Fractions on a Number Line

Fractions can be made interesting by representing them on number line. The representation of fractions on a number line is a good means of engagement for students to understand them easily. 

In this blog, we will guide you on how you can represent different fractions in the number line. 

Before delving into the details, first, we will learn about number lines.

Number Line

The number line is a horizontal straight line that represents equal interval marks along its length. The numbers on a number line increase from left to right and decrease from right to left.

Steps to Plot the Fraction on the Number Line

Representing fractions on the number line involves simple steps. Students will enjoy drawing lines and plotting fractions. Let’s learn the steps to plot the fraction on the number line. 

1. Draw a straight number line.
2. Identify the fraction to be plotted on a number line. The fraction may be a proper, improper fraction, or mixed fraction.
3. For proper fractions, draw the number line from 0 to 1. Now divide the line into equal parts equivalent to the denominator of the fraction, i.e. if the denominator is 5, divide the line into five equivalent parts. 
4. For mixed fractions, draw the line starting from the quotient (whole number) of the fraction and divide it into parts equivalent to the remainder (denominator).
5.  In case of improper fractions, convert them into a mixed number or fraction and plot on the number line accordingly.   
6. Always start counting from the left side.
7. Finally, after you locate the fraction, mark it on the line accordingly. 

Proper Fractions on Number Line

Proper fractions are fractions having a numerator less than the denominator. Let’s learn to plot the proper fractions on number line through simple steps with an example. 

Example: 

Represent 3/6 on the number line. 

1. Draw a horizontal line and represent a number between 0 and 1 because a fraction is proper. 
2. Now, divide it into 6 equal parts because the denominator of the fraction is 6.  

3.From the left side, start counting the number of times equal to the numerator of the fraction. The point where you get the acquired fraction is the representation of the fraction on a number line. 

Mixed Fractions on a Number Line

A mixed fraction is also known as a mixed number. It is a fraction that contains a whole number and a proper fraction. You will learn to plot the mixed fractions on a number line with an example.

Example:

Represent

on the number line. 

1. Draw a number line starting with the whole number of the fraction. The whole number is 5, so, start drawing with 5 and end at 6. 
2. Divide the line into 8 parts according to the denominator.

3.Now jump from the right side of the line to the left side equivalent to the numerator. The numerator is 6, so, jump six times. 

4.Mark on this point. It is the point that represents

on the number line. 

Improper Fractions on a Number Line

Improper fractions are those that have a numerator greater than a denominator. Let’s learn how to plot the improper fractions on a number line with an example. 

Example: 

Plot

on a number line.

1. The fraction is improper. So, first convert it into a mixed fraction. 

On conversion, we get

1. Now draw a line starting from the whole number of a fraction.
2. The whole number is 4. So start the line with 4 and end at 5. 
3. Divide it into 5 equal parts because the denominator is 5.

4.Now, from the left side make 4 jumps rightward. 

5.Mark the point. This is the point of representation of

on a number line.

Finding Equivalent Fractions With a Number Line

Equivalence fractions have different numerators and denominators, but we get the same value when simplifying them. For example, we have two fractions with different numerators and denominators, i.e.

We get  1/6 on simplifying 6/36. So, they are equivalent fractions. 

We follow a simple method for finding equivalent fractions with a number line.

Example: 

 We have a fraction

We will find its equivalent fractions on the number line step by step.

1. Draw a number line with 0 and 1 on the respective ends.
2. Divide the line into two parts, with the denominator being two, and mark 1/2 it in the center of the line.

3.In the next step, subdivide the line into four parts. Now mark 24 in the center line.

4.Now further divide the line into eight lines. You will see 48 at the center of the number line.

5.In the final step, you will see that all equivalent fractions will appear at the same position as given below.

So,

are equivalent fractions. Therefore,

Comparing Fractions on a Number Line

We can also compare fractions on the number line. Comparing fractions on a number line involves an easy method. As we know, the number in a number line increases when we go from left to right. 

So, the fractions on the left side will be smaller than the fractions on the right side. 

In the below example, the fraction

 is smaller than

is smaller than

It shows that we can compare fractions on a number line.