Fractions on the Number Line

Fraction Number line

A fraction is a number that represents a part of a whole. The whole can represent a group of objects or a single object. Consider the fraction 8/10; it is read as ‘eight-tenth,’ which means eight parts out of ten equal parts in which the whole is divided. In the fraction 8/12, 8 is known as the numerator, and 12 is known as a denominator. In this chapter, we will also learn about fractions on the number line.


Some More examples of fraction

The fraction 3/5 is read as ‘three-fifth,’ which means 3 parts out of 5 equal parts in which the whole is divided. In the fraction 3/5, 3 is the numerator, and 5 is the denominator.

Similarly, fraction 5/12 is read as ‘fifth-twelfth,’ which means 5 parts out of 12 equal parts in which the whole is divided. In the fraction 5/12, 5 is the numerator, and 12 is the denominator.

Now let us learn how fractions are represented on a number line.


How to Represent Fraction on a Number Line

Representing fractions on a number line means that we can show fractions on a number line. To represent half (1/2) on the number line, draw a number line and mark a point A to represent 1. Mark another point O to represent 0.

Now divide the gap between O and A equally in two parts. Let Point T represent the point of division. Then point T is ½ of O and A.

Now to represent 1/3 on a number line, divide the gap between O and A into 3 equal parts. Let Q be the new point of division along with T. Now, T represents 1/3 and Q represents 2/3, as 2/3 means 2 sections of 3 equal parts as shown in the diagram.

By using the same method point, A represents 3/3, and point O represents 0/3.

Therefore, we have 3/3 = 1 and 0/3 = 0.

This is how to represent fraction on number line.

To represent 3/5 on a number line we now divide the gap between 0 and 1 into 5 equal parts and take first 3 parts from 0 as shown in the figure below.

Now, we get a fraction 3/5 on a number line.

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


Absolute Value and the Number Line

Absolute value is the distance between numbers on the number line. It goes from 0 without taking into consideration in which direction from zero the number lies. A negative number can never be the absolute value.

For Example: 

  1. The absolute value of 5 is 5

Distance from 0:5 units


  1. The absolute value of -5 is 5 

Distance from 0:5 units


  1. The absolute value of 2+ -7 is 5 

The distance of sum from 0:5 units

Always remember that the absolute value of 0 is 0. This is the reason we never say that the absolute value of a number is positive. Zero is neither positive nor negative.

The symbol representing absolute value is two straight lines surrounding the number or the expression you want to indicate absolute value.

For example:

|4| = 4 means the absolute value of 4 is 4 

|-7| = 7 means the absolute value of -7 is 7

|-2 -x| means the absolute value of -2 minus x

-|y| means the negative of the absolute value of y.


Solved Examples of Fraction

  1. Mrs Raina has 24 apples. She gave away ¼ of them

Find out how many apples she gave away?

How many apples is she left with?

Solution: here fraction ¼ indicates giving away 1 part out of 4 equal parts

So, we arrange 24 apples in four equal groups. 

Now each group contains 24/4 = 6 apples

Thus, ¼ of 24 is 6 

Therefore, Mrs Raina gave away 6 apples.

Now, the number of apples remaining with Mrs Raina = 24 – 6 = 18 apples.


  1. What fraction of a day is 8 hours?

Solution: here, we know that one day has 12 hours 

Therefore, 8 hours = 8/12 of a day

Hence, 8 hours is 8/12 part of the day.


  1. Determine 2/3 in a collection of 9 balls

Solution: to find 2/3 collections of 9 balls, we must divide the collection of 9 balls into 3 equal parts and take 2 such parts. Each row has 9/3 = 3 balls. 

When we take 2 rows out of 3 rows, it represents 2/3 of 9 balls. There are 6 balls in two rows. 

Hence, 2/3 of 9 balls = 6 balls.

Fun Facts on Fractions

  1. A blank number line was originally proposed as a visual model or diagram for solving subtraction and addition operations. 

  2. An empty or blank number line is a visual diagram of a number line with no numbers or markers and is mostly used for solving word problems.

FAQ (Frequently Asked Questions)

1. What Does the Denominator on a Fraction Represent on the Number Line?

A fraction consists of two parts – the numerator and the denominator. The denominator shows how many equal parts an item was divided into. The word is derived from the Latin word ‘denomino’ (to name). It indicates the number of parts that would equal to 1. If you have 2/2 then it is equal to 1. It means the space between 0 and 1 needs to be split into half. The numerator of your fraction tells you to start at zero and count one unit of size ¼.

2. What Fraction is Equivalent to ¼?

Fractions equivalent to ½ are 2/4, 3/6, 4/8, 5/10,6/12 and so on

Fractions equivalent to 1/3 are 2/6, 3/9, 4/12, 5/15 and so on

Fractions equivalent to ¼ are 2/8, 3/12, 4/16, 5/20 and so on

Fractions equivalent to 1/5 are 2/10, 3/15, 4/20, 5/25 and so on.

So for 1/4, the possible options are 2/8, 3/12, 4/16, 5/20, 6/24, or 7/28. Interestingly these are called equivalent fractions because evaluating these fractions will always give us the same result, i.e. 1/4.