Speed Drills: Ratio, Proportion and Scaling
A speed drill on ratio, proportion and scaling builds speed at three closely related skills that 11+ papers often test together: simplifying and sharing an amount in a ratio, scaling a recipe or quantity up or down, and using direct proportion to compare value for money or find an unknown amount. All three rely on the same underlying idea, that quantities stay in the same fixed relationship to each other, so training them together builds the mental habit of finding 'one part' or 'one unit' and scaling from there.
Method
- To simplify a ratio, divide both, or all, parts by their highest common factor, for example 12:18 simplifies to 2:3 by dividing by 6.
- To share an amount in a given ratio, add the parts to find the total number of parts, divide the amount by this total to find the value of one part, then multiply by each ratio number.
- To scale a recipe or quantity, find the scale factor between the given and target amount, for example doubling or dividing by 4, then apply that same factor to every ingredient or quantity.
- For direct proportion and value for money, find the cost or amount for one unit first, then multiply by the number of units needed, or compare two 'cost per one unit' figures directly.
- Always check a shared ratio answer by adding the parts back together, they must total the original amount.
- Work with the simplest form of a ratio wherever possible, since smaller numbers are faster to scale mentally.
Worked example
Share 45 sweets between two friends in the ratio 4:5. How many sweets does each friend get?
- Add the ratio parts to find the total number of parts: 4 + 5 = 9.
- Divide the amount by the total parts to find the value of one part: 45 / 9 = 5.
- Multiply by each ratio number: the first friend gets 4 x 5 = 20 sweets, the second gets 5 x 5 = 25 sweets.
- Check: 20 + 25 = 45, which matches the original amount.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Write 45:27 in its simplest form, working in your head. Which single number should you spot as the common factor?Show answer
Answer: 9 is the common factor, so 45:27 simplifies to 5:3. Spotting the largest common factor in one step is what saves time in a drill; halving repeatedly would not work here because both numbers are odd.
Q2Share 32 counters between two people in the ratio 3:5.Show answer
Answer: 12 and 20
Q3A recipe for 4 people needs 200g of flour. How much flour is needed for 6 people?Show answer
Answer: 300g
Q45 pens cost 2 pounds 50. What is the cost of one pen?Show answer
Answer: 50p
Q5Simplify the ratio 24:36.Show answer
Answer: 2:3
Q6A model car is built at a scale of 1:20. If the real car is 4 metres long, how long is the model in cm?Show answer
Answer: 20 cm, since 4 m = 400 cm and 400 / 20 = 20
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A fruit drink is made by mixing squash and water in the ratio 2:7. A jug contains 630 ml of the drink in total. How much squash and how much water does it contain?
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Shop A sells 6 identical pencils for 1 pound 20. Shop B sells 10 of the same pencils for 1 pound 90. Which shop offers better value per pencil, and by how much per pencil?
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Free printable worksheet
Want more practice on paper? Download the speed drills: ratio, proportion and scaling worksheet pack - 18 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 5 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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