Mathematics · Class 8
Rational Numbers
Closure, commutativity, associativity, and representation of rationals.
4 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Class 8 rational numbers revisit properties, representation on number line, finding rational numbers between two rationals, and laws of exponents for integers — preparing for algebraic manipulation.
Properties
- Closure, commutativity, associativity for addition and multiplication
- Distributive property: a(b+c) = ab + ac
- Role of 0 and 1 as identities
Between Two Rationals
Infinitely many rationals lie between any two rationals. Method: find average (a+b)/2 or use common denominator.
Laws of Exponents (Integers)
Product
aᵐ × aⁿ = aᵐ⁺ⁿ
Negative power
a⁻ᵐ = 1/aᵐ
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Find Between
Find a rational between 1/3 and 1/2.
- 1Average: (1/3+1/2)/2
- 2= (5/6)/2 = 5/12
Answer
5/12 (one of infinitely many)
Example 2: Simplify
Simplify (−2)³ × (−2)⁴.
- 1Same base: add exponents
- 2(−2)⁷ = −128
Answer
−128
Key Points to Remember
- ✓ Standard form: positive denominator
- ✓ Rational numbers dense on number line
- ✓ Exponent laws apply to integer exponents
Exam Tips
- • Show common denominator method
- • Reduce fractions to lowest terms
Practice MCQs — Rational Numbers
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Multiplicative inverse of −3/4 is: