Fractions expand our number system beyond whole numbers and integers. They help us denote any decimal number with a higher precision. Representation of Fractions on the number line is important in order to understand how fractions represent part of a whole.

We all know that a fraction is a number which is not a whole number, (such as 1/2, 5/7 etc). Let us see how fractional numbers are represented on the number line.

We know how to represent whole numbers on the number line. Let us consider the image shown, here, the digits 0 and 1 are represented on the number line.

If we divide the number line into two equal parts, as shown in the figure below, what value does that mid-point hold? Definitely, half of what the graduation between 0 and 1 holds.

So, the point represents (1-0)/2 = ½

Thus we saw, in order to represent a fraction on the number line, we need to divide the line segment between two whole numbers into n equal parts where n represents the denominator of the fraction. For example, if we have to represent the fraction 1/5 on the number line, hence, we need to divide the line segment between 0 and 1 into five equal parts, where the first point as shown in the figure represents the fraction 1/5, the second represents 2/5 and so on.

We must note that, 0/5 = 0 here and 5/5 = 1.

Here we saw the representation of proper fraction on the number line. In order to represent improper fractions, we first convert them into mixed fractions. The same procedure, as shown above, is used with the whole number as the starting point.

Let us understand the representation with the help of a simple example.

Example 1: Represent 43/5 on the number line.

Solution: We first convert 43/5 into the mixed fraction.

\(\frac{43}{5} = 8\frac{3}{5}\)

Now, we start from 8 and divide the section between 8 and 9 into 5 equal parts (5 being the denominator). The third point, as shown in the figure, represents our required fraction.

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