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Teaching mathematics
Teaching mathematics

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Mixtures and solutions

Proportionality is used when producing mixtures and solutions. For example, to make concrete you need 1 part cement, 3 parts sand, and 3 parts aggregate.

This is a ratio of 1:3:3, or it can be said that the proportion of cement is 1/7.

Activity 11 Example problem: orange drink

Timing: Allow 10 minutes
  • A bottle contains 750 ml of concentrated orange squash.
  • It is enough to make fifteen 250 ml glasses of diluted orange drink.
  • How much water is needed to make 10 litres of this drink?


This question tackles proportion in a real-life context. It is a multistep problem as, first, the total amount of diluted drink needs to be calculated before then comparing ratios.

This problem comes from the Nrich website. Suggested approaches and solutions can be found via the link in the ‘Further reading’ section.