Class 8 · Chapter 1

Rational Numbers

Properties of rational numbers; representation on the number line; operations.

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Detailed theory

Rationals are closed under

+, -, \times, \div

(except division by zero). They are commutative and associative under

+

and

\times

. Distributive:

a(b + c) = ab + ac

Key concepts & formulas

A rational number is

\dfrac{p}{q}

where

q \ne 0

Rational numbers are closed under

+, -, \times

and

\div

(except

\div

0

Between any two rationals lie infinitely many.

0

is the additive identity;

1

is the multiplicative identity.

Additive inverse of

\dfrac{p}{q}

-\dfrac{p}{q}

; multiplicative inverse is

\dfrac{q}{p}

(

p\ne 0