Ratios, Proportions, and Rates

Ratio, proportion, and rate questions appear frequently in the UCAT Quantitative Reasoning subtest. They require you to scale quantities, divide amounts fairly, convert between units, and work with rates such as speed, density, and flow. This lesson covers the essential techniques with worked examples.

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Simplifying Ratios

A ratio compares two or more quantities. To simplify, divide all parts by their highest common factor (HCF).

Original Ratio	HCF	Simplified
12 : 8	4	3 : 2
45 : 30 : 15	15	3 : 2 : 1
100 : 250	50	2 : 5

Ratios from Different Units

If quantities are in different units, convert to the same unit first:

Example: Express 2 hours to 45 minutes as a ratio.

• Convert: 2 hours = 120 minutes
• Ratio: 120 : 45
• Simplify (HCF = 15): 8 : 3

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Sharing in a Ratio

When a total quantity is divided in a given ratio: