Ratio, Proportion and Rates of Change

Ratio and proportion describe relationships between quantities. They appear in map scales, recipes, currency exchange, speed, and many other real-life contexts.

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Ratio

A ratio compares two or more quantities of the same type. The ratio 3 : 5 means "for every 3 parts of A, there are 5 parts of B."

Simplifying Ratios

Divide all parts by their HCF. Example: 18 : 24 → HCF = 6 → 3 : 4

Dividing in a Given Ratio

Add the parts, find the value of one part, then multiply.

Example: Share £72 in the ratio 3 : 5. Total parts = 8; one part = £72 ÷ 8 = £9 → 3 × £9 = £27 and 5 × £9 = £45

Ratio and Fractions

The ratio 3 : 5 means the first quantity is 3/8 of the total; the second is 5/8.

Using Ratio to Find Unknown Quantities

If the ratio of red to blue counters is 2 : 7, and there are 56 blue counters, how many red? 2/7 = r/56 → r = 16

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Scale Factors and Scale Drawings