# Fraction on the Number Line: Representation of Fraction on the Number Line

Glide to success with Doorsteptutor material for IAS/Mains/Optional Mathematics: fully solved questions with step-by-step explanation- practice your way to success.

Download PDF of This Page (Size: 149K) ↧

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

Fraction is a number which is not a whole number, Let us see how fractional numbers are represented on the number line.

## Representation of Fraction on the Number Line

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

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 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 , the second represents and so on.

We must note that, here and

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.

## Absolute Value and the Number Line

The below number line represents the integers that include from to . Here, the positive integers go to the right of 0 such as and so on whereas, the negative integers go to the left of 0 such as and so on.

The distance between 0 and the number place on the number line is called the number’s absolute value. The absolute value of the number can be denoted using short vertical lines on the either side of the number. For example, the absolute value of is written as It is noted that the distance is always a positive value or 0.

### Example

Example 1: Represent on the number line.

Solution: We first convert into the mixed fraction.

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.

Example: 2 Represent on the number line.

Solution:

We first convert into the mixed fraction.

Now, we start from 5 and divide the section between 5 and 6 into 5 equal parts (5 being the denominator). The third point, as shown in the figure, represents our required fraction.