11 Plus Ratio, Proportion and Percentage Questions

Ratio, proportion, fractions and percentages are related ideas in mathematics, but they are not interchangeable. A ratio compares quantities in stated parts; a fraction may describe one part of a whole; a percentage expresses a number of parts per hundred. Some methods connect across these topics, while the question wording still matters.

This guide gives examples from Year 5 and Year 6 national curriculum content, then labels percentage-change and reverse-percentage questions as extensions beyond the KS2 programme. These curriculum references describe what pupils are taught in England; they do not specify every local 11+ test. Check your target school's current format and sample material.

Several examples also show tempting wrong answers. These can help you discuss how a child reasoned, but one error is not enough to diagnose a lasting misconception.

Milestone one: Year 5, when percentages formally begin

The national curriculum asks Year 5 pupils to "recognise the per cent symbol (%) and understand that per cent relates to 'number of parts per hundred'", and to write percentages as a fraction with denominator 100 and as a decimal (national curriculum programmes of study). This Year 5 content can be useful preparation when it is relevant to a child’s local test and current learning.

The concrete milestone here is content domain reference 5F12: pupils must "solve problems that require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25" (2016 key stage 2 mathematics test framework). This names the fraction-percentage equivalents and denominator multiples included in that Year 5 programme statement; it is not a requirement to memorise every possible fraction.

Fraction	Decimal	Percentage
1/2	0.5	50%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
2/5	0.4	40%
4/5	0.8	80%
1/10	0.1	10%
1/100	0.01	1%

For example, ask how to write 4/5 as a percentage. One method is to use the equivalent 80/100. Ask your child to explain the connection, then practise timed questions only if the local test uses time limits.

Milestone two: ratio notation, and why 2:3 is not two thirds

Year 6 is the first year group in which "Ratio and proportion" appears as a named domain in the national curriculum. Before that the ideas live inside fractions and multiplication. So a Year 5 child meeting ratio notation for the first time may be encountering a newly named topic, not falling behind.

Two skills, both cheap to build:

• Simplifying. 18:24 becomes 3:4 by dividing both sides by the highest common factor, 6. Exactly the same move as simplifying a fraction.
• Converting a ratio to a fraction. In a box of 35 pens with blue to red in the ratio 3:4, red is 4/7 of the pens, not 4/3 and not 3/4.

In a part-to-part ratio such as 2:3, there are 5 shares altogether. The first quantity is 2/5 of the whole amount. Writing 2/3 instead treats the ratio as though it were already a fraction of the total. Ask your child to name what the ratio compares before converting it.

Milestone three: sharing in a ratio, two methods to compare

The Year 6 KS2 mathematics framework includes unequal sharing and grouping using fractions and multiples (content reference 6R4). A bar model and a unitary method are two ways to reason through these examples; use the method your child can explain.

The problem. Amy and Ben share money in the ratio 3:4. Altogether they have £42. How much does Amy get?

Unitary method. Total parts = 3 + 4 = 7. One part = 42 divided by 7 = £6. Amy = 3 x 6 = £18.

Bar model. Draw two bars, one of 3 equal blocks and one of 4, aligned. Seven blocks in total cover £42, so each block is £6. Amy's bar is three blocks: £18.

Identical answer, identical arithmetic. Now change one word.

The problem again. Amy and Ben share money in the ratio 3:4. Ben receives £6 more than Amy. How much do they share altogether?

Bar model. Draw the bars. Ben's bar sticks out by exactly one block, and that overhang is the £6. So one block is £6 and the seven blocks total £42. The picture does the reasoning for you.

Unitary method. You must first reason that the difference 4 - 3 = 1 part corresponds to £6, which is precisely the step children skip.

One way to choose: a bar model can make a given difference or share visible. If a total is split into a known number of equal parts, a unitary calculation may be straightforward. Neither method is always fastest; focus on understanding why the parts match the given information.

