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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.