Rational
Numbers
Complete chapter resources for CBSE Class 8 Maths — topic breakdown, key properties, sample questions, previous year board questions, and instant AI question paper generation.
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- Rational number form: p/q, where p, q ∈ Z, q ≠ 0
- Additive inverse of p/q: −p/q
- Multiplicative inverse of p/q: q/p (p ≠ 0)
- Distributive law: a(b + c) = ab + ac
- Mean (between a and b): (a + b) / 2
- Standard form: q > 0, gcd(|p|, q) = 1
What this chapter covers
A rational number is any number that can be expressed in the form p/q, where p and q are integers and q ≠ 0. Chapter 1 of NCERT Class 8 Mathematics extends students' understanding beyond fractions and integers to the complete set of rational numbers, including negative rationals. The chapter establishes that integers and fractions are subsets of the rational numbers and introduces the concept of standard form — a rational number in standard form has a positive denominator with no common factor other than 1 between the numerator and denominator.
A major focus is the systematic study of properties of rational numbers under the four arithmetic operations: closure, commutativity, associativity, and the distributive property of multiplication over addition. Students learn which operations are closed for rational numbers (addition, subtraction, multiplication — but division by zero is undefined) and confirm that addition and multiplication are both commutative and associative, while subtraction and division are neither. The existence of additive identity (0), multiplicative identity (1), additive inverses, and multiplicative inverses is explored in depth.
The chapter also covers representation of rational numbers on the number line and a key theoretical result: between any two rational numbers there are infinitely many rational numbers. This density property is used in problems asking students to find one or more rational numbers lying between two given values — typically using the mean method or by converting to a common denominator. These skills form the foundation for understanding real numbers in Class 9.
What's inside Chapter 1
As per NCERT Class 8 Mathematics (CBSE syllabus)
How this chapter fits in
Useful for setting question difficulty and cross-chapter papers.
Numbers
Marks & question-type breakdown
Typical pattern based on CBSE Class 8 school examination papers across multiple years.
| Question type | Marks | Typical count | What's usually tested |
|---|---|---|---|
| MCQ / Fill in the Blank | 1 | 1–2 | Identify a property, state the additive/multiplicative inverse, or classify a number |
| Very Short Answer | 2 | 1 | Simplify an expression, find standard form, or verify a property for given values |
| Short Answer | 3 | 1 | Find rational numbers between two given numbers, represent on number line |
| Long Answer / Application | 4–5 | 0–1 | Multi-step property verification or word problem with rational number operations |
| Total (approximate) | 4–6 | 3–4 | Weightage varies across schools and examination sets |
8 sample questions — generated by MarksZen AI
Aligned to CBSE Class 8 Maths Chapter 1. Covers all question types across Easy, Medium, and Hard difficulty.
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From CBSE board examinations
Board-style questions from past Class 8 Maths examinations — Rational Numbers chapter.
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- All 4 topics of this chapter
- MCQ + short answer + word problems
- Answer key included
- PDF export ready