Teaching mathematics
Teaching mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Teaching mathematics

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.


Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371