Percentage change | OCR GCSE Maths Notes

Visual model

Percentage change uses a multiplier

originalnew

\times 1.15

15% increase: multiply by 1.15

Gold-standard guide

20 mins

What you will learn

Calculate percentage increases, decreases and reverse percentages.

Use a clear step-by-step method for percentage change.

Check your answer and avoid the most common exam mistake.

Useful before you start

Core number skillsEarlier ratio, proportion and rates of change skillsShowing clear working

Core knowledge

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

Multiplier method: new value = original × multiplier

Step 1

Find the sale price of the coat

Multiplier = 1 − 0.18 = 0.82

Step 2

Set up the reverse percentage for the bag

The £52 represents 65% of the original (100% − 35% = 65%)

Step 3

Divide to find the original price

Original = £52 ÷ 0.65 = £80

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing

Multiplier

increase by r% means multiply by 1 + r/100.

Reverse

$starting value = final valu\frac{e}{total} multiplier.$

Worked example

A coat costs £85. It is reduced by 18% in a sale. Find the sale price. Then find the original price of a bag that costs £52 after a 35% reduction.

Find the sale price of the coat: Multiplier = 1 − 0.18 = 0.82. Sale price = £85 × 0.82 = £69.70.

Set up the reverse percentage for the bag: The £52 represents 65% of the original (100% − 35% = 65%). 65.

Divide to find the original price: Original = £52 ÷ 0.65 = £80.

Final answer

Sale price of coat = £69.70; original price of bag = £80

Question ladder

Build up to the hardest questions

Do them in order. If you miss a step, read the solution, then redo the question without looking.

Workedreasoning

A coat costs £85. It is reduced by 18% in a sale. Find the sale price. Then find the original price of a bag that costs £52 after a 35% reduction.

3 marks4 minspercentage-change-worked

Show solution

Worked solution

1.Find the sale price of the coat: Multiplier = 1 − 0.18 = 0.82. Sale price = £85 × 0.82 = £69.70.
2.Set up the reverse percentage for the bag: The £52 represents 65% of the original (100% − 35% = 65%). 65.
3.Divide to find the original price: Original = £52 ÷ 0.65 = £80.

Final answer

Sale price of coat = £69.70; original price of bag = £80

Mark points

M1: find the sale price of the coat
M1: set up the reverse percentage for the bag
M1: divide to find the original price
A1: Sale price of coat = £69.70; original price of bag = £80

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

Diagnosticrecall

Increase £240 by 12%.

1 mark2 minspercentage-change-q1

Show solution

Worked solution

1.Spot the skill: Multiplier method: new value = original × multiplier.
2.Use the find the sale price of the coat stage first, then set up the reverse percentage for the bag.
3.Keep the final answer visible: £268.80.

Final answer

£268.80

Mark points

M1: use the correct multiplier method: new value = original × multiplier.for an increase of p%: multiply by (1 + p/100). for a decrease of p%: multiply by (1 − p/100).for reverse percentage: divide by the multiplier.
A1: £268.80

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

Easyprocedure

A TV costs £374 after a 15% reduction. Find the original price.

2 marks3 minspercentage-change-q2

Show solution

Worked solution

1.Spot the skill: Multiplier method: new value = original × multiplier.
2.Use the set up the reverse percentage for the bag stage first, then divide to find the original price.
3.Keep the final answer visible: £440.

Final answer

£440

Mark points

M1: use the correct multiplier method: new value = original × multiplier.for an increase of p%: multiply by (1 + p/100). for a decrease of p%: multiply by (1 − p/100).for reverse percentage: divide by the multiplier.
A1: £440

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

Mediumreasoning

A salary rises from £28,000 to £30,520. Find the percentage increase.

3 marks4 minspercentage-change-q3

Show solution

Worked solution

1.Spot the skill: Multiplier method: new value = original × multiplier.
2.Use the divide to find the original price stage first, then find the sale price of the coat.
3.Keep the final answer visible: 9%.

Final answer

Mark points

M1: use the correct multiplier method: new value = original × multiplier.for an increase of p%: multiply by (1 + p/100). for a decrease of p%: multiply by (1 − p/100).for reverse percentage: divide by the multiplier.
A1: 9%

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

Hardproblem solving

A car depreciates by 20% per year. It was worth £12,000 new. Find its value after 2 years.

3 marks5 minspercentage-change-q4

Show solution

Worked solution

1.Spot the skill: Multiplier method: new value = original × multiplier.
2.Use the find the sale price of the coat stage first, then set up the reverse percentage for the bag.
3.Keep the final answer visible: £7,680.

Final answer

£7,680

Mark points

M1: use the correct multiplier method: new value = original × multiplier.for an increase of p%: multiply by (1 + p/100). for a decrease of p%: multiply by (1 − p/100).for reverse percentage: divide by the multiplier.
A1: £7,680

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

Exam-stylemulti-step

After a 40% increase, a price is £56. What was the original price?

4 marks6 minspercentage-change-q5

Show solution

Worked solution

1.Spot the skill: Multiplier method: new value = original × multiplier.
2.Use the set up the reverse percentage for the bag stage first, then divide to find the original price.
3.Keep the final answer visible: £40.

Final answer

£40

Mark points

M1: use the correct multiplier method: new value = original × multiplier.for an increase of p%: multiply by (1 + p/100). for a decrease of p%: multiply by (1 − p/100).for reverse percentage: divide by the multiplier.
A1: £40

Watch out

For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

Grade 9 stretchproblem solving

A population grows by 10% each year. After 2 years it is 1452. Find the original population.

4 marks7 minsreverse-percentage-g9

Show solution

Worked solution

1.Use the multiplier 1.1 twice.
2.Divide by 1.1².

Final answer

1200

Mark points

M1: use 1452 / 1.1²
A1: 1200

Watch out

Do not rush straight into arithmetic. Select the relevant method and show a complete chain of working.

Timed checkpoint

12 mins - 9 marks

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.

1Percentage change - 2 marksIncrease £240 by 12%.Mark answer

Answer

£268.80

2Ratio and sharing - 2 marksTwo people share profit in ratio 5:3. Total profit £640. Find each share.Mark answer

Answer

£400 and £240

3Fractions and ratios - 2 marksA map scale is 1:25,000. Express as a fraction.Mark answer

Answer

$\frac{1}{2}5$ ,000

4Direct and inverse proportion - 3 marksy ∝ 1/x². When x = 2, y = 9. Find y when x = 6.Mark answer

Answer

Mastery check

I can explain the method for percentage change.
I can show clear working without skipping key steps.
I can avoid this mistake: For reverse percentage, students multiply by the multiplier instead of dividing. 80 (wrong).Always divide to reverse a percentage change.

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Explain percentage change from the beginning.Give me a hint for a percentage change question.Quiz me on percentage change.

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