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Number System – Complete Notes

Detailed notes with formulas, examples and practice questions.

CA Foundation Business Mathematics 25 Pages 4.8 (124)
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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

  1. Closure Property: The sum, difference, product and division (except by zero) of two rational numbers is always a rational number.
  2. Commutative Property: For any two rational numbers a and b,
    a + b = b + a and a × b = b × a
  3. Associative Property: For any three rational numbers a, b and c,
    (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c)
  4. Distributive Property: For any three rational numbers a, b and c,
    a × (b + c) = a × b + a × c
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