Rational Number: A number that can be expressed in the form p/q, where p and q are integers and q ≠ 0, is called a rational number. The numbers etc. are rational numbers.
Any operation addition, multiplication, division or subtraction can be done with rational numbers.
The operations addition and multiplication are
Commutative for rational numbers.
Associative for rational numbers.
The rational number 0 is the additive identity for rational numbers.
The rational number 1 is the multiplicative identity for rational numbers.
The additive inverse of the rational number p/q is –p/q because p/q – p/q = 0.
The reciprocal or multiplicative inverse of the rational number p/q is a/b if p/q x a/b = 1.
Distributive property of rational numbers state that p(q + r) = pq + pr and p(q - r) = pq – qr where p, q, r are any three rational numbers.
Rational numbers can be represented on a number line.
Rational numbers are classified as Positive and Negative rational numbers. A positive rational number has both numerator and denominator positive. Negative rational number has either denominator or numerator negative. For example, 2/7 is a positive rational number whereas -3/7 is a negative rational number
Positive rational numbers are greater than negative rational numbers.
The number 0 is neither a positive nor a negative rational number.
Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.