Speed Drills: Ratio, Proportion and Scaling Set 2
The second Ratio, Proportion and Scaling speed drill continues practising the same three closely linked skills, sharing an amount in a given ratio, scaling a recipe or quantity by a fixed factor, and using direct proportion to compare value for money, with a fresh set of numbers so the underlying 'find one part' method becomes fully automatic rather than something worked out fresh each time.
Before you start
Make sure you're comfortable with these topics first:
Method
- To simplify a ratio quickly, look for the largest number that divides every part exactly, rather than dividing by small factors one at a time.
- To share an amount in a given ratio, add the parts to find the total number of parts, divide the whole amount by this total to find the value of one part, then multiply that value by each ratio number.
- To scale a recipe or quantity, work out the single scale factor that connects the given amount to the target amount, then multiply every ingredient or quantity by that same factor.
- For direct proportion and value-for-money questions, find the cost or amount for a single unit first, then either multiply up or compare two 'per unit' figures directly.
- Keep the numbers as small as possible throughout by simplifying a ratio or cancelling a fraction before you scale it, since smaller numbers are quicker to multiply mentally.
- Check a shared-ratio answer immediately by adding the shares back together; they must total the original amount, and a mismatch means a step was applied to the wrong number.
Worked example
Share 72 counters between two people in the ratio 5:3.
- Add the ratio parts to find the total number of parts: 5 + 3 = 8.
- Divide the amount by the total parts to find the value of one part: 72 / 8 = 9.
- Multiply by each ratio number: the first person gets 5 x 9 = 45 counters, the second gets 3 x 9 = 27 counters.
- Check: 45 + 27 = 72, which matches the original amount.
- The final answer is 45 and 27.
Practice questions
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Q1Simplify the ratio 56:35, working in your head. What is the largest number you can spot as a common factor?Show answer
Answer: 7 is the common factor, so 56:35 simplifies to 8:5.
Q2Share 54 counters between two people in the ratio 4:5.Show answer
Answer: 24 and 30
Q3A recipe for 5 people needs 250g of butter. How much butter is needed for 8 people?Show answer
Answer: 400g
Q48 rulers cost 4 pounds. What is the cost of 3 rulers?Show answer
Answer: 1 pound 50 (3 x 50p)
Q5Simplify the ratio 42:56.Show answer
Answer: 3:4
Q6A model train is built at a scale of 1:50. If the real train is 15 metres long, how long is the model in cm?Show answer
Answer: 30 cm, since 15 m = 1500 cm and 1500 / 50 = 30
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A fruit punch is made by mixing juice and lemonade in the ratio 3:5. A jug contains 720 ml of punch in total. How much juice and how much lemonade does it contain?
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Shop A sells 4 identical notebooks for 3 pounds 20. Shop B sells 9 of the same notebooks for 6 pounds 30. Which shop offers better value per notebook, and by how much per notebook?
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A photograph measuring 10 cm by 15 cm is enlarged in the ratio 1:3. Work out the area of the enlarged photograph.
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Free printable worksheet
Want more practice on paper? Download the speed drills: ratio, proportion and scaling set 2 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 21 of 11+ Maths Workbook 1, the whole course as one free printable PDF.
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