Key Terms
- Ratio: A comparison of two or more quantities of the same kind
- Simplest form: A ratio where the parts share no common factor (divide by HCF)
- Parts: In ratio a:b, there are a + b parts in total
- Equivalent ratios: Ratios with the same value (like equivalent fractions)
- Scale factor: The multiplier used to scale one ratio to another
Must-Know Facts
- Order matters: 2:3 is different from 3:2
- Always convert to same units before simplifying
- To share in ratio a:b: total parts = a + b; one part = total ÷ (a + b)
- In ratio 3:5, first person gets 3/8, second gets 5/8 of the total
- HCF × LCM method used to simplify large ratios
- Check: your shares must add up to the original total
Key Methods
- Simplify: divide all parts by HCF
- Sharing: find total parts, find one part = total ÷ parts, multiply by each ratio number
- Missing value: find scale factor (known value ÷ ratio part), apply to other part
- Combining ratios: make shared quantity the same in both ratios
Common Mistakes
- Reversing the order: 2:3 and 3:2 mean different things — always match the ratio to the correct quantity in the same order given
- Not converting units: 2 m : 50 cm must become 200 cm : 50 cm = 4:1 before simplifying
- Not simplifying fully: Divide both parts by their HCF — 10:15 should become 2:3, not 5:7.5
- Wrong total parts when sharing: For ratio 3:5, total parts = 8, not 5 — divide the amount by 8 to find one part
This topic summary covers Knowledge Organiser: Ratio — Basics within Ratio Basics for GCSE Mathematics. Revise Ratio Basics in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 15 of 15 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Ratio Basics
Write the ratio 12:18 in its simplest form.
Explain the difference between the ratio 3:5 and the ratio 5:3.
Quick recall flashcards
Order in Ratios
Order MATTERS!
Boys:Girls = 3:5 means:
• 3 boys for every 5 girls
Girls:Boys = 5:3 means:
• 5 girls for every 3 boys
Different meanings!
What is a ratio?
A comparison of quantities of the same kind
Written as a:b or a/b
Example: 3:5 means '3 parts to 5 parts'