Ratio and Proportion

Ratio and proportion questions are popular in the CEM 11+ exam. They test whether you can compare quantities, share amounts fairly, and scale values up or down. CEM may present these as straightforward ratio problems or hide them inside word problems and real-life scenarios. This lesson will make sure you are fully prepared.

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What Is a Ratio?

A ratio compares two or more quantities. It tells you how much of one thing there is compared to another.

• The ratio of boys to girls is 3 : 5 means for every 3 boys there are 5 girls.
• Ratios can be written with a colon (3 : 5) or as a fraction (3/5).

Simplifying Ratios

Simplify a ratio by dividing both parts by their Highest Common Factor (HCF).

Original Ratio	HCF	Simplified
12 : 18	6	2 : 3
20 : 35	5	4 : 7
8 : 12 : 20	4	2 : 3 : 5

Converting Units Before Simplifying

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