# Rational number on number line

In this chapter we will learn to represent rational number on number line with solved examples.

To understand this chapter you should have basic understanding of the concept of rational number & fraction.

## How to represent rational number on number line ?

Here we will discuss two cases of number line representation.

(a) Proper fraction representation

(b) Improper fraction representation

Hence, we have to first identify the type of rational number and then select suitable method for representation on number line.

### Proper Fraction representation

A rational number is a proper fraction when the numerator is less than denominator.

\mathtt{\frac{2}{3} ,\ \frac{5}{7} \ \&\ \frac{11}{13}} are some of the examples of proper fraction.

Note that the value of proper fraction is always less than 1. Hence on number line the fraction will be located between 0 & 1 ( or -1 if fraction is negative }

#### Method to represent proper fraction on number

Let 2/3 is the given rational number.

(a) Divide the area between 0 & 1 into parts same as the denominator.

Here ” 3 ” is the denominator, so we will divide the area into three equal parts.

(b) Now select the point mentioned by numerator.

Here ” 2″ is the numerator, so we will select point 2/3 on the number line.

Hence, the green circle represents the given rational number.

I hope you understood the concept. Let us practice some related questions.

Example 01
Represent number 3/5 on number line.

Solution
The number 3/5 is proper fraction since numerator is less than denominator.

The value of fraction is less than 1, so its position will lie between 0 & 1 on number line.

(a) Divide the area between 0 & 1 into 5 equal parts.

(b) Number 3 is the numerator. So select the third point from 0.

Hence, the green circle represent the rational number 3/5.

Example 02
Represent the rational number -2/7 on the number line.

Solution
Since the number is negative, it’s position will be between 0 & -1.

(a) Divide the area between 0 & 1 into 7 parts.

(b) The numerator is -2, so select the 2nd point from number 0.

Hence, the green circle represent the rational number -2/7

Note:
When fraction is negative number, start counting from left of 0 to locate the position.

### Improper Fraction representation

The rational number in which numerator is greater than denominator is called improper fraction.

Since numerator > denominator, the value of rational number is always greater than 1.

Follow the below steps for number line representation

Let the given number is 5/2.

(a) Convert the improper fraction into mixed fraction.

\mathtt{\frac{5}{2} \Longrightarrow 2\frac{1}{2}}

The mixed number \mathtt{2\frac{1}{2}} gives following information;

Whole number 2 ⟹ It tells that number lies between 2 & 3 on number line.

Fraction 1/2 ⟹ gives the exact position of point.

Learn to convert improper fraction into mixed fraction by clicking red link.

(b) Locate the initial position

The whole number of mixed fractions tells initial position of rational number.

In mixed number \mathtt{2\frac{1}{2}} , the whole number is “2”.

So we will select the area between 2 & 3 on number line.

(c) Locate the exact position

In mixed number, the fraction part tells the exact position of point.

The fraction part is 1/2.

Now we have to follow the similar process used in proper fraction.

Here;
Denominator is 2.
It tells that the area between 2 & 3 will be divided into two parts.

Numerator is 1
It tells that we have to select the first point after number 2.

Hence, the green circle tell the exact location of rational number 5/2 on number line.

Conclusion
The process of representing improper fraction is almost same as proper fraction.

In improper fraction, the only additional step is to find the mixed fraction for finding initial position.

I hope you understood the concept, let us look at some solved examples.

Example 01
Represent the rational number 18/5 on number line

Solution
Since numerator > denominator, the given number is improper fraction.

To represent in number line, follow the below steps;

(a) Convert into mixed fraction

\mathtt{\frac{18}{5} \Longrightarrow 3\frac{3}{5}}

In the above mixed fraction;
⟹ ” 3 ” is the whole number

⟹ 3/5 is the fraction

(b) Locate initial position

In the mixed fraction \mathtt{3\frac{3}{5}} , the whole number “3” signifies that the given rational number lies between 3 & 4.

(c) Locate exact position

In mixed fraction \mathtt{3\frac{3}{5}} , the fraction part will tell the exact position of number.

In fraction 3 / 5, the denominator is 5. It tells to divide the area into 5 equal part.

In fraction 3/5, the numerator ” 3″ tells to select the third point after number 3.

The green circle tells the exact location of rational number 18 / 5.

Example 02
Represent the rational number -4/3 on number line.

Solution
Since the number is negative, it will lies on left side of 0 on number line.

(a) Convert improper fraction into mixed number

\mathtt{\frac{-4}{3} \Longrightarrow -1\frac{1}{3}}

In the above mixed number;
⟹ ” -1 ” is the integer
⟹ 1/3 is the fraction

(b) Locate initial position

In the mixed number \mathtt{-1\frac{1}{3}} , the integer “-1” signifies that the number lies between -1 & -2.

(c) Locate exact position

In the mixed number \mathtt{-1\frac{1}{3}} , the fraction part 1/3 will tell the exact position of rational number.

In fraction 1/3, the denominator is 3. It tells to divide the area into three equal parts.

In fraction 1/3, the numerator 1 tells to select first point after number -1.

Here the green circle represents the position of rational number -4/3