⚖️ Ratio Province · Ratio foundations

Ratio problems

Use labelled parts and equal scaling to solve ratio problems accurately. In this lesson, focus on a ratio compares parts in a fixed order.

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Understand Ratio problems

Use labelled parts and equal scaling to solve ratio problems accurately. In this lesson, focus on a ratio compares parts in a fixed order.

A ratio compares parts in a fixed order. Simplifying divides every part by the same factor; sharing converts the total into equal-value parts before rebuilding each share. For ratio problems, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Ratio problems: A ratio compares parts in a fixed order. Scale the answer back to the original or add shares to recover the total. Keep the ratio problems representation visible until the final line.

Picture the idea

Build coloured ratio bars, resize equal parts and compare equivalent recipes or treasure shares. Use the model to explain one change you notice while working on ratio problems.

Check as you go

Scale the answer back to the original or add shares to recover the total. Write that check beside the final ratio problems answer.

Key vocabulary

ratiopartsimplifyequivalent ratioshareproblems

Rules and key facts

Given information: Ratio problems — Paint is mixed red : white = 3:2. If 6 ml is red, how many ml is white? Method choice: Write each labelled part against its own total before comparing or scaling. Keep ratio parts in the stated order and scale every part by the same factor. Calculation or reasoning: 3 parts became 6, so multiply by 2. White paint is 2 × 2 = 4 ml. Final answer: 4. Check: Keep ratio parts in the stated order and scale every part by the same factor.

  • Keep the stated order visible.
  • Find a common factor or the total number of parts.
  • Apply the same scale factor to every part.
  • Check that simplified parts or shares preserve the original comparison. Record the check explicitly for ratio problems.

Step-by-step method

  1. Keep the stated order visible.
  2. Find a common factor or the total number of parts.
  3. Apply the same scale factor to every part.
  4. Check that simplified parts or shares preserve the original comparison. Record the check explicitly for ratio problems.

What you need first

  • Recognise the vocabulary: ratio, part, simplify.
  • Be able to explain the purpose of ratio problems before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Recipes
  • Mixing paint and sharing costs

Visual / interactive

See the idea, then move it around

Skip to Practice

Build coloured ratio bars, resize equal parts and compare equivalent recipes or treasure shares. Use the model to explain one change you notice while working on ratio problems.

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: Ratio problems — Paint is mixed red : white = 3:2. If 6 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 6, so multiply by 2. White paint is 2 × 2 = 4 ml. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Keep the stated order visible.
  2. Find a common factor or the total number of parts.
  3. Apply the same scale factor to every part.
Secure example

Use the normal method

Given information: Ratio problems — Paint is mixed red : white = 3:14. If 30 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 30, so multiply by 10. White paint is 14 × 10 = 140 ml. Final answer: 140. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the ratio problems result against the original information.

Challenge example

Stretch the idea

Given information: Ratio problems — Paint is mixed red : white = 3:13. If 21 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 21, so multiply by 7. White paint is 13 × 7 = 91 ml. Final answer: 91. 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: Ratio problems — Paint is mixed red : white = 3:12. If 12 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 12, so multiply by 4. White paint is 12 × 4 = 48 ml. Final answer: 48. 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

  • Swapping the order of the parts. This is a key trap when answering ratio problems questions.
  • Dividing only one part of a ratio.

How to check your answer

Scale the answer back to the original or add shares to recover the total. Write that check beside the final ratio problems answer.

Extension challenge

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

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Ratio problems challenge

Use treasure split controls to solve three checked ratio problems rounds. Solve at least two of three marked rounds and use feedback to correct any error.

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Boss challenge

Challenge Ratio problems Guardian

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Study cards

Core idea

Ratio problems: A ratio compares parts in a fixed order. Scale the answer back to the original or add shares to recover the total. Keep the ratio problems representation visible until the final line.

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Key vocabulary

ratio · part · simplify · equivalent ratio · share · problems

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Rules

Keep the stated order visible. Find a common factor or the total number of parts. Apply the same scale factor to every part. Check that simplified parts or shares preserve the original comparison. Record the check explicitly for ratio problems.

Tap to mark reviewed
Formula / fact

Given information: Ratio problems — Paint is mixed red : white = 3:2. If 6 ml is red, how many ml is white? Method choice: Write each labelled part against its own total before comparing or scaling. Keep ratio parts in the stated order and scale every part by the same factor. Calculation or reasoning: 3 parts became 6, so multiply by 2. White paint is 2 × 2 = 4 ml. Final answer: 4. Check: Keep ratio parts in the stated order and scale every part by the same factor.

Tap to mark reviewed
Foundation example

Given information: Ratio problems — Paint is mixed red : white = 3:2. If 6 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 6, so multiply by 2. White paint is 2 × 2 = 4 ml. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Ratio problems — Paint is mixed red : white = 3:14. If 30 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 30, so multiply by 10. White paint is 14 × 10 = 140 ml. Final answer: 140. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Ratio problems — Paint is mixed red : white = 3:13. If 21 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 21, so multiply by 7. White paint is 13 × 7 = 91 ml. Final answer: 91. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Ratio problems — Paint is mixed red : white = 3:12. If 12 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 12, so multiply by 4. White paint is 12 × 4 = 48 ml. Final answer: 48. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Swapping the order of the parts. This is a key trap when answering ratio problems questions.

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Exam tip

For ratio problems, show the key representation before the final calculation. Use this final check: Scale the answer back to the original or add shares to recover the total.

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Real-world use

Recipes, Mixing paint and sharing costs

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Checklist

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

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Flashcards

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Help for Ratio problems

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

Simple explanation

Ratio problems: A ratio compares parts in a fixed order. Scale the answer back to the original or add shares to recover the total. Keep the ratio problems representation visible until the final line.

Think of ratio problems 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. Keep the stated order visible.
  2. Find a common factor or the total number of parts.
  3. Apply the same scale factor to every part.
  4. Check that simplified parts or shares preserve the original comparison. Record the check explicitly for ratio problems.

Hint 1

Start by naming the given information and the exact result required for ratio problems.

Hint 2

Keep the stated order visible.

Full worked solution

Given information: Ratio problems — Paint is mixed red : white = 3:2. If 6 ml is red, how many ml is white? Method choice: use the ratio problems method and show each step with the stated values. Calculation or reasoning: 3 parts became 6, so multiply by 2. White paint is 2 × 2 = 4 ml. Final answer: 4. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Keep the stated order visible. → Find a common factor or the total number of parts. → Apply the same scale factor to every part. → Check that simplified parts or shares preserve the original comparison. Record the check explicitly for ratio problems.

Common mistake warning

Swapping the order of the parts. This is a key trap when answering ratio problems questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain ratio problems in my own words.
  • I can use these words accurately: ratio, part, simplify.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Swapping the order of the parts.
  • I can apply this check: Scale the answer back to the original or add shares to recover the total.
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