Simplify ratios, share totals and scale proportions
Compare quantities in common units · Share a total using ratio parts · Scale a fixed proportion
Section Paper 1 · Historical Core · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Fractions and unit conversions
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Compare quantities in common units
- Share a total using ratio parts
- Scale a fixed proportion
Common units and ratio order
A ratio compares quantities in a stated order. Convert to the same units before simplifying: 50 cm : 2 m = 50 : 200 = 1 : 4. Equivalent ratios multiply or divide every part by the same non-zero factor.
A share ratio 2 : 3 means 5 parts altogether; the first share is 2/5 of the total, not 2/3. A part-to-part ratio and a part-to-whole fraction answer different questions.
Scale a fixed relationship
For a fixed recipe or mixture, scale every ingredient by the same multiplier. For a unit rate, divide the output by its input quantity, then multiply by the required quantity. State the assumption that the proportions or rate remain unchanged.
Sources for this lesson
Pause and explain
In a red:blue ratio of 2:3, what fraction of the total is red?
Worked example
Share 84 in the ratio 2 : 5.
Show the worked solution
- There are 7 equal parts.
- Each is 84/7 = 12; the shares are 24 and 60.
Answer 24 and 60, in that order.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Simplify 300 g : 1.2 kg.
Give me a hint
Use grams for both quantities.
Compare my reasoning
- 1.2 kg = 1200 g.
- 300 : 1200 = 1 : 4.
1 : 4.
Look for these in your work
- Convert units first
- Preserve order
Share 90 among three groups in ratio 2 : 3 : 4.
Give me a hint
Add the ratio parts.
Compare my reasoning
- There are 9 parts, each worth 10.
- The shares are 20, 30 and 40.
20, 30, 40.
Look for these in your work
- Use all three parts
- Check the shares total 90
A recipe uses 250 g flour for 4 portions. For 10 portions, how much is needed if the recipe scales directly?
Give me a hint
Scale by 10/4.
Compare my reasoning
- Multiplier = 2.5.
- 250 × 2.5 = 625 g.
625 g, assuming unchanged proportions.
Look for these in your work
- Apply one multiplier
- State the scaling assumption
Common mistakes
- Do not mix units in a ratio.
- Do not divide the total by just one ratio part.
What can you explain now?
In a red:blue ratio of 2:3, what fraction of the total is red?
Compare with the explanation
2/5.
The whole has 2 + 3 = 5 parts.
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Make it stick
In a red:blue ratio of 2:3, what fraction of the total is red?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.