Representations of Fractions on a Number Line

In representations of fractions on a number line we can show fractions on a number line.

We have learnt the representation of whole numbers on the number line. Now, we will learn the representation of fractions on number line.

In order to represent \(\frac{1}{2}\) on the number line, draw the number line and mark a point A to represent 1.

Now, divide the gap between O and A into two equal parts. Let T be the point of division. Then, point T represents \(\frac{1}{2}\).

Representations of Fractions on a Number Line

To represent \(\frac{1}{3}\) on a number line, we divide the gap between O and A into 3 equal parts. Let T and Q be the points of division. Then, T represents \(\frac{1}{3}\) and Q represents \(\frac{2}{3}\), because \(\frac{2}{3}\) means 2 parts out of 3 equal parts as shown below.

Fractions on a Number Line

By using the same procedure, point O represents \(\frac{0}{3}\) and point A represents \(\frac{3}{3}\). 

Thus, we have \(\frac{0}{3}\) = 0 and \(\frac{3}{3}\) = 1.

Representations of Fractions on a Number Line

In order to represent \(\frac{3}{5}\) on a number line, we divide the gap between 0 and 1 into 5 equal parts and take first 3 parts from 0 as shown below.

Represent 3/5 on a Number Line

Fraction \(\frac{3}{5}\) on a Number Line


Consider the fractions, \(\frac{1}{2}\), \(\frac{1}{3}\) and \(\frac{2}{3}\).

Each of them is greater than 0 and less than 1, so each of them lies between 0 and 1.

We draw a number line and mark two points on it and name them as 0 and 1.


1. Represent \(\frac{1}{2}\) on the Number Line:

To represent \(\frac{1}{2}\) on the number line, we divide the gap between 0 and 1 into two equal parts.

Let A be the point of division.

Then A represents \(\frac{1}{2}\)

See below figure:

Fraction 1/2 on the Number Line


2. Represent \(\frac{1}{3}\) and \(\frac{2}{3}\) on the Number Line:

To represent \(\frac{1}{3}\) on a number line, we divide the gap between O and C into 3 equal parts. Let A and B be the points of division. Then, A represents \(\frac{1}{3}\) and B represents \(\frac{2}{3}\)

Represent 1/3 and 2/3 on the Number Line

Then, OC = 1 or \(\frac{3}{3}\);

         OA = AB = BC = \(\frac{1}{3}\) and

         OB = OA + AB = \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{2}{3}\)


3. Represent \(\frac{3}{5}\) on the Number Line:

Again to present \(\frac{3}{5}\) on a number line, we divide the gap between 0 and 1 into 5 equal parts and take first 3 parts from 0 as shown in the figure.

Represent 3/5 on the Number Line

Thus, point C represents \(\frac{3}{5}\)



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Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Interesting Fact about Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions




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