⚖️ Ratio Province · Percentage reasoning

Comparing percentages

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

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Understand Comparing percentages

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

Start here

Comparing percentages: Percentages compare with 100. Apply the forward multiplier to the answer and confirm that it reproduces the stated final amount. Keep the comparing percentages 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 comparing percentages.

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 comparing percentages answer.

Key vocabulary

percentagemultiplieroriginal valuechangedecimalcomparingpercentages

Rules and key facts

Given information: Comparing percentages — Which is greater: 10% of 40 or 6? Answer with the greater value. 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: 10% of 40 = 4; compare 4 with 6. Final answer: 6. 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 comparing percentages.

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 comparing percentages.

What you need first

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

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: Comparing percentages — Which is greater: 10% of 40 or 6? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 10% of 40 = 4; compare 4 with 6. Final answer: 6. 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: Comparing percentages — Which is greater: 20% of 200 or 42? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 20% of 200 = 40; compare 40 with 42. Final answer: 42. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the comparing percentages result against the original information.

Challenge example

Stretch the idea

Given information: Comparing percentages — Which is greater: 25% of 140 or 37? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 25% of 140 = 35; compare 35 with 37. Final answer: 37. 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: Comparing percentages — Which is greater: 40% of 80 or 34? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 40% of 80 = 32; compare 32 with 34. Final answer: 34. 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 comparing percentages 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 comparing percentages answer.

Extension challenge

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

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Comparing percentages challenge

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

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Challenge Comparing percentages Guardian

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Study cards

Core idea

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

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Key vocabulary

percentage · multiplier · original value · change · decimal · comparing · percentages

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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 comparing percentages.

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Formula / fact

Given information: Comparing percentages — Which is greater: 10% of 40 or 6? Answer with the greater value. 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: 10% of 40 = 4; compare 4 with 6. Final answer: 6. Check: An increase uses a multiplier above 1; a decrease uses a multiplier below 1.

Tap to mark reviewed
Foundation example

Given information: Comparing percentages — Which is greater: 10% of 40 or 6? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 10% of 40 = 4; compare 4 with 6. Final answer: 6. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Comparing percentages — Which is greater: 20% of 200 or 42? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 20% of 200 = 40; compare 40 with 42. Final answer: 42. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Comparing percentages — Which is greater: 25% of 140 or 37? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 25% of 140 = 35; compare 35 with 37. Final answer: 37. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Comparing percentages — Which is greater: 40% of 80 or 34? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 40% of 80 = 32; compare 32 with 34. Final answer: 34. 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 comparing percentages questions.

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Exam tip

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

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Flashcards

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Help for Comparing percentages

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Simple explanation

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

Think of comparing percentages 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 comparing percentages.

Hint 1

Start by naming the given information and the exact result required for comparing percentages.

Hint 2

Identify whether the known amount is original or final.

Full worked solution

Given information: Comparing percentages — Which is greater: 10% of 40 or 6? Answer with the greater value. Method choice: use the comparing percentages method and show each step with the stated values. Calculation or reasoning: 10% of 40 = 4; compare 4 with 6. Final answer: 6. 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 comparing percentages.

Common mistake warning

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

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain comparing percentages 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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