Introduction to Rational Numbers
Understand what rational numbers are and how they are classified.
What Are Rational Numbers?
Rational numbers form the foundation of all numerical mathematics. A rational number is any number expressible as p/q where p and q are integers and q ≠ 0. This first lesson in Class 8 Mathematics establishes the vocabulary and classification system you will use throughout the entire year.
Core Concepts to Master
- Every integer is rational (e.g. -3 = -3/1) — integers are a subset of Q, the set of rational numbers.
- Zero is rational (0 = 0/q for any non-zero q) but 1/0 is undefined — the denominator can never be zero.
- Standard form of p/q requires HCF(p,q) = 1 and q > 0 — always reduce to standard form before writing your answer.
- Positive rational numbers have p and q with the same sign; negative rational numbers have opposite signs.
- Between any two distinct rational numbers lie infinitely many others — rational numbers are dense on the number line.
Why This Lesson Is the Gateway
Every subsequent chapter in Class 8 Mathematics — linear equations, proportions, algebraic expressions — uses rational numbers as its raw material. A student who can confidently identify, classify and express rational numbers will find the rest of the year far more manageable. Take notes on every definition in this lesson.
How to Use This Lesson
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