⚖️ Ratio Province · Percentage change

Percentage decrease

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

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Understand Percentage decrease

Connect fractions, decimals and multipliers to calculate percentage decrease. 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 decrease, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Percentage decrease: Percentages compare with 100. Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Keep the percentage decrease 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 decrease.

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 decrease answer.

Key vocabulary

percentagemultiplieroriginal valuechangedecimaldecrease

Rules and key facts

Given information: Percentage decrease — Decrease £80 by 5%. 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: Use multiplier 0.95: 80 × 0.95 = 76. Final answer: 76. 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 decrease.

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 decrease.

What you need first

  • Recognise the vocabulary: percentage, multiplier, original value.
  • Be able to explain the purpose of percentage decrease 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 decrease.

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 decrease — Decrease £80 by 5%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.95: 80 × 0.95 = 76. Final answer: 76. 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 decrease — Decrease £400 by 15%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.85: 400 × 0.85 = 340. Final answer: 340. Check: substitute or compare with the original information to confirm the result fits the question.

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

Challenge example

Stretch the idea

Given information: Percentage decrease — Decrease £280 by 25%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.75: 280 × 0.75 = 210. Final answer: 210. 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 decrease — Decrease £160 by 10%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.9: 160 × 0.9 = 144. Final answer: 144. 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 decrease 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 decrease answer.

Extension challenge

Create a percentage decrease 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 decrease challenge

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

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Boss challenge

Challenge Percentage decrease Guardian

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Percentage decrease Guardian

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Study cards

Core idea

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

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Key vocabulary

percentage · multiplier · original value · change · decimal · decrease

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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 decrease.

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Formula / fact

Given information: Percentage decrease — Decrease £80 by 5%. 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: Use multiplier 0.95: 80 × 0.95 = 76. Final answer: 76. Check: An increase uses a multiplier above 1; a decrease uses a multiplier below 1.

Tap to mark reviewed
Foundation example

Given information: Percentage decrease — Decrease £80 by 5%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.95: 80 × 0.95 = 76. Final answer: 76. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Percentage decrease — Decrease £400 by 15%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.85: 400 × 0.85 = 340. Final answer: 340. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Percentage decrease — Decrease £280 by 25%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.75: 280 × 0.75 = 210. Final answer: 210. 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 decrease — Decrease £160 by 10%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.9: 160 × 0.9 = 144. Final answer: 144. 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 decrease questions.

Tap to mark reviewed
Exam tip

For percentage decrease, 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 decrease, use the method, check for mistakes, and answer an exam-style question.

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Flashcards

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Help for Percentage decrease

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Simple explanation

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

Think of percentage decrease 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 decrease.

Hint 1

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

Hint 2

Identify whether the known amount is original or final.

Full worked solution

Given information: Percentage decrease — Decrease £80 by 5%. Method choice: use the percentage decrease method and show each step with the stated values. Calculation or reasoning: Use multiplier 0.95: 80 × 0.95 = 76. Final answer: 76. 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 decrease.

Common mistake warning

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

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain percentage decrease 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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