Laws of Algebra for Rational Numbers

We will discuss about the Laws of algebra for rational numbers.

If a ∈ Q, b ∈ Q, c ∈ Q, where Q is the set of rational numbers then

(i) a + b ∈ Q

(ii) a + b = b + a

(iii) (a + b) + c = a + (b + c)

(iv) a + (-a) = 0, -a being the negative rational of a

(v) a × b ∈ Q

(vi) a × b = b × a

(vii) a × (b × c) = (a × b) × c

(viii) a × (b + c) = a × b + a × c (Distributive law)

(ix) a × b = b × c ⟹ a = 0 or b = c (Cancellation law)

Rational Numbers

Decimal Representation of Rational Numbers

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