CBSE Notes Class 8 Maths Chapter 1 Rational Numbers

1.0Introduction to Rational Numbers 

In Maths, Rational Numbers are numbers that can be written in fractions where the numerator can be any number while the denominator can not be zero.

2.0CBSE Class 8 Maths Chapter 1 Rational Numbers - Revision Notes

What are Rational Numbers? 

A rational number is any number that can be written in the form of $\frac{p}{q}$ or in a fraction. Rationals can be both negative and positive.

• Here, p and q are integers. 
• p and q do not have a common factor other than 1. 
• $\mathrm{q}\ne 0$.

3.0Properties of Rational Numbers

In Maths, rational numbers possess some special properties, such as the following: 

1. Closure Property: Closure property refers to if we perform any operation (addition, multiplication, subtraction) on any number, say, for example, a Rational number, the resultant will also be a Rational Number. 

2. Commutativity: This property means that you can swap the order of addition or multiplication, and the result will not change. 

3. Associative: This property means that when you do operations on a group of numbers, no matter how you group the numbers, the result will always be the same. 

4. Additive Inverse: An additive inverse of a number is a number that, when added to the original number, becomes 0. Like, 1 / 2 is the additive inverse of -1 / 2. 
5. Multiplicative Inverse: It is a number that, when multiplied by the original number, the resultant becomes 1. Like, ¾ is the multiplicative inverse of 4/3.
6. Distributive Property: In maths, multiplying a number by a sum of several numbers added together (or subtracted together) is the same thing as multiplying the number by each term separately and then adding (or subtracting) the results.

$a\times (b+c)=(a\times b)+(a\times c)$

$a\times (b-c)=(a\times b)-(a\times c)$

4.0Representation of Rational Number on a Number Line

In Maths, a rational number, we plot it on the number line at a place related to its value. A number line is just a straight line with equally spaced marks where every mark represents a number.

• Points that lie to the right of zero are plotted.
• Negative rational numbers are located to the left of zero.
• Then comes zero in the middle.

How do you find rational numbers between two numbers?

Let’s see an example: 

Find three rational numbers between $-\frac{2}{3}$and $\frac{2}{5}$. 

Solution: First, equal the denominator of both numbers by taking LCM. 

 LCM of 3 and 5 is 15. Multiply $-\frac{2}{3}$ with 5 and $\frac{2}{5}$ with 3 in both the numerator and denominator of the numbers. 

The resultant, $-\frac{10}{15}$ and $\frac{6}{15}$

The three rational numbers will be $\frac{2}{15},\frac{4}{5},-\frac{8}{5}$.

5.0Key Features of CBSE Math Class 8 of Chapter 1

• Content is updated and aligned with the latest CBSE curriculum. 
• The notes provide a step-by-step guide along with solved examples to help students better understand questions based on rational numbers. 
• The language used in the notes is easy to understand and has clear concepts that are ideal for self-learning. 
• These notes also FAQs based on some rare but important questions.