Rational Numbers Class 8 Notes CBSE Maths Chapter 1 (Free PDF Download)

1. Rational Numbers are numbers in the form of $\dfrac{p}{q}$ such that $q>0$. It is denoted by “Q”.

2. If the numerator and denominator are coprime and $q>0$ then the Rational Number is of the standard form.

3. Types of Rational Numbers:

i. Positive Rational Numbers: The sign of both the numerator and denominator are the same, i.e., either both are positive or both are negative. Ex: $\dfrac{2}{3},\dfrac{-7}{-8},...$

ii. Negative Rational Numbers: The sign of both the numerator and denominator are the same, i.e., if the numerator is negative, the denominator will be positive. Similarly, if the numerator is positive, the denominator is negative. Ex: $\dfrac{2}{-3},\dfrac{-7}{8},...$

iii. Zero Rational Numbers: The numerator is always zero. Ex: $\dfrac{0}{3},\dfrac{0}{8},...$

4. Properties of Rational Numbers:

I. Closure Property: The addition, subtraction and multiplication operations result in closure Property, i.e., for any two rational numbers in these operations, the answer is always a rational number.

ii. Commutative Property: The various order of rational numbers in the operations like addition and multiplication results in the same answer. 

Ex: $\dfrac{2}{3}+\dfrac{4}{8}=\dfrac{4}{8}+\dfrac{2}{3},...$

iii. Associative Property: The grouping order does not matter in the operations like addition or multiplication, i.e., the place where we add the parenthesis does not change the answer. Ex: $\dfrac{8}{9}+\left( \dfrac{4}{5}+\dfrac{6}{7} \right)=\left( \dfrac{8}{9}+\dfrac{4}{5} \right)+\dfrac{6}{7}$

iv. Distributive Property: The rational numbers are distributed in the following way:

• $a\left( b+c \right)=ab+ac$

• $a\left( b-c \right)=ab-ac$

v. General Properties: 

• A rational number can be a fraction or not, but vice versa is true.

• Rational numbers can be denoted on a number line.

• There is $'n'$ number of rational numbers between any two rational numbers.

5. Role of Zero: Also known as the Additive Identity

Whenever $'0'$ is added to any rational number, the answer is the Rational number itself.

Ex: If $'a'$ is any rational number, then $a+0=0+a=a$

6. Role of One: Also known as the Multiplicative Identity.

Whenever $'1'$ is multiplied by any rational number, the answer is the Rational number itself.

Ex: If $'a'$ is any rational number, then $a\times 1=1\times a=a$

7. Additive Inverse:

The Additive Inverse of any rational number is the same rational number with the opposite sign. The additive inverse of $\dfrac{a}{b}$ is $-\dfrac{a}{b}$. Similarly, the additive inverse of $-\dfrac{a}{b}$ is $\dfrac{a}{b}$, where $\dfrac{a}{b}$ is the rational number.

8. Multiplicative Inverse: Also known as the Reciprocal.

The Multiplicative Inverse of any rational number is the inverse of the same rational number. The multiplicative inverse of $\dfrac{a}{b}$ is $\dfrac{b}{a}$. Similarly, the multiplicative inverse of $\dfrac{b}{a}$ is $\dfrac{a}{b}$, where $\dfrac{a}{b}$ and $\dfrac{b}{a}$ is any rational number.

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Chapter wise Revision Notes for Class 8 Maths

• Chapter 2 - Linear Equations in One Variable Notes

• Chapter 3 - Understanding Quadrilaterals Notes

• Chapter 4 - Practical Geometry Notes

• Chapter 5 - Data Handling Notes

• Chapter 6 - Squares and Square Roots Notes

• Chapter 7 - Cubes and Cube Roots Notes

• Chapter 8 - Comparing Quantities Notes

• Chapter 9 - Algebraic Expressions and Identities Notes

• Chapter 10 - Visualising Solid Shapes Notes

• Chapter 11 - Mensuration Notes

• Chapter 12 - Exponents and Powers Notes

• Chapter 13 - Direct and Inverse Proportions Notes

• Chapter 14 - Factorisation Notes

• Chapter 15 - Introduction to Graphs Notes

• Chapter 16 - Playing with Numbers Notes

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