4. Rational Numbers
A number which can be expressed in the form of p⁄q, where p and q are integers and q ≠ 0, is called a rational number.
Example:
3⁄4,
-7⁄5,
9⁄2,
-3 (= -3⁄1)
are all rational numbers.
Important Points
- Every integer is a rational number.
- Every fraction is a rational number.
- The set of rational numbers is denoted by Q.
4.1 Properties of Rational Numbers
- Closure Property: The sum, difference, product and division (except by zero) of two rational numbers is always a rational number.
- Commutative Property: For any two rational numbers a and b,
a + b = b + a and a × b = b × a
- Associative Property: For any three rational numbers a, b and c,
(a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)
- Distributive Property: For any three rational numbers a, b and c,
a × (b + c) = a × b + a × c