Rational Numbers

JCERT · Class 7 · Chapter 4 · Rational Numbers. Topic notes aligned to the official chapter; these are not solutions to every textbook exercise.

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Why This Chapter Matters

JCERT · Class 7 · Chapter 4 · Rational Numbers. Topic notes aligned to the official chapter; these are not solutions to every textbook exercise.

Before You Begin (Prerequisites)

Revise relevant arithmetic and ideas from the previous grade.

What You Will Learn (Core Objectives)

A rational number p/q has integer p and nonzero integer q. In standard form the denominator is positive and numerator and denominator are coprime. Use common positive denominators to compare. The additive inverse changes the sign; a nonzero rational has a reciprocal.

Chapter Roadmap & Progression

1 Syllabus, textbook and notes alignm...

2 Concept and method

3 Check and common pitfall

Complete Concept Guide (100% Curriculum Coverage)

Syllabus, textbook and notes alignment

JCERT · Regular schools (Non-SOE) · Class 7 · Chapter 4 — Rational Numbers
Official syllabus pages 67–88. Official syllabus · Prescribed Hindi book (22 chapters) · Separate supplementary reference.

These topic notes and teaching examples are not a complete answer key to every textbook question. English notes use this same JCERT chapter order; a matching English textbook PDF has not been verified.

Official Hindi PDF for this exact chapter

Concept and method

A rational number p/q has integer p and nonzero integer q. In standard form the denominator is positive and numerator and denominator are coprime. Use common positive denominators to compare. The additive inverse changes the sign; a nonzero rational has a reciprocal.

Check and common pitfall

Divide both terms by their HCF, 2. Zero has no reciprocal.

Key Formulas, Identities & Theorems

Key relationships

p/q + r/s = (ps + rq)/qs; (p/q) × (q/p) = 1 (p,q ≠ 0)

Observe the stated conditions and units.

Conceptual Solved Examples & Case Studies

Example 1

Write the standard form and additive inverse of −6/8.

Step-by-Step Solution:

−6/8 = −3/4; −3/4 + 3/4 = 0

Divide both terms by their HCF, 2. Zero has no reciprocal.

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