⚖️ Ratio Province · Percentage change

Percentage change

Connect fractions, decimals and multipliers to calculate percentage change. In this lesson, focus on percentages compare with 100.

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Understand Percentage change

Connect fractions, decimals and multipliers to calculate percentage change. In this lesson, focus on percentages compare with 100.

Percentages compare with 100. A multiplier combines the original 100% with an increase or decrease in one decimal calculation. For percentage change, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Percentage change: Percentages compare with 100. Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Keep the percentage change representation visible until the final line.

Picture the idea

Fill a 100-cell bar, adjust a multiplier dial and compare original, change and final values. Use the model to explain one change you notice while working on percentage change.

Check as you go

Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Write that check beside the final percentage change answer.

Key vocabulary

percentagemultiplieroriginal valuechangedecimal

Rules and key facts

Given information: Percentage change — A price changes from £40 to £42. Find the percentage increase. Method choice: Turn the percentage into a decimal before using a multiplier. An increase uses a multiplier above 1; a decrease uses a multiplier below 1. Calculation or reasoning: Increase = 42 − 40 = 2. Divide by the original amount 40, then multiply by 100: 2 ÷ 40 × 100 = 5%. Check: 5% of 40 is 2. Final answer: 5. Check: An increase uses a multiplier above 1; a decrease uses a multiplier below 1.

  • Identify whether the known amount is original or final.
  • Convert the percentage to a decimal multiplier.
  • Multiply for a forward change or divide for a reverse change.
  • Estimate and label the final answer in context. Record the check explicitly for percentage change.

Step-by-step method

  1. Identify whether the known amount is original or final.
  2. Convert the percentage to a decimal multiplier.
  3. Multiply for a forward change or divide for a reverse change.
  4. Estimate and label the final answer in context. Record the check explicitly for percentage change.

What you need first

  • Recognise the vocabulary: percentage, multiplier, original value.
  • Be able to explain the purpose of percentage change before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Sales and interest
  • Population change

Visual / interactive

See the idea, then move it around

Skip to Practice

Fill a 100-cell bar, adjust a multiplier dial and compare original, change and final values. Use the model to explain one change you notice while working on percentage change.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
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Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Percentage change — A price changes from £40 to £42. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 2. Divide by original 40, then × 100 = 5%. Final answer: 5. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Identify whether the known amount is original or final.
  2. Convert the percentage to a decimal multiplier.
  3. Multiply for a forward change or divide for a reverse change.
Secure example

Use the normal method

Given information: Percentage change — A price changes from £200 to £220.00000000000003. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 20.00000000000003. Divide by original 200, then × 100 = 10%. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the percentage change result against the original information.

Challenge example

Stretch the idea

Given information: Percentage change — A price changes from £140 to £161. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 21. Divide by original 140, then × 100 = 15%. Final answer: 15. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Percentage change — A price changes from £80 to £96. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 16. Divide by original 80, then × 100 = 20%. Final answer: 20. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Underline the units and command word. Show the key calculation and write the answer in context.

Common mistakes

  • Subtracting the stated percentage from a final amount in a reverse problem. This is a key trap when answering percentage change questions.
  • Using 0.2 instead of 1.2 for a 20% increase.

How to check your answer

Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Write that check beside the final percentage change answer.

Extension challenge

Create a percentage change problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

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Percentage change challenge

Use multiplier battle controls to solve three checked percentage change rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Boss challenge

Challenge Percentage change Guardian

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Percentage change Guardian

Timed mixed-difficulty battle. Practice first if you want, or jump in and learn from feedback.

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Study cards

Core idea

Percentage change: Percentages compare with 100. Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Keep the percentage change representation visible until the final line.

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Key vocabulary

percentage · multiplier · original value · change · decimal

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Rules

Identify whether the known amount is original or final. Convert the percentage to a decimal multiplier. Multiply for a forward change or divide for a reverse change. Estimate and label the final answer in context. Record the check explicitly for percentage change.

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Formula / fact

Given information: Percentage change — A price changes from £40 to £42. Find the percentage increase. Method choice: Turn the percentage into a decimal before using a multiplier. An increase uses a multiplier above 1; a decrease uses a multiplier below 1. Calculation or reasoning: Increase = 42 − 40 = 2. Divide by the original amount 40, then multiply by 100: 2 ÷ 40 × 100 = 5%. Check: 5% of 40 is 2. Final answer: 5. Check: An increase uses a multiplier above 1; a decrease uses a multiplier below 1.

Tap to mark reviewed
Foundation example

Given information: Percentage change — A price changes from £40 to £42. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 2. Divide by original 40, then × 100 = 5%. Final answer: 5. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Percentage change — A price changes from £200 to £220.00000000000003. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 20.00000000000003. Divide by original 200, then × 100 = 10%. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Percentage change — A price changes from £140 to £161. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 21. Divide by original 140, then × 100 = 15%. Final answer: 15. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Percentage change — A price changes from £80 to £96. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 16. Divide by original 80, then × 100 = 20%. Final answer: 20. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Subtracting the stated percentage from a final amount in a reverse problem. This is a key trap when answering percentage change questions.

Tap to mark reviewed
Exam tip

For percentage change, show the key representation before the final calculation. Use this final check: Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount.

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Real-world use

Sales and interest, Population change

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Checklist

I can explain percentage change, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

I’m Stuck

Help for Percentage change

Use this whenever a question feels confusing. Nothing here is locked.

Simple explanation

Percentage change: Percentages compare with 100. Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Keep the percentage change representation visible until the final line.

Think of percentage change as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Identify whether the known amount is original or final.
  2. Convert the percentage to a decimal multiplier.
  3. Multiply for a forward change or divide for a reverse change.
  4. Estimate and label the final answer in context. Record the check explicitly for percentage change.

Hint 1

Start by naming the given information and the exact result required for percentage change.

Hint 2

Identify whether the known amount is original or final.

Full worked solution

Given information: Percentage change — A price changes from £40 to £42. Find the percentage increase. Method choice: use the percentage change method and show each step with the stated values. Calculation or reasoning: Increase = 2. Divide by original 40, then × 100 = 5%. Final answer: 5. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Identify whether the known amount is original or final. → Convert the percentage to a decimal multiplier. → Multiply for a forward change or divide for a reverse change. → Estimate and label the final answer in context. Record the check explicitly for percentage change.

Common mistake warning

Subtracting the stated percentage from a final amount in a reverse problem. This is a key trap when answering percentage change questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain percentage change in my own words.
  • I can use these words accurately: percentage, multiplier, original value.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Subtracting the stated percentage from a final amount in a reverse problem.
  • I can apply this check: Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount.
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