Ratios and Rates

Ratios and rates appear frequently in UCAT DM data interpretation questions. They test whether you can compare quantities that are expressed in different units or formats, scale values proportionally, and identify when a direct comparison is invalid. This lesson covers the essential techniques.

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What Is a Ratio?

A ratio compares two or more quantities using the same unit. It can be written as:

• 3:2 (colon notation)
• 3/2 (fraction notation)
• "3 to 2" (verbal notation)

Simplifying Ratios

Divide all parts by their highest common factor.

Original ratio	Simplified
15:10	3:2
24:36:12	2:3:1
100:250	2:5

Sharing in a Ratio

A research grant of £120,000 is split between three departments in the ratio 3:2:1. How much does each department receive?

• Total parts = 3 + 2 + 1 = 6
• One part = £120,000 / 6 = £20,000
• Department A = 3 × £20,000 = £60,000
• Department B = 2 × £20,000 = £40,000
• Department C = 1 × £20,000 = £20,000

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What Is a Rate?