skill: Use a multiplier: for a 15% decrease, the multiplier is 1 − 0.15 = 0.85.
- 2.Use the write the percentage remaining stage first, then convert to a decimal multiplier.
- 3.Keep the final answer visible: 9261.
9261
- 85.one multiplication gives the final answer directly, which is faster and less error-prone than finding 15% and subtracting.
- A1: 9261
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
Exam-stylemulti-stepAfter two successive discounts of 10% and 20%, what single percentage discount is equivalent? Show working.
4 marks6 minspercentages-q5Show solution
After two successive discounts of 10% and 20%, what single percentage discount is equivalent? Show working.
- 1.Spot the skill: Use a multiplier: for a 15% decrease, the multiplier is 1 − 0.15 = 0.85.
- 2.Use the convert to a decimal multiplier stage first, then multiply the original price.
- 3.Keep the final answer visible: 28%.
28%
- 85.one multiplication gives the final answer directly, which is faster and less error-prone than finding 15% and subtracting.
- A1: 28%
Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
Grade 9 stretchproblem solvingAfter a 15% increase, a price is £621. Find the original price.
4 marks7 minspercentage-g9Show solution
After a 15% increase, a price is £621. Find the original price.
- 1.Use the multiplier 1.15.
- 2.Divide the final price by the multiplier.
£540
- M1: use 621 / 1.15
- A1: £540
Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.
Hard exam-stylemulti-step problemA laptop is reduced by 12% in a sale. The sale price is £528. Find the original price.
3 marks6 minspercentage-paperShow solution
A laptop is reduced by 12% in a sale. The sale price is £528. Find the original price.
- 1.A 12% reduction leaves 88%.
- 2.Use the multiplier 0.88.
- 3.Divide the sale price by the multiplier.
£600
- M1: use 528 / 0.88
- A1: obtain £600
Read the full question before calculating. Keep each stage of your working visible.
Switch between skills
Set a timer and attempt all four questions before opening any answers. This is closer to the way skills appear in a real paper.
1Percentages - 2 marksFind 35% of 240Mark answer
84
2Calculations and order of operations - 2 marksWork out (6 + 2) × 3 − 5Mark answer
19
3Integers, decimals and place value - 2 marksOrder these from smallest to largest: 0.3, 0.03, 0.303, 0.033Mark answer
0.03, 0.033, 0.3, 0.303
4Fractions - 3 marksA recipe needs ¾ cup of sugar. How much sugar is needed for 2½ batches?Mark answer
1⅞ cups
- I can explain the method for percentages.
- I can show clear working without skipping key steps.
- I can avoid this mistake: Students find 15% of £360 = £54, then forget to subtract it from £360, giving £54 as their final answer.The question asks for the sale price, not the reduction. Always re-read what is being asked.Using the multiplier method avoids this mistake entirely.
This guide follows the Pearson Edexcel GCSE Mathematics 1MA1 specification. Practice questions are original Learnova questions shaped around official content and exam skills.