Rational Numbers

Rational numbers are the numbers that can be expressed in p/q form, where p and q are both integers and q ≠0.
It comes from the word ‘ratio‘. Every rational number can be written as ratio of two integers.
All fractions are rational numbers, but all rational numbers are not fractions.
Positive Rationals: Numerator and Denominator both are either positive or negative. Example: 4/7,(-3/4)
Negative Rationals: Numerator and Denominator both are of opposite signs. Example: (-2/11), (3/-4)
Rational numbers are closed under the operations of addition, subtraction and multiplication.
The operations addition and multiplication are
(i) commutative for rational numbers.
(ii) associative for rational numbers.
The additive identity of rational numbers is 0.
The multiplicative identity of rational numbers is 1.
The additive inverse of the rational number a/b is -a/b and vice-versa.
The reciprocal or multiplicative inverse of the rational number a/b is b/a.
Distributivity of rational numbers: For all rational numbers a, b and c,
a(b + c) = ab + ac and and a(b – c) = ab – ac
Rational numbers can be represented on a number line.
Between any two given rational numbers there are countless rational numbers.
Reciprocal of 1 is 1 and that of -1 is also 1.
Reciprocal of 0 is Not Defined.

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