Ratio & Proportion
Year 8 🔢 Number Simplify ratios, share in a ratio, solve proportion problems.
⚖️ Ratio
A ratio compares two or more quantities. We write it as $a : b$.
Always simplify ratios by dividing by the HCF. 6:9 = 2:3
Sharing in a ratio: Share £60 in ratio 1:3
Total parts = 4. Each part = £15.
Shares: £15 and £45
Total parts = 4. Each part = £15.
Shares: £15 and £45
📏 Direct Proportion
Two quantities are in direct proportion if they increase at the same rate.
Direct Proportion
$$\frac{y}{x} = k \qquad \Rightarrow \qquad y = kx$$📉 Inverse Proportion
Two quantities are in inverse proportion if one increases as the other decreases.
Inverse Proportion
$$xy = k \qquad \Rightarrow \qquad y = \frac{k}{x}$$
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
Interactive Demonstration — Ratio & Proportion
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Interactive demonstration available in the Calculator tab!
⚖️ Ratio & Proportion Calculator
Share in a Ratio
Direct Proportion