Three-part ratios behave identically. Share 72 marbles in the ratio 1:2:5: eight parts, 72 divided by 8 = 9, largest share = 5 x 9 = 45.

The examples above compare separate shares. Some questions instead give a part-to-whole ratio, so read the labels carefully.

Milestone four: recipes, rates and scale factors

The KS2 curriculum also includes scaling by simple fractions, simple rates, relative sizes and scale factors. Here are further worked examples in those contexts.

5C8c: scaling by simple fractions and problems involving simple rates. A recipe for 4 people uses 300 g of flour; how much for 6? Find one person's share (300 divided by 4 = 75 g), then multiply (6 x 75 = 450 g). Or scale by the multiplier 6/4 = 1.5 directly. If your child gives a different answer, ask them to show how the flour amount changes when the number of people changes. The answer alone cannot identify their method.

6R1: relative sizes of two quantities, missing values found by integer multiplication and division. Six notebooks cost £7.50, so ten cost £12.50 (one notebook = 125p). Work in pence to avoid decimal slips.

6R3: similar shapes where the scale factor is known or can be found. Enlarge a 4.5 cm side by scale factor 3 and you get 13.5 cm. A scale factor of 5 also turns a 7 cm map length into 35 cm.

Inverse proportion is beyond the KS2 programme, so treat this as an extension and use it only if your target school’s materials include it. Example: assume each painter works at the same constant rate, the job stays the same and adding painters does not change anyone’s rate. If four painters take 9 days, the total is 36 painter-days; six painters would take 6 days. A direct-proportion calculation would give 13.5 days, which is not sensible here because adding painters should reduce the time.

Milestone five: percentages without a calculator

Content domain reference 6R2 requires "calculation of percentages, for example 15% of 360, and the use of percentages for comparison", and 6F11 requires recall of equivalences between simple fractions, decimals and percentages. Check your target test’s equipment rules. For a non-calculator paper, percentage building blocks can make these calculations easier.

The blocks: 50% is halving, 25% is halving twice, 10% is dividing by 10, 5% is half of 10%, 1% is a tenth of 10%. Everything else is assembled.

• 15% of 360: 10% = 36, 5% = 18, total 54.
• 65% of 240: 50% = 120, 10% = 24, 5% = 12, total 156.
• 12.5% of 96: that is 1/8, so halve three times: 48, 24, 12.

To see the blocks on a bar model, enter a percentage and an amount below. The other tab shares an amount in a ratio, using the unitary method from milestone three.

The KS2 curriculum also includes using percentages for comparison. Priya scored 18 out of 25 on a quiz and Tom scored 68% on the same quiz. Who earned a higher percentage of the available marks? Scale 18/25 to hundredths (multiply both by 4) to get 72%, so Priya wins by 4 percentage points. The whole trick is turning the denominator into 100.

Try moving between a fraction and a percentage of the same amount.

Milestone six: the stretch shelf, and why it is optional for some children

The KS2 curriculum includes some percentage calculations but does not name percentage increase, decrease or original-value problems in its Year 6 programme. The KS2 mathematics test framework's percentage content includes calculations and comparison; it does not list these change and original-value problem types. Treat them as extension work unless your target test materials include them.

Test content varies by school and area. Warwickshire says the West Midlands tests may go beyond the levels children are expected to reach by the end of KS2 (Warwickshire County Council). Use published sample material from the school you are considering before adding extension topics.

If your child is still learning the core material, you may choose to focus on that first. If they are comfortable with it and the target test includes these extension types, practise them too.

1. Decrease. An £80 coat is reduced by 15%. 10% = £8, 5% = £4, so 15% = £12 and the sale price is £68.
2. Increase as a percentage. A ticket rises from £250 to £280. The increase is £30; 30/250 = 12/100 = 12%. Always divide by the original.
3. Reverse percentages. After a 10% reduction a game costs £18. The £18 is 90% of the original, so 1% = £0.20 and 100% = £20. The trap answer is £19.80, from adding 10% back on to £18, which takes 10% of the wrong number.

