Representing Fractions 1

< 16.4 Fractions as Numbers 2 | Topic Index | 16.6 Representing Fractions 2 >

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

We will give the visual representations of &ldquo;half&rdquo; using the above, before explaining them.
 * 1) Continuous Representation 				Area Concept (sharing rotis, paper folding or sketching)Length concept (ribbon, string or marked ruler)
 * 2) Set (Discrete) Representation (toffees, tokens)

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

Continuous Representation (Area &amp; Line)

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

Line (continuous) Representation

Normally, this is neglected in schools. But if it is done, then it is a good way to introduce the idea of a number line. It also gives a visual understanding of fractions as numbers. The meter/ yard ruler with 36 inch divisions provides a number of ways a ruler can be divided into different fractions.

 

 

Discrete representation

The 3rdrepresentation represents the part and whole as 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.

< 16.4 Fractions as Numbers 2 | Topic Index | 16.6 Representing Fractions 2 >