11+ Ratio and Proportion Practice & Guide

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.

Maths: ratio 11+ at a glance

Understanding Ratio Basics for the 11+

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).

Tackling Proportion Problems

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.

Strategies for 11+ Ratio and Proportion 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.

Try Maths: ratio 11+ practice questions

Question 1
A bag contains red and blue marbles in the ratio 3:5. If there are 12 red marbles, how many blue marbles are there?
Answer: 20. The ratio of red to blue marbles is 3:5. If there are 12 red marbles, and the 'red' part of the ratio is 3, then each 'part' represents 12 ÷ 3 = 4 marbles. Since the 'blue' part of the ratio is 5, there are 5 × 4 = 20 blue marbles.
Question 2
Share £72 in the ratio 4:5.
Answer: £32 and £40. First, find the total number of parts in the ratio: 4 + 5 = 9 parts. Next, find the value of one part: £72 ÷ 9 = £8. Finally, multiply the value of one part by each number in the ratio: 4 parts = 4 × £8 = £32, and 5 parts = 5 × £8 = £40. So, the money is shared as £32 and £40.
Question 3
A recipe requires 2 eggs for every 250g of flour. If a baker uses 750g of flour, how many eggs will they need?
Answer: 6. The amount of flour used is 750g. The recipe uses 250g of flour for 2 eggs. To find out how many times more flour is used: 750g ÷ 250g = 3. So, the baker needs 3 times the number of eggs: 2 eggs × 3 = 6 eggs.
Question 4
Simplify the ratio 18:24 to its simplest form.
Answer: 3:4. To simplify a ratio, find the highest common factor (HCF) of both numbers and divide both by it. The HCF of 18 and 24 is 6. Divide both numbers by 6: 18 ÷ 6 = 3, and 24 ÷ 6 = 4. So, the simplified ratio is 3:4.

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Frequently asked questions

What is the difference between ratio and proportion?

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).

Are ratio and proportion tested in all 11+ exams?

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.

How can my child best practice ratio and proportion?

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.

What common mistakes do children make with ratio questions?

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.