Ratio Introduction Quizzes
Visual overview of Ratio Introduction.
Introduction
Ratios compare quantities and tell us how much of one thing there is relative to another. They drive GCSE problems in recipes, mixtures, map scales, probability and finance. Mastering ratios lets you simplify, scale, and divide amounts accurately.
Example: red:blue beads \(=2:3\) means for every 2 red there are 3 blue.
Core Concepts
What is a Ratio?
A ratio compares two or more quantities using a common unit.
- Colon form: \(2:3\)
- Fraction form: \(\tfrac{2}{3}\)
- Words: “2 to 3”
Simplifying Ratios
Divide all parts by their highest common factor (HCF).
- \(8:12 \rightarrow 2:3\) (divide by 4)
- \(15:20 \rightarrow 3:4\) (divide by 5)
Equivalent Ratios
Multiply or divide all parts by the same non-zero number.
- \(2:3 \rightarrow 4:6 \rightarrow 10:15\)
- \(5:7 \rightarrow 15:21\)
Ratios with Three or More Parts
Each part shows its share of the total.
- Red:Blue:Green \(=2:3:5\) → total parts \(=10\)
Dividing a Quantity in a Given Ratio (Unit Method)
- Add the parts to get the total number of parts.
- Find the value of one part \(=\dfrac{\text{total amount}}{\text{total parts}}\).
- Multiply by each part to get each share.
Example
Divide £120 in the ratio \(2:3\).
- Total parts \(=5\) → one part \(=120\div5=£24\)
- Shares: \(2\times24=£48\) and \(3\times24=£72\)
Ratios and Fractions
Turn a ratio into fractions of the whole by dividing each part by the total parts.
- \(2:3\) → total \(=5\) → first fraction \(=\tfrac{2}{5}\), second \(=\tfrac{3}{5}\)
Scaling Quantities
Use equivalent ratios or the value-of-one-part idea.
Example (Recipe)
Flour:sugar \(=3:2\). If flour \(=9\) cups, sugar \(=?\)
- Flour is \(3\) parts → one part \(=9\div3=3\)
- Sugar \(=2\times3=6\) cups
Real-Life Uses
- Cooking/mixtures (paint, cement, chemicals)
- Maps and scale drawings
- Financial splits and investments
- Probability comparisons
Worked Examples
Example 1 (Foundation): Simplify
Simplify \(18:24\).
- HCF\(=6\) → \(3:4\)
Example 2 (Foundation): Equivalent Ratio
Find an equivalent ratio to \(5:7\).
- Multiply by \(3\) → \(15:21\)
Example 3 (Foundation): Three Parts
Red:Blue:Green \(=2:3:5\), total \(=50\).
- Total parts \(=10\) → one part \(=5\)
- Red \(=10\), Blue \(=15\), Green \(=25\)
Example 4 (Higher): Divide Money
Divide £180 in the ratio \(4:5\).
- Total parts \(=9\) → one part \(=£20\)
- Shares: \(£80\) and \(£100\)
Example 5 (Higher): Fractions from a Ratio
Boys:Girls \(=3:7\), total \(=50\).
- Fractions: boys \(\tfrac{3}{10}\), girls \(\tfrac{7}{10}\)
- Counts: \(15\) boys, \(35\) girls
Example 6 (Higher): Scale a Recipe
Sugar:Flour \(=2:5\). If flour \(=10\) cups, sugar \(=?\)
- Flour is \(5\) parts → one part \(=2\)
- Sugar \(=2\times2=4\) cups
Example 7 (Higher): Paint Mix
Red:Blue \(=3:2\). Need \(30\) L red; how much blue?
- Red is \(3\) parts → one part \(=10\) L
- Blue \(=2\times10=20\) L
Common Mistakes
- Not simplifying before working.
- Forgetting to convert units first.
- Adding parts wrongly or missing a part in three-term ratios.
- Mixing part–part with part–whole fractions.
- Not keeping proportional scaling (multiplying one side only).
Strategies & Tips
- Simplify early using HCF.
- Use the value-of-one-part method for divisions and scaling.
- Convert ratios to fractions to cross-check.
- Keep units consistent throughout.
- For three-part ratios, always total the parts first.
Summary / Call-to-Action
Ratios let you compare, scale, and split amounts reliably. With the unit method, equivalent ratios, and fraction checks, ratio problems become routine.
- Practise simplifying and finding equivalents.
- Drill the value-of-one-part method on money and recipe problems.
- Apply to map scales, mixtures and probability.