Ratio and proportion are fundamental mathematical concepts frequently tested in 11+ entrance exams. These topics assess a child's ability to understand relationships between quantities and scale them appropriately. Strong proficiency in this area is crucial for success in the quantitative sections of the exam.
This guide offers practical advice, key facts, and practice questions to help your child develop a solid understanding of ratio and proportion as it applies to the 11+ syllabus. Consistent practice and a clear grasp of the underlying principles will build confidence.
Ratio is a way to compare parts of a whole or different quantities. For example, if a fruit bowl has 3 apples and 2 bananas, the ratio of apples to bananas is 3:2. It's important for children to understand that ratios can be simplified, much like fractions. If there are 6 red marbles and 4 blue marbles, the ratio 6:4 can be simplified by dividing both numbers by their highest common factor (2), resulting in a simplified ratio of 3:2.
When tackling 11+ ratio problems, encourage your child to identify what is being compared and to write the ratio in the correct order. For instance, a ratio of 'boys to girls' must be written with the number of boys first. Practice simplifying ratios and finding equivalent ratios (e.g., 2:3 is equivalent to 4:6).
Proportion often involves scaling quantities up or down based on a given ratio. If a recipe for 4 people requires 200g of flour, a proportion problem might ask how much flour is needed for 6 people. Here, the relationship is directly proportional: as the number of people increases, the amount of flour increases.
A common strategy for proportion problems is to find the 'value of one part'. Using the recipe example, if 200g is for 4 people, then 1 person needs 200g ÷ 4 = 50g of flour. Then, for 6 people, it would be 50g × 6 = 300g. This method helps break down complex problems into manageable steps. Children should also be aware of inverse proportion, though it is less common in entry-level 11+ questions.
Visual aids can be very effective. Drawing diagrams, using bar models, or even physical objects can help children visualise the parts of a ratio and how they relate to the whole. For example, when sharing an amount in a given ratio, drawing boxes representing each part can make the calculation clearer.
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Start free →A ratio compares two or more quantities (e.g., 3:2). Proportion deals with the equality of two ratios or how quantities change in relation to each other (e.g., if 3 apples cost £1, then 6 apples cost £2).
Yes, ratio and proportion are core mathematical topics and are very commonly tested across all major 11+ exam boards, including GL Assessment, CEM, and independent school papers. The complexity may vary.
Regular practice with varied question types is key. Encourage them to draw diagrams, use the unitary method (finding the value of one part), and check their answers. Practising past papers and using dedicated 11+ resources can also be very beneficial.
Common mistakes include not simplifying ratios fully, mixing up the order of the ratio (e.g., writing 2:3 instead of 3:2), or incorrectly calculating the 'value of one part' when sharing amounts. Careful reading of the question is essential.