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Fractions

When whole numbers are divided into equal parts, we get fractions. There are different ways of representing a fraction. They are –

a/b. Sometimes it is also represented by a ÷ b. In a calculator, the fraction button is shown as:

fraction button in calculator

If a bar of chocolate is to be broken into equal parts among 6 children, what proportion of the chocolate bar will each child get?

block of chocolate with 6 pieces

We need to divide the chocolate by 6, i.e. 1 ÷ 6, and each will get “one-sixth” or “one part out of six” of the chocolate bar, and this is given by 1/6.

So a fraction can be defined here as the number of parts desired by the total number of equal parts. Graphically this can be shown as –

fraction of one-sixth

To represent a fraction pictorially, we draw a whole shape (square or a circle typically), and divide it equally into the number of parts in question (here 6). Then we shade the number of parts required (1 here).

We call the dividing line as the fraction line or vinculum. The number above the dividing line is called numerator and the number below the line is called the denominator.

Remember, the denominator in the fraction cannot be zero. Why? This is because we cannot divide any number by nothing i.e. zero.

 

Let’s look at another example.

fraction of two-sixth

From the adjacent picture

  1. what is the shaded fraction?
  2. what is the unshaded fraction?

 

There are 6 equal parts in this picture. The number of shaded parts is 2 and the number of unshaded parts is 4.

Fraction of shaded parts  =  {number of shaded parts}/{total number of equal parts}  =  2/6

Fraction of unshaded parts  =  {number of unshaded parts}/{total number of equal parts}  =  4/6