Ratio

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Understanding Ratio & Proportion

Ratios compare quantities. They appear everywhere: recipes, maps, mixing paint, sharing money. Mastering ratios helps you solve many real-world problems.

Key Points:

A ratio compares two or more quantities: 3:2 means "3 parts to 2 parts"
Ratios can be simplified like fractions - divide all parts by the same number
To share an amount in a ratio, add the parts and divide the total
Proportion means two ratios are equal - use cross-multiplication to solve

Top Tips

  • Always check your answer adds up to the original total when sharing
  • The unitary method (finding the value of 1) works for most proportion questions
  • Read carefully: "ratio of boys to girls" means boys:girls, not girls:boys

Worked Examples

1Step 1: Find the highest common factor (HCF) of 45 and 30
2Step 2: Factors of 45: 1, 3, 5, 9, 15, 45. Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
3Step 3: HCF = 15
4Step 4: Divide both parts by 15: 45÷15 : 30÷15 = 3:2
Answer: 3:2

🎬 Video Tutorials

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Writing & Simplifying Ratios

⏱️ 8:45

Learn how to write and simplify ratios step by step.

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Sharing in a Ratio

⏱️ 7:32

How to share amounts in a given ratio.

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Expressing Ratios as Fractions

⏱️ 9:15

Convert ratios to fractions and percentages.

🔗 More videos: Visit Maths Genie, Corbett Maths, or BBC Bitesize for more free GCSE maths resources!

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Rules to Follow

💡 Click on any rule to see more details!

Simplify a Ratio

Divide all parts by the highest common factor. Exa...

Share in a Ratio

Add ratio parts, divide total by sum, multiply eac...

Ratio to Fraction

Each part becomes fraction of total. In ratio 2:3,...

Direct Proportion

If one quantity doubles, the other doubles too. Us...

Common Trap

Don't confuse ratio 2:3 with fraction 2/3. The rat...