Class 8 Maths, Chapter 1 (Rational Numbers) notes

Class 8 Rational Numbers Notes

Class 8 Maths – Rational Numbers Notes

1. What are Rational Numbers?

A rational number is any number that can be written in the form p/q, where:

  • p and q are integers
  • q ≠ 0

Examples: 2/3, -5/7, 0 (0/1), -4 (-4/1)

2. Properties of Rational Numbers

A. Closure Property

  • Addition: Closed ✅
  • Subtraction: Closed ✅
  • Multiplication: Closed ✅
  • Division: Closed if divisor ≠ 0 ✅

B. Commutative Property

  • Addition and Multiplication: Commutative ✅
  • Subtraction and Division: Not Commutative ❌

C. Associative Property

  • Addition and Multiplication: Associative ✅
  • Subtraction and Division: Not Associative ❌

D. Distributive Property

a × (b + c) = a × b + a × c ✅

E. Identity Elements

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

F. Inverse

  • Additive Inverse of a is -a
  • Multiplicative Inverse of a/b is b/a (a ≠ 0)

3. Number Line Representation

Positive rational numbers lie to the right of 0; Negative rational numbers lie to the left of 0.

Example: Mark −3/4, 0, 1/2, 5/4 on number line.

4. Standard Form of Rational Numbers

A rational number is in standard form when:

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

Example: -6/9 → divide by 3 → -2/3

5. Comparison of Rational Numbers

Make denominators the same using LCM, then compare numerators.

Example: Compare 3/4 and 2/5 → 15/20 > 8/20

6. Rational Numbers Between Two Rational Numbers

Use average method:

Between 1/3 and 2/3 → (1/3 + 2/3)/2 = 1/2

7. Operations on Rational Numbers

  • Add/Subtract: Make LCM of denominators, then add/subtract numerators
  • Multiply: Multiply numerators and denominators directly
  • Divide: Multiply by reciprocal of divisor

8. Important Tips

  • Every integer is a rational number
  • 0 is a rational number
  • Rational number × reciprocal = 1 (except for 0)

ЁЯУЭ Practice Questions

  1. Express in standard form: a) 18/24, b) -36/-48
  2. Find 3 rational numbers between 1/4 and 1/2
  3. Add: 2/5 + 3/10
  4. Multiply: -2/3 × 5/7
  5. Divide: 4/9 ÷ 2/3
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