11+ ratio and proportion: a clear method

Almost every 11+ ratio and proportion question can be solved by finding the value of one single part first, then multiplying to build whichever share or total the question asks for. Labelling the ratio columns before calculating prevents the common slip of dividing by the total number of parts when the question has only given you one share.

In 11+ Mathematics, ratio and proportion problems often appear as recipes, paint mixes, map scales, or money-sharing puzzles. GL Assessment says the school or local authority chooses the subjects and the balance of question types, so check your own test’s guidance.^[1] Teaching your child to write a neat labelled line of working turns all of those story settings into the same calm three-step routine.

A three-step method

1. Write what each number in the ratio stands for

Ratio order matters: “flour and sugar in the ratio 3 : 2” means flour is 3 parts and sugar is 2 parts. Write initial letters above the ratio (F : S = 3 : 2) and, if the question mentions the whole mixture or a total amount to share, add a Total column on the end (3 + 2 = 5 parts).

Next, look at the number given in the question and write it directly underneath the column it belongs to:

• Total given: “Share 250 g in the ratio 3 : 2” puts 250 g under the Total (5 parts) column.
• One share given: “Sam uses 150 g of sugar” puts 150 g under the Sugar (2 parts) column.
• Difference given: “There is 40 g more flour than sugar” puts 40 g under the Difference (3 − 2 = 1 part) between the two shares.

2. Find what one part is worth

Divide the known amount by the number of parts in that same column. When 2 parts of sugar weigh 150 g, divide 150 ÷ 2 to find that 1 part = 75 g. Writing 1 part = … on its own line keeps the calculation clear and stops your child from losing track halfway through a multi-step problem.

3. Multiply to build the amount asked for, then check by simplifying

Check what the final sentence of the question asks for — the other share, the difference between the shares, or the total weight of the whole mixture — and multiply the value of 1 part by that number of parts. Finish by including the unit (g, ml, cm, £) and checking that your final numbers simplify back to the original ratio (225 : 150 divided by 75 gives 3 : 2).

Common mistakes

• Reading the ratio in the wrong order: If a question introduces “red and blue beads in the ratio 2 : 5” and later asks “How many blue beads and how many red beads?”, labelling R : B at the start prevents swapping the two numbers.
• Dividing by the total parts when the question gives only one share: In the worked example above, 150 g is the sugar (2 parts), not the whole mixture (5 parts). Always match the given number to its own part count.
• Reading 3 : 2 as “flour is 3/2 of the mixture” instead of 3/5: When a question asks what fraction of the whole mixture is flour, the denominator is the total number of parts (3 + 2 = 5), so flour is 3/5 of the mixture.
• Leaving out units or mixing units: If a recipe gives 1.2 kg of flour and asks for sugar in grams, convert 1.2 kg to 1,200 g before finding one part.

Practise little and often

1. Use kitchen recipes or squash dilution (1 part squash to 4 parts water) to ask quick oral questions: “If I use 200 ml of water, what is 1 part worth?”
2. Give your child two short problems side by side — one where the total is given and one where one share is given — and ask them to label the columns before calculating.
3. Ask them to check every answer by simplifying the final amounts back to the starting ratio.

Keep practising Mathematics

When your child is ready to try five original 11+ maths questions with step-by-step explanations, start the free 5-question quiz below.