Representing Fractions 1

We will now see the three visual representations of fractions in detail. There are 3 methods, which can be classified under 2 broad headings.

1. Continuous Representation

   1. Area Concept (sharing rotis, paper folding or sketching)

   2. Length concept (ribbon, string or running track)

2. Set (Discrete) Representation (toffees, tokens)

We will give the visual representations of “half” using the above, before explaining them.

In continuous representation, the values of the part whole have to be measured, using some unit of measurement. In discrete representation, the part & the whole can be counted. Each representation has its advantages & disadvantages.

Continuous Representation (Area & Length)

Continuous representations (dividing rotis & sandwiches) are easy to understand and can be used in the earlier stages. But for understanding arithmetic operations on fractions, discrete representations are better.

Length/ Number Line (continuous) Representation

Normally, this is neglected in schools. This is unfortunate since its modification as "number line" representation is the best way to enable students understand that fractions are also numbers.

One of the major "conceptual" difficulties faced by students is to think of fractions as numbers, in the same way they think about whole numbers. Representing fractions on a number line is the best way to make this understanding easier.

It is intuitive for a student to think that the number 4 1/2 comes between 4 & 5 on the number line. It enable students to compare, add & subtract simple fractions. This can convince them that fractions can indeed be thought of as numbers.

The meter/ yard ruler with 36-inch/ 100 cm divisions provides a number of ways a certain length can be divided into different fractions.

Discrete representation

The 3rd representation represents the part and whole as related but discrete aspects that need to be counted.

We can think of this representation as a strip of tablets where we can buy tablets only in terms of strips. Hence if a strip contains 12 tablets and we want 6 tablets, we ask for half a strip.

In this representation, the convention is to take the individual units (in this case tablets) as the smallest which cannot be broken into smaller parts. We choose a whole such that the required fractional parts can be represented in terms of complete tablets without breaking them.

Discrete representations are more abstract than continuous representations. Hence, they should be introduced at a later stage. But they are very convenient to understand fraction operations.