Class 7 · Chapter 9

Rational Numbers

Introduction to rational numbers; operations on rationals; representation on number line.

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

Any number that can be written as

p/q

with integers

p, q

and

q \ne 0

. Integers and fractions are all rationals. E.g.

-3, 2/5, 0.75

Key concepts & formulas

A rational number is

\dfrac{p}{q}

where

q\ne 0

Rationals are closed under

+, -, \times, \div

(except

\div 0

Standard form of a rational: denominator positive and gcd

(p,q)=1

Between any two rationals lies another rational.

-\dfrac{p}{q} = \dfrac{-p}{q} = \dfrac{p}{-q}