Interpretations of Fractions

Part of a whole In this interpretation we take a whole object and ‘split it’ into equal parts. Two equal parts are called halves, four equal parts are called quarters and so on.

Part of a set of objects Here we are looking at what fraction of the set of objects has a particular characteristic. This interpretation has a link to percentages. Half of the squares are blue.

As a number on the number line In this interpretation we consider one half as a number half way between 0 and 1 on the number line, and two and a quarter as a number between 2 and 3 on the number line. This interpretation can be linked to measurement.

As a division Here we are interested in finding, for example, one half of a set of objects. We understand that one half of 10 is the same as 10 divided by 2 as shown above.

As a ratio Here we are comparing two objects or sets of objects. For example Rover’s height is twice Bruno’s height and hence Bruno is half as tall as Rover.

As a probability If we throw a dice then the probability of getting a six is one out of six which is one sixth. Notice how the expression ‘out of’ is linked directly to ‘divided by’.