Ratio and Proportion

Key Facts and Exam Tips

The order in which a ratio is stated is important. If the ratio of cakes to biscuits is 3:2, for example, this means there are 3 cakes for every 2 biscuits. When calculating with ratios, keep both the words and the figures in the same order as they are given in the question.

A ratio can be simplified or ‘cancelled down’ if the numbers share a common factor. Each number in the ratio is divided by this common factor.

Examination questions often give recipes that serve a certain number of people, and ask you to find how much of each ingredient would be needed to serve a different number of people. One way to do this is to find the amounts that would be needed for one person and then to multiply these by the number of people stated in the question.

Some questions are easier to do mentally by, for example, doubling, trebling or halving quantities: use the most appropriate method for the amounts given.

When working with recipes, note the units used in the question for each ingredient and take care to use these units correctly in finding your answers. You should be familiar with common units used for weight and for measuring liquids, and know both the metric and imperial systems.

When sharing a quantity in a given ratio, you need to find how many parts the quantity is to be divided into altogether: this is done by adding together the numbers in the ratio. Then divide the quantity by the total number of parts to work out the size of one part. To calculate the size of each share, multiply one of these parts by each of the numbers in the ratio.

Remember to check that your answer is sensible by comparing it with the information given in the question. If you add together all the shares, the total should be the same as the original quantity.

If your calculation produces long or recurring decimals you should be careful to avoid introducing errors by rounding too early. It is safest to work with the full accuracy of your calculator and only to round the final solution.

Check whether the question asks for a particular degree of accuracy, such as ‘1 decimal place’ or ‘3 significant figures’, and if so round your final answer appropriately. If a degree of accuracy is not specified, make a sensible choice: for example, round money to the nearest penny or pound.