£19.80 is a possible trap answer: it adds 10% of the reduced price instead of finding the original whole.

Milestone seven: check the answer format

Check the response format early, alongside method practice. Formats vary by region, which is why the full map of 11+ maths topics and question types is worth reading alongside this one.

GL Assessment says tests may cover one or more of English, maths, verbal reasoning and non-verbal reasoning, with subjects and question-type balance chosen by local authorities or schools. It says its English and maths papers are mainly based on curriculum content reached in early Year 6 (GL Assessment). In Buckinghamshire, the Secondary Transfer Test is two papers, all questions are multiple-choice, and children record answers on a separate answer sheet, with maths combined with non-verbal and spatial reasoning in one paper; each paper runs about 45 minutes, or 60 including introduction and examples (Buckinghamshire Council). The West Midlands tests are multiple-choice too. Our guide to Buckinghamshire's test covers the local detail.

Three things to check for your local test:

• How unanswered questions are treated. Check the authority’s or school’s scoring guidance before deciding whether to guess.
• You can work backwards. For "after a 10% reduction the price is £18", take 10% off each option and see which lands on £18. Faster than the forward method for some children.
• Answer recording. If the local test uses a separate answer sheet, practise following its instructions and checking that each answer is in the intended place. Our answer sheet guide explains the routine.

Milestone eight: discuss the wrong answer, do not just mark it

A wrong answer can point to a question or step to review. It does not identify one specific cause by itself, so ask your child to explain their thinking. The explanations below are possibilities to check against their working:

• Answer 20 for "share 40 in the ratio 2:3". They divided the total by 2 (the count of numbers written) instead of by 5 shares. Fix: bar model, count blocks aloud.
• Answer 2/3 for "what fraction is the first share in 2:3". Ratio read as a fraction. Fix: always write the total shares first.
• Answer £19.80 for the reverse percentage. They added 10% back to the reduced price. Fix: label which number is 100%.
• A different flour amount for the recipe. Ask how the child scaled from four people to six. Check their multiplier and arithmetic before deciding what to explain again.
• Answer £6 for "Ben gets £6 more, find the total". They stopped at one part. Fix: underline what the question asks before starting.
• Answer 13.5 days for six painters. Direct proportion applied to an inverse situation. Fix: a sanity check sentence.

A short note about questions to revisit can help you choose the next practice task.

Milestone nine: the last four weeks

If a four-week practice plan fits your schedule, this is one example. Adjust the sessions to the local test and your child’s workload:

• Week 1: core ratio. Simplifying, ratio to fraction, sharing a total. Both methods on every question.
• Week 2: proportion and scale. Recipes, rates, unit conversion, scale factors. Insist on the multiplier being stated.
• Week 3: percentages. The 5F12 equivalence list to instant recall, building blocks, comparison questions.
• Week 4: mixed and timed. Shuffled questions under the clock, on an answer sheet if your area is multiple-choice, then a single diagnosis pass.

Download the printable ratio, proportion and percentage practice sheet (PDF): it has 25 questions grouped into core, further-practice and stretch sections, with an answer and method key. These section labels describe our practice set, not official test levels. It is free to download. For more topic-by-topic sets, see our 11+ maths worksheets by topic.

Common questions from parents

Could ratio appear in an 11+ test? Test content varies. The Year 6 national curriculum includes ratio and proportion, and GL says its English and maths papers are mainly based on content reached in early Year 6. Check the admissions authority or school's current sample material.

Should we buy a paid question archive? First check what your child needs to practise and whether free official samples or school materials cover it.

How much stretch work is sensible? Check your target school’s published sample questions and syllabus. Add extension work only if it matches the test your child will sit.

My child gets the right answer but cannot explain it. Ask them to show or describe one step. A bar model is one way to make the quantities visible.