Class 8 Mathematics

Chapter 1 – Rational Numbers (CBSE)

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1. What are Rational Numbers?

A Rational Number is a number that can be written in the form

p / q

where p and q are integers and q ≠ 0.

Examples:

• 1/2
• -3/5
• 0 = 0/1
• 4 = 4/1

2. Types of Rational Numbers

• Positive Rational Numbers: 2/3, 5/7
• Negative Rational Numbers: -4/9, -7/11
• Zero: 0

3. Properties of Rational Numbers

a) Closure Property

Rational numbers are closed under:

• Addition
• Subtraction
• Multiplication

Note: Not closed under division (division by zero is not allowed).

b) Commutative Property

• a + b = b + a
• a × b = b × a

Not true for subtraction and division.

c) Associative Property

• (a + b) + c = a + (b + c)
• (a × b) × c = a × (b × c)

d) Identity Property

• Additive Identity: 0 → a + 0 = a
• Multiplicative Identity: 1 → a × 1 = a

e) Inverse Property

• Additive inverse of a/b is −a/b
• Multiplicative inverse of a/b is b/a (a ≠ 0)

4. Rational Numbers on Number Line

• Positive rational numbers lie to the right of 0
• Negative rational numbers lie to the left of 0
• Greater denominator → smaller parts

5. Standard Form of Rational Numbers

A rational number is in standard form if:

• Denominator is positive
• Numerator and denominator have no common factor except 1

Example: −4 / −6 = 2 / 3

6. Exam Tips ⭐

• Simplify answers completely
• Be careful with signs (+ / −)
• Write steps clearly for full marks

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Prepared for CBSE Class 8 Students
Shaktimatha Learning