Knowledge Organiser: Simplifying Ratios
Part of Ratio Problems · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Simplifying Ratios within Ratio Problems for GCSE Mathematics. Revise Ratio Problems in Ratio & Proportion for GCSE Mathematics with 14 exam-style questions and 3 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 8 of 8 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 8 of 8
Practice
14 questions
Recall
3 flashcards
Knowledge Organiser: Simplifying Ratios
Key Terms
- Ratio: A comparison of two or more quantities using the : notation
- HCF: Highest Common Factor — the largest number that divides all parts exactly
- Simplest form: A ratio where the numbers share no common factor other than 1
- Equivalent ratios: Ratios that represent the same relationship (e.g. 2:3 and 4:6)
- Unit conversion: Changing quantities to the same unit before simplifying
Must-Know Facts
- Convert all quantities to the same units BEFORE simplifying
- Divide ALL parts of the ratio by the HCF
- Keep simplifying until no common factor remains
- For decimals: multiply all parts by 10 (or 100) first to get whole numbers
- For fractions: multiply all parts by the LCM of the denominators
- Use the smallest unit to avoid decimals (pence not pounds; cm not m)
Key Methods
- Step 1: convert to same units
- Step 2: find HCF of all parts
- Step 3: divide every part by the HCF
- Step 4: check no further simplification is possible
- Shortcut: divide by 2, then 3, then 5 if the HCF is not obvious
Common Mistakes
- Not converting units first: 2 km : 500 m must become 2000 m : 500 m before simplifying — ratios must have the same units throughout
- Dividing by a small factor instead of the HCF: 12:18 ÷ 2 = 6:9 — still not fully simplified; use HCF = 6 to get 2:3 in one step
- Reversing the ratio order: The order of a ratio matches the order of the quantities described — "boys to girls" is not the same as "girls to boys"
- Leaving decimals in a simplified ratio: If simplifying gives 1.5:2, multiply both by 2 to get 3:4 — ratios must always use whole numbers
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Practice Questions for Ratio Problems
A recipe uses flour and sugar in the ratio 5:2. What fraction of the mixture is flour?
The ratio of apples to oranges in a basket is 2:3. Sarah says "2/3 of the fruits are apples." Explain why Sarah is wrong.
Quick Recall Flashcards
14 questions on Ratio Problems — practise free
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