Practice Rule of three
The rule of three uses a known pair of quantities to find another value in a proportional relationship.
Decide first whether the relationship is direct or inverse.
Exercises with solutions
Check that the relationship is proportional: doubling the quantity must double the corresponding value. Divide to find the value for 1, then multiply by the requested quantity. This rule does not apply to inverse proportion.
Exercise 1
3 notebooks cost €4.50. What do 5 identical notebooks cost?
Show solution and working
€7.50
One notebook costs €4.50 ÷ 3 = €1.50. Five cost 5 × €1.50 = €7.50.
Exercise 2
4 servings need 300 g of rice. How much is needed for 6 servings?
Show solution and working
450 g
One serving needs 300 g ÷ 4 = 75 g. Six need 6 × 75 g = 450 g.
Exercise 3
At a constant speed a bicycle travels 18 km in 60 minutes. How far does it travel in 25 minutes?
Show solution and working
7.5 km
Each minute covers 18 ÷ 60 = 0.3 km. In 25 minutes: 25 × 0.3 km = 7.5 km.
Exercise 4
A taxi charges €4 plus €2 per kilometre. Is its total fare proportional to the distance?
Show solution and working
No.
1 km costs €6 and 2 km costs €8. Doubling the distance does not double the fare because of the fixed fee.
Common mistake
Check the relationship first. Fixed fees, bulk discounts or changing speeds can make the relationship non-proportional.
Free maths worksheets with worked solutions
Percentages: free German worksheet with solutions (PDF)
Foundations from Grade 6: questions 1–6. Questions 7–10 extend the foundations.
PDF and questions in German
Maths by grade
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