# Ratios, fractions, decimals and percentages

*The use of number to quantify physical systems, processes and quantities runs across pretty much all of the three sciences and so the need to be confident with numbers and simple calculations is effectively a core skill in all subjects and most topics. However, it can be easy to make assumptions about the confidence and fluency students have with number and this can become a barrier to their understanding. If they struggle with the numbers this can impact their understanding of the real thing that the number is representing. Summarised below are some of the common challenges students may face and then there are some example activities and resources that you may wish to use.*

It is important that students understand that ratios, fractions, decimals and percentages are all just ways of describing divisions of a whole number. Ratios are fractions which express how many times one number can be divided by another. The ratio p : q corresponds to the fraction ^{p}/_{q}

Pupils need to be confident and fluent with fractions as numbers on a number line as well as operators. So 1/2 can be interpreted as a number on the number line between 0 and 1 and also as an operator divide by 2.

Decimals can also be described as fractions where the denominator is a power of 10 . We write decimal fractions with a decimal point. Percentages are fractions where the denominator is 100.

In many cases students see these different representations as unrelated and the connections are not made. Encourage students to move between the different representations and discuss what makes a particular representation more appropriate in a given situation. For example when rearranging an equation student often make the mistake of wanting to convert fractions to decimals which makes the processes involved less transparent.

Suggest that students are flexible in the way they choose which representation to use and also in the way they work using mental, written or calculator strategies. The representation used should be accurate and convenient given the context. For example finding 25% of a quantity is equivalent to finding a quarter so divide by 4.

Students will have their own mental strategies, for example finding a quarter by halving and halving again. But, to make sure they understand what they are doing and can generalise it may be useful to check they understand that the line in a fraction stands for divide.

Students may think that it is impossible to have more than 100% or a fraction greater than 1. Emphasise scientific contexts where such proportions have real meaning.

Based on the fact that ^{1}/_{10 } is 0.1 pupils may wrongly generalise that, for example, ^{1}/_{6 } is 0.6.

Ratio is a way of comparing quantities, parts of a single quantity, e.g. mixing paint or one quantity with another quantity, e.g. real life distance and distance on a map.

When ratio is used to compare one quantity with another, some connected phrases are ‘to every’ or ‘for every’ or ‘as many as’, e.g. the scale drawing shows 1cm to every 50cm

### Nuffield Science Calculations

This resource has a comprehensive set of equations and calculations from across all the science subjects. There are step by step worked examples, questions and answers (at the back) for pretty much any topic that may crop up acorss all the sciences. Some of the advice in the opening sections may approach things differently, for example the authors seem to favour the triangles, which is generally advised against. However there are lots of good examples here.

### Ratios and Proportions

This video resource from Teachers TV demonstrates a practical application of ratio and proportion. The number of guests requires the adaptation of recipes for both food and drink. Graphics are used effectively throughout the video to explain ratios as a 'part to part relationship' and proportion as a 'part to whole'. This could be used as a review before embarking on work that involves the use of ratio.

### Fractions, Decimals and Percentages

Produced by the Learning and Skills Improvement Service (LSIS), these resources are aimed at mathematics practitioners but you could use the two units “Fractions: misconception - exposing and discussing common misconceptions and “Fractions: collaborative tasks - creating connections between topics” to check students prior knowledge before using fractions in a science context.

The aim of the first is to explore and resolve typical misconceptions that learners may have about fractions.

Students often struggle to decode word questions to identify the mathematics they need. The aim of the second is to identify different types of questions involving fractions and to promote understanding of how to calculate with fractions. You could adapt the word problems to include examples in a scientific